TSTP Solution File: ITP038^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP038^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:48:34 EDT 2024
% Result : Theorem 3.31s 0.90s
% Output : Refutation 3.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP038^2 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 15:25:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (14221)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.41 % (14236)WARNING: value z3 for option sas not known
% 0.14/0.41 % (14234)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.41 % (14235)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.41 % (14237)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.41 % (14236)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)
% 0.14/0.41 % (14238)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)
% 0.14/0.41 % (14239)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)
% 0.14/0.41 % (14240)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)
% 0.22/0.47 % (14240)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.48 % Exception at run slice level
% 0.22/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.48 % Exception at run slice level
% 0.22/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.50 % (14296)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.50 % (14298)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)
% 0.22/0.50 % Exception at run slice level
% 0.22/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.52 % (14308)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)
% 0.22/0.56 % (14298)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.56 % (14296)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.34/0.58 % Exception at run slice level
% 1.34/0.58 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.52/0.60 % (14340)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)
% 3.12/0.87 % (14238)First to succeed.
% 3.31/0.90 % (14238)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14221"
% 3.31/0.90 % (14238)Refutation found. Thanks to Tanya!
% 3.31/0.90 % SZS status Theorem for theBenchmark
% 3.31/0.90 % SZS output start Proof for theBenchmark
% 3.31/0.90 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_6, type, set: $tType > $tType).
% 3.31/0.90 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_8, type, bounde2145540817linfun: ($tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_9, type, product_unit: $tType).
% 3.31/0.90 thf(type_def_10, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_11, type, sum_sum: ($tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_12, type, real: $tType).
% 3.31/0.90 thf(type_def_13, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_14, type, trm: ($tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_15, type, frechet_good_interp: ($tType * $tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_16, type, frechet_strm: ($tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_17, type, formula: ($tType * $tType * $tType) > $tType).
% 3.31/0.90 thf(type_def_18, type, a: $tType).
% 3.31/0.90 thf(type_def_19, type, b: $tType).
% 3.31/0.90 thf(type_def_20, type, c: $tType).
% 3.31/0.90 thf(type_def_21, type, sc: $tType).
% 3.31/0.90 thf(type_def_22, type, sf: $tType).
% 3.31/0.90 thf(type_def_23, type, sz: $tType).
% 3.31/0.90 thf(type_def_24, type, list: $tType > $tType).
% 3.31/0.90 thf(func_def_0, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 3.31/0.90 thf(func_def_1, type, frechet_good_interp: ($tType * $tType * $tType) > $tType).
% 3.31/0.90 thf(func_def_2, type, bounde2145540817linfun: ($tType * $tType) > $tType).
% 3.31/0.90 thf(func_def_3, type, frechet_strm: ($tType * $tType) > $tType).
% 3.31/0.90 thf(func_def_4, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 3.31/0.90 thf(func_def_5, type, product_unit: $tType).
% 3.31/0.90 thf(func_def_6, type, product_prod: ($tType * $tType) > $tType).
% 3.31/0.90 thf(func_def_7, type, formula: ($tType * $tType * $tType) > $tType).
% 3.31/0.90 thf(func_def_8, type, sum_sum: ($tType * $tType) > $tType).
% 3.31/0.90 thf(func_def_9, type, trm: ($tType * $tType) > $tType).
% 3.31/0.90 thf(func_def_10, type, real: $tType).
% 3.31/0.90 thf(func_def_11, type, list: $tType > $tType).
% 3.31/0.90 thf(func_def_12, type, set: $tType > $tType).
% 3.31/0.90 thf(func_def_13, type, sz: $tType).
% 3.31/0.90 thf(func_def_14, type, sf: $tType).
% 3.31/0.90 thf(func_def_15, type, sc: $tType).
% 3.31/0.90 thf(func_def_16, type, c: $tType).
% 3.31/0.90 thf(func_def_17, type, b: $tType).
% 3.31/0.90 thf(func_def_18, type, a: $tType).
% 3.31/0.90 thf(func_def_19, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_20, type, cARD_1: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_21, type, type: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_22, type, ord: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_23, type, top: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_24, type, order: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_25, type, finite_finite: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_26, type, linorder: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_27, type, preorder: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_28, type, order_top: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_29, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_30, type, euclid1678468529ng_gcd: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_31, type, euclid1155270486miring: !>[X0: $tType]:($o)).
% 3.31/0.90 thf(func_def_32, type, bNF_eq_onp: !>[X0: $tType]:((X0 > $o) > X0 > X0 > $o)).
% 3.31/0.90 thf(func_def_33, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:(set(X0) > (X0 > X1) > (X0 > X2) > set(product_prod(X1,X2)))).
% 3.31/0.90 thf(func_def_34, type, bounde688532126linfun: !>[X0: $tType, X1: $tType]:((X0 > X1) > bounde2145540817linfun(X0,X1))).
% 3.31/0.90 thf(func_def_35, type, denotational_Iagree: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext(X0,X1,X2,product_unit) > denota1663640101rp_ext(X0,X1,X2,product_unit) > set(sum_sum(X0,sum_sum(X1,X2))) > $o)).
% 3.31/0.90 thf(func_def_36, type, denotational_Vagree: !>[X0: $tType]:(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)) > product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)) > set(sum_sum(X0,X0)) > $o)).
% 3.31/0.90 thf(func_def_37, type, denota2078997598vative: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext(X0,X1,X2,product_unit) > trm(X0,X2) > product_prod(finite_Cartesian_vec(real,X2),finite_Cartesian_vec(real,X2)) > real)).
% 3.31/0.90 thf(func_def_38, type, denotational_frechet: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext(X0,X1,X2,product_unit) > trm(X0,X2) > finite_Cartesian_vec(real,X2) > finite_Cartesian_vec(real,X2) > real)).
% 3.31/0.90 thf(func_def_39, type, denota2077489681interp: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext(X0,X1,X2,product_unit) > $o)).
% 3.31/0.90 thf(func_def_40, type, denota126604975rm_sem: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext(X0,X1,X2,product_unit) > trm(X0,X2) > finite_Cartesian_vec(real,X2) > real)).
% 3.31/0.90 thf(func_def_41, type, frechet_blin_frechet: !>[X0: $tType, X1: $tType, X2: $tType]:(frechet_good_interp(X0,X1,X2) > frechet_strm(X0,X2) > finite_Cartesian_vec(real,X2) > bounde2145540817linfun(finite_Cartesian_vec(real,X2),real))).
% 3.31/0.90 thf(func_def_42, type, freche457001096interp: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext(X0,X1,X2,product_unit) > frechet_good_interp(X0,X1,X2) > $o)).
% 3.31/0.90 thf(func_def_43, type, frechet_cr_strm: !>[X0: $tType, X1: $tType]:(trm(X0,X1) > frechet_strm(X0,X1) > $o)).
% 3.31/0.90 thf(func_def_44, type, freche227871258interp: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext(X0,X1,X2,product_unit) > frechet_good_interp(X0,X1,X2))).
% 3.31/0.90 thf(func_def_45, type, freche229654227interp: !>[X0: $tType, X1: $tType, X2: $tType]:(frechet_good_interp(X0,X1,X2) > denota1663640101rp_ext(X0,X1,X2,product_unit))).
% 3.31/0.90 thf(func_def_46, type, frechet_raw_term: !>[X0: $tType, X1: $tType]:(frechet_strm(X0,X1) > trm(X0,X1))).
% 3.31/0.90 thf(func_def_47, type, frechet_simple_term: !>[X0: $tType, X1: $tType]:(trm(X0,X1) > frechet_strm(X0,X1))).
% 3.31/0.90 thf(func_def_48, type, ids: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > X0 > X0 > X1 > X1 > X1 > X2 > X2 > X2 > X2 > $o)).
% 3.31/0.90 thf(func_def_49, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.31/0.90 thf(func_def_50, type, quotient: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > (X1 > X0) > (X0 > X1 > $o) > $o)).
% 3.31/0.90 thf(func_def_51, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.31/0.90 thf(func_def_52, type, top_top: !>[X0: $tType]:(X0)).
% 3.31/0.90 thf(func_def_53, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod(X0,X1))).
% 3.31/0.90 thf(func_def_54, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod(X0,X1) > X2)).
% 3.31/0.90 thf(func_def_55, type, product_fst: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X0)).
% 3.31/0.90 thf(func_def_56, type, product_snd: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X1)).
% 3.31/0.90 thf(func_def_57, type, collect: !>[X0: $tType]:((X0 > $o) > set(X0))).
% 3.31/0.90 thf(func_def_58, type, static_FVDiff: !>[X0: $tType, X1: $tType]:(trm(X0,X1) > set(sum_sum(X1,X1)))).
% 3.31/0.90 thf(func_def_59, type, static_FVT: !>[X0: $tType, X1: $tType]:(trm(X0,X1) > set(sum_sum(X1,X1)))).
% 3.31/0.90 thf(func_def_60, type, static_SIGT: !>[X0: $tType, X1: $tType]:(trm(X0,X1) > set(X0))).
% 3.31/0.90 thf(func_def_61, type, sum_Inl: !>[X0: $tType, X1: $tType]:(X0 > sum_sum(X0,X1))).
% 3.31/0.90 thf(func_def_62, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum(X0,X2) > X1)).
% 3.31/0.90 thf(func_def_63, type, predicational: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > formula(X1,X0,X2))).
% 3.31/0.90 thf(func_def_64, type, dfree: !>[X0: $tType, X1: $tType]:(trm(X0,X1) > $o)).
% 3.31/0.90 thf(func_def_65, type, p: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > formula(X1,X0,X2))).
% 3.31/0.90 thf(func_def_66, type, empty: !>[X0: $tType, X1: $tType]:(X0 > trm(X1,X0))).
% 3.31/0.90 thf(func_def_67, type, f0: !>[X0: $tType, X1: $tType]:(X0 > trm(X0,X1))).
% 3.31/0.90 thf(func_def_68, type, function: !>[X0: $tType, X1: $tType]:(X0 > (X1 > trm(X0,X1)) > trm(X0,X1))).
% 3.31/0.90 thf(func_def_69, type, plus: !>[X0: $tType, X1: $tType]:(trm(X0,X1) > trm(X0,X1) > trm(X0,X1))).
% 3.31/0.90 thf(func_def_70, type, times: !>[X0: $tType, X1: $tType]:(trm(X0,X1) > trm(X0,X1) > trm(X0,X1))).
% 3.31/0.90 thf(func_def_71, type, topolo2071040574ous_on: !>[X0: $tType, X1: $tType]:(set(X0) > (X0 > X1) > $o)).
% 3.31/0.90 thf(func_def_72, type, type_definition: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > set(X1) > $o)).
% 3.31/0.90 thf(func_def_73, type, member: !>[X0: $tType]:(X0 > set(X0) > $o)).
% 3.31/0.90 thf(func_def_74, type, i: denota1663640101rp_ext(a,b,c,product_unit)).
% 3.31/0.90 thf(func_def_75, type, j: denota1663640101rp_ext(a,b,c,product_unit)).
% 3.31/0.90 thf(func_def_76, type, nu: product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c))).
% 3.31/0.90 thf(func_def_77, type, nu2: product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c))).
% 3.31/0.90 thf(func_def_78, type, t1: trm(a,c)).
% 3.31/0.90 thf(func_def_79, type, t2: trm(a,c)).
% 3.31/0.90 thf(func_def_83, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 3.31/0.90 thf(func_def_84, type, vAND: $o > $o > $o).
% 3.31/0.90 thf(func_def_85, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.31/0.90 thf(func_def_86, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
% 3.31/0.90 thf(func_def_87, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 3.31/0.90 thf(func_def_88, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 3.31/0.90 thf(func_def_89, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 3.31/0.90 thf(func_def_90, type, vIMP: $o > $o > $o).
% 3.31/0.90 thf(func_def_91, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
% 3.31/0.90 thf(func_def_92, type, iCOMB: !>[X0: $tType]:(X0 > X0)).
% 3.31/0.90 thf(func_def_93, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 3.31/0.90 thf(func_def_94, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 3.31/0.90 thf(func_def_95, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 3.31/0.90 thf(func_def_96, type, sP3: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 3.31/0.90 thf(func_def_97, type, sK4: !>[X0: $tType]:(product_prod(X0,X0) > X0)).
% 3.31/0.90 thf(func_def_98, type, sK5: !>[X0: $tType]:(product_prod(X0,X0) > X0)).
% 3.31/0.90 thf(func_def_99, type, sK6: !>[X0: $tType]:(product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,X0))))) > X0)).
% 3.31/0.90 thf(func_def_100, type, sK7: !>[X0: $tType]:(product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,X0))))) > X0)).
% 3.31/0.90 thf(func_def_101, type, sK8: !>[X0: $tType]:(product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,X0))))) > X0)).
% 3.31/0.90 thf(func_def_102, type, sK9: !>[X0: $tType]:(product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,X0))))) > X0)).
% 3.31/0.90 thf(func_def_103, type, sK10: !>[X0: $tType]:(product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,X0))))) > X0)).
% 3.31/0.90 thf(func_def_104, type, sK11: !>[X0: $tType]:(product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,product_prod(X0,X0))))) > X0)).
% 3.31/0.90 thf(func_def_105, type, sK12: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.31/0.90 thf(func_def_106, type, sK13: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.31/0.90 thf(func_def_107, type, sK14: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.31/0.90 thf(func_def_108, type, sK15: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.31/0.90 thf(func_def_109, type, sK16: product_prod(denota1663640101rp_ext(sf,sc,sz,product_unit),product_prod(list(formula(sf,sc,sz)),list(formula(sf,sc,sz)))) > denota1663640101rp_ext(sf,sc,sz,product_unit)).
% 3.31/0.90 thf(func_def_110, type, sK17: product_prod(denota1663640101rp_ext(sf,sc,sz,product_unit),product_prod(list(formula(sf,sc,sz)),list(formula(sf,sc,sz)))) > product_prod(list(formula(sf,sc,sz)),list(formula(sf,sc,sz)))).
% 3.31/0.90 thf(func_def_111, type, sK18: !>[X0: $tType]:(X0)).
% 3.31/0.90 thf(func_def_112, type, sK19: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 3.31/0.90 thf(func_def_113, type, sK20: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 3.31/0.90 thf(func_def_114, type, sK21: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 3.31/0.90 thf(func_def_115, type, sK22: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 3.31/0.90 thf(func_def_116, type, sK23: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 3.31/0.90 thf(func_def_117, type, sK24: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 3.31/0.90 thf(func_def_118, type, sK25: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 3.31/0.90 thf(func_def_119, type, sK26: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 3.31/0.90 thf(func_def_120, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > real > (X1 > real) > set(X1) > X1)).
% 3.31/0.90 thf(func_def_121, type, sK28: !>[X0: $tType]:(set(X0) > X0)).
% 3.31/0.90 thf(func_def_122, type, sK29: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.31/0.90 thf(func_def_123, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > X0) > set(X2) > X1)).
% 3.31/0.90 thf(func_def_124, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext(X2,X1,X0,product_unit) > frechet_good_interp(X2,X1,X0))).
% 3.31/0.90 thf(func_def_125, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType]:(frechet_good_interp(X2,X1,X0) > denota1663640101rp_ext(X2,X1,X0,product_unit))).
% 3.31/0.90 thf(func_def_126, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2) > denota1663640101rp_ext(X2,X0,X1,product_unit))).
% 3.31/0.90 thf(func_def_127, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2) > X2)).
% 3.31/0.90 thf(func_def_128, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:((frechet_good_interp(X2,X1,X0) > $o) > denota1663640101rp_ext(X2,X1,X0,product_unit))).
% 3.31/0.90 thf(func_def_129, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext(X2,X1,X0,product_unit) > $o) > frechet_good_interp(X2,X1,X0))).
% 3.31/0.90 thf(func_def_130, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(denota1663640101rp_ext(X2,X1,X0,product_unit),product_prod(list(formula(X2,X1,X0)),list(formula(X2,X1,X0)))) > denota1663640101rp_ext(X2,X1,X0,product_unit))).
% 3.31/0.90 thf(func_def_131, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(denota1663640101rp_ext(X2,X1,X0,product_unit),product_prod(list(formula(X2,X1,X0)),list(formula(X2,X1,X0)))) > product_prod(list(formula(X2,X1,X0)),list(formula(X2,X1,X0))))).
% 3.31/0.90 thf(func_def_132, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext(X2,X1,X0,product_unit) > product_prod(list(formula(X2,X1,X0)),list(formula(X2,X1,X0))) > $o) > denota1663640101rp_ext(X2,X1,X0,product_unit))).
% 3.31/0.90 thf(func_def_133, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext(X2,X1,X0,product_unit) > product_prod(list(formula(X2,X1,X0)),list(formula(X2,X1,X0))) > $o) > product_prod(list(formula(X2,X1,X0)),list(formula(X2,X1,X0))))).
% 3.31/0.90 thf(func_def_134, type, sK41: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.31/0.90 thf(func_def_135, type, sK42: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.31/0.90 thf(func_def_136, type, sK43: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.31/0.90 thf(func_def_137, type, sK44: !>[X0: $tType]:(set(X0) > set(X0) > X0)).
% 3.31/0.90 thf(func_def_138, type, sK45: !>[X0: $tType, X1: $tType]:(trm(X1,X0) > frechet_strm(X1,X0))).
% 3.31/0.90 thf(func_def_139, type, sK46: !>[X0: $tType, X1: $tType]:(frechet_strm(X1,X0) > trm(X1,X0))).
% 3.31/0.90 thf(func_def_140, type, sK47: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X0)).
% 3.31/0.90 thf(func_def_141, type, sK48: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X1)).
% 3.31/0.90 thf(func_def_142, type, sK49: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X0)).
% 3.31/0.90 thf(func_def_143, type, sK50: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X1)).
% 3.31/0.90 thf(func_def_144, type, sK51: !>[X0: $tType, X1: $tType]:(product_prod(trm(X0,X1),X1) > trm(X0,X1))).
% 3.31/0.90 thf(func_def_145, type, sK52: !>[X0: $tType, X1: $tType]:(product_prod(trm(X0,X1),X1) > X1)).
% 3.31/0.90 thf(func_def_146, type, sK53: !>[X0: $tType, X1: $tType]:((trm(X0,X1) > X1 > $o) > trm(X0,X1))).
% 3.31/0.90 thf(func_def_147, type, sK54: !>[X0: $tType, X1: $tType]:((trm(X0,X1) > X1 > $o) > X1)).
% 3.31/0.90 thf(func_def_148, type, sK55: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.31/0.90 thf(func_def_149, type, sK56: !>[X0: $tType, X1: $tType]:((frechet_strm(X1,X0) > $o) > trm(X1,X0))).
% 3.31/0.90 thf(func_def_150, type, sK57: !>[X0: $tType, X1: $tType]:((X1 > trm(X0,X1)) > X1)).
% 3.31/0.90 thf(func_def_151, type, sK58: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X1)).
% 3.31/0.90 thf(func_def_152, type, sK59: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X0)).
% 3.31/0.90 thf(func_def_153, type, sK60: !>[X0: $tType, X1: $tType]:(set(product_prod(X1,X0)) > set(product_prod(X1,X0)) > X1)).
% 3.31/0.90 thf(func_def_154, type, sK61: !>[X0: $tType, X1: $tType]:(set(product_prod(X1,X0)) > set(product_prod(X1,X0)) > X0)).
% 3.31/0.90 thf(func_def_155, type, sK62: !>[X0: $tType, X1: $tType]:((product_prod(X1,X0) > $o) > X1)).
% 3.31/0.90 thf(func_def_156, type, sK63: !>[X0: $tType, X1: $tType]:((product_prod(X1,X0) > $o) > X0)).
% 3.31/0.90 thf(func_def_157, type, sK64: !>[X0: $tType, X1: $tType]:((product_prod(X1,X0) > $o) > X1)).
% 3.31/0.90 thf(func_def_158, type, sK65: !>[X0: $tType, X1: $tType]:((product_prod(X1,X0) > $o) > X0)).
% 3.31/0.90 thf(func_def_159, type, sK66: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 3.31/0.90 thf(func_def_160, type, sK67: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 3.31/0.90 thf(func_def_161, type, sK68: !>[X0: $tType, X1: $tType]:((trm(X1,X0) > $o) > frechet_strm(X1,X0))).
% 3.31/0.90 thf(func_def_162, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(X0,product_prod(X1,X2)) > X0)).
% 3.31/0.90 thf(func_def_163, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(X0,product_prod(X1,X2)) > X1)).
% 3.31/0.90 thf(func_def_164, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(X0,product_prod(X1,X2)) > X2)).
% 3.31/0.90 thf(func_def_165, type, sK72: !>[X0: $tType, X1: $tType]:((frechet_strm(X1,X0) > $o) > trm(X1,X0))).
% 3.31/0.90 thf(func_def_166, type, sK73: !>[X0: $tType, X1: $tType]:((trm(X1,X0) > $o) > frechet_strm(X1,X0))).
% 3.31/0.90 thf(func_def_167, type, sK74: !>[X0: $tType, X1: $tType]:(trm(X1,X0) > frechet_strm(X1,X0))).
% 3.31/0.90 thf(func_def_168, type, sK75: !>[X0: $tType, X1: $tType]:(frechet_strm(X1,X0) > trm(X1,X0))).
% 3.31/0.90 thf(func_def_169, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod(X2,product_prod(X1,X0)) > $o) > X2)).
% 3.31/0.90 thf(func_def_170, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod(X2,product_prod(X1,X0)) > $o) > X1)).
% 3.31/0.90 thf(func_def_171, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod(X2,product_prod(X1,X0)) > $o) > X0)).
% 3.31/0.90 thf(func_def_172, type, sK79: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > set(X0) > X0)).
% 3.31/0.90 thf(func_def_173, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0)).
% 3.31/0.90 thf(func_def_174, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1)).
% 3.31/0.90 thf(func_def_175, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2)).
% 3.31/0.90 thf(func_def_176, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3)).
% 3.31/0.90 thf(func_def_177, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType]:((frechet_good_interp(X2,X1,X0) > $o) > denota1663640101rp_ext(X2,X1,X0,product_unit))).
% 3.31/0.90 thf(func_def_178, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext(X2,X1,X0,product_unit) > $o) > frechet_good_interp(X2,X1,X0))).
% 3.31/0.90 thf(func_def_179, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext(X2,X1,X0,product_unit) > frechet_good_interp(X2,X1,X0))).
% 3.31/0.90 thf(func_def_180, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType]:(frechet_good_interp(X2,X1,X0) > denota1663640101rp_ext(X2,X1,X0,product_unit))).
% 3.31/0.90 thf(func_def_181, type, sK88: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X1 > X0) > X1)).
% 3.31/0.90 thf(func_def_182, type, sK89: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X1 > X0) > X1)).
% 3.31/0.90 thf(func_def_183, type, sK90: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X1) > X0)).
% 3.31/0.90 thf(func_def_184, type, sK91: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > X0)).
% 3.31/0.90 thf(func_def_185, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o) > X3)).
% 3.31/0.90 thf(func_def_186, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o) > X2)).
% 3.31/0.90 thf(func_def_187, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o) > X1)).
% 3.31/0.90 thf(func_def_188, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o) > X0)).
% 3.31/0.90 thf(func_def_189, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0)).
% 3.31/0.90 thf(func_def_190, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1)).
% 3.31/0.90 thf(func_def_191, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2)).
% 3.31/0.90 thf(func_def_192, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3)).
% 3.31/0.90 thf(func_def_193, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4)).
% 3.31/0.90 thf(func_def_194, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X4)).
% 3.31/0.90 thf(func_def_195, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X3)).
% 3.31/0.90 thf(func_def_196, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X2)).
% 3.31/0.90 thf(func_def_197, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X1)).
% 3.31/0.90 thf(func_def_198, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X0)).
% 3.31/0.90 thf(func_def_199, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0)).
% 3.31/0.90 thf(func_def_200, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1)).
% 3.31/0.90 thf(func_def_201, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2)).
% 3.31/0.90 thf(func_def_202, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3)).
% 3.31/0.90 thf(func_def_203, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4)).
% 3.31/0.90 thf(func_def_204, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5)).
% 3.31/0.90 thf(func_def_205, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X5)).
% 3.31/0.90 thf(func_def_206, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X4)).
% 3.31/0.90 thf(func_def_207, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X3)).
% 3.31/0.90 thf(func_def_208, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X2)).
% 3.31/0.90 thf(func_def_209, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X1)).
% 3.31/0.90 thf(func_def_210, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X0)).
% 3.31/0.90 thf(func_def_211, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X0)).
% 3.31/0.90 thf(func_def_212, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X1)).
% 3.31/0.90 thf(func_def_213, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X2)).
% 3.31/0.90 thf(func_def_214, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X3)).
% 3.31/0.90 thf(func_def_215, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X4)).
% 3.31/0.90 thf(func_def_216, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X5)).
% 3.31/0.90 thf(func_def_217, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X6)).
% 3.31/0.90 thf(func_def_218, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X6)).
% 3.31/0.90 thf(func_def_219, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X5)).
% 3.31/0.90 thf(func_def_220, type, sK127: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X4)).
% 3.31/0.90 thf(func_def_221, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X3)).
% 3.31/0.90 thf(func_def_222, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X2)).
% 3.31/0.90 thf(func_def_223, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X1)).
% 3.31/0.90 thf(func_def_224, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X0)).
% 3.31/0.90 thf(func_def_226, type, vOR: $o > $o > $o).
% 3.31/0.90 thf(func_def_227, type, vNOT: $o > $o).
% 3.31/0.90 thf(func_def_228, type, sK133: !>[X0: $tType]:((X0 > $o) > set(X0) > X0)).
% 3.31/0.90 thf(func_def_229, type, sK134: !>[X0: $tType, X1: $tType]:((X1 > trm(X0,X1)) > X1)).
% 3.31/0.90 thf(func_def_230, type, sK135: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.31/0.90 thf(f6407,plain,(
% 3.31/0.90 $false),
% 3.31/0.90 inference(avatar_sat_refutation,[],[f2040,f2045,f2050,f2055,f2060,f2065,f2070,f2075,f2080,f2085,f2090,f2095,f2100,f2105,f2110,f2115,f2120,f2125,f2130,f2135,f2140,f2145,f2150,f2155,f2160,f2165,f2170,f2175,f2180,f2184,f2188,f2192,f2196,f2200,f2204,f2236,f2240,f2244,f2248,f2252,f2287,f2319,f2341,f2345,f2349,f2353,f2357,f2361,f2366,f2370,f2427,f2432,f2437,f2442,f2446,f2450,f2454,f2458,f2462,f2466,f2470,f2474,f2478,f2482,f2486,f2490,f2494,f2498,f2502,f2506,f2510,f2515,f2519,f2523,f2570,f2699,f2740,f2746,f2750,f2754,f2758,f2762,f2767,f2771,f2795,f2807,f2812,f2816,f2828,f2832,f2836,f2846,f2850,f2855,f2859,f2890,f2894,f2898,f2914,f2918,f2924,f2932,f2946,f2964,f2975,f2979,f2983,f2987,f2991,f2995,f2999,f3003,f3011,f3015,f3043,f3047,f3051,f3078,f3087,f3093,f3097,f3118,f3126,f3135,f3139,f3143,f3147,f3151,f3155,f3299,f3303,f3307,f3311,f3315,f3352,f3356,f3360,f3364,f3368,f3379,f3400,f3404,f3408,f3469,f3492,f3496,f3500,f3504,f3561,f3565,f3586,f3590,f3602,f3606,f3610,f3750,f3756,f3763,f3767,f3771,f3787,f3830,f3834,f3838,f3861,f3910,f3932,f3936,f3970,f3974,f3986,f3990,f3994,f4028,f4058,f4068,f4072,f4231,f4235,f4239,f4245,f4320,f4339,f4343,f4383,f4388,f4393,f4397,f4401,f4740,f4762,f4889,f4893,f4897,f5198,f5228,f5232,f5236,f5240,f5245,f5442,f5464,f5468,f5491,f5495,f5499,f5841,f5845,f5849,f5917,f5952,f5966,f5970,f5974,f6107,f6133,f6145,f6157,f6171,f6227,f6236,f6240,f6268,f6301,f6305,f6345,f6349,f6367,f6379,f6406])).
% 3.31/0.90 thf(f6406,plain,(
% 3.31/0.90 ~spl132_8 | ~spl132_35 | spl132_77 | ~spl132_186 | ~spl132_227),
% 3.31/0.90 inference(avatar_split_clause,[],[f6363,f6347,f4385,f2737,f2202,f2072])).
% 3.31/0.90 thf(f2072,plain,(
% 3.31/0.90 spl132_8 <=> (finite_finite(c) = $true)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_8])])).
% 3.31/0.90 thf(f2202,plain,(
% 3.31/0.90 spl132_35 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_35])])).
% 3.31/0.90 thf(f2737,plain,(
% 3.31/0.90 spl132_77 <=> (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2)) = $true)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_77])])).
% 3.31/0.90 thf(f4385,plain,(
% 3.31/0.90 spl132_186 <=> (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),vAPP(trm(a,c),trm(a,c),vAPP(trm(a,c),sTfun(trm(a,c),trm(a,c)),plus(a,c),t1),t2))) = $true)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_186])])).
% 3.31/0.90 thf(f6347,plain,(
% 3.31/0.90 spl132_227 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5)))) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_227])])).
% 3.31/0.90 thf(f6363,plain,(
% 3.31/0.90 (finite_finite(c) != $true) | (~spl132_35 | spl132_77 | ~spl132_186 | ~spl132_227)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f6362])).
% 3.31/0.90 thf(f6362,plain,(
% 3.31/0.90 ($true = $false) | (finite_finite(c) != $true) | (~spl132_35 | spl132_77 | ~spl132_186 | ~spl132_227)),
% 3.31/0.90 inference(forward_demodulation,[],[f6361,f2742])).
% 3.31/0.90 thf(f2742,plain,(
% 3.31/0.90 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2)) = $false) | (~spl132_35 | spl132_77)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f2741])).
% 3.31/0.90 thf(f2741,plain,(
% 3.31/0.90 ($true != $true) | (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2)) = $false) | (~spl132_35 | spl132_77)),
% 3.31/0.90 inference(superposition,[],[f2739,f2203])).
% 3.31/0.90 thf(f2203,plain,(
% 3.31/0.90 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl132_35),
% 3.31/0.90 inference(avatar_component_clause,[],[f2202])).
% 3.31/0.90 thf(f2739,plain,(
% 3.31/0.90 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2)) != $true) | spl132_77),
% 3.31/0.90 inference(avatar_component_clause,[],[f2737])).
% 3.31/0.90 thf(f6361,plain,(
% 3.31/0.90 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2)) = $true) | (finite_finite(c) != $true) | (~spl132_186 | ~spl132_227)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f6358])).
% 3.31/0.90 thf(f6358,plain,(
% 3.31/0.90 ($true != $true) | (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2)) = $true) | (finite_finite(c) != $true) | (~spl132_186 | ~spl132_227)),
% 3.31/0.90 inference(superposition,[],[f6348,f4387])).
% 3.31/0.90 thf(f4387,plain,(
% 3.31/0.90 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),vAPP(trm(a,c),trm(a,c),vAPP(trm(a,c),sTfun(trm(a,c),trm(a,c)),plus(a,c),t1),t2))) = $true) | ~spl132_186),
% 3.31/0.90 inference(avatar_component_clause,[],[f4385])).
% 3.31/0.90 thf(f6348,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5)))) | ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5))) | (finite_finite(X0) != $true)) ) | ~spl132_227),
% 3.31/0.90 inference(avatar_component_clause,[],[f6347])).
% 3.31/0.90 thf(f6379,plain,(
% 3.31/0.90 spl132_229),
% 3.31/0.90 inference(avatar_split_clause,[],[f1637,f6377])).
% 3.31/0.90 thf(f6377,plain,(
% 3.31/0.90 spl132_229 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((freche457001096interp(X2,X1,X0) = vAPP(sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(frechet_good_interp(X2,X1,X0),$o)),cCOMB,vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o))),bCOMB,vEQ(denota1663640101rp_ext(X2,X1,X0,product_unit))),freche229654227interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_229])])).
% 3.31/0.90 thf(f1637,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((freche457001096interp(X2,X1,X0) = vAPP(sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(frechet_good_interp(X2,X1,X0),$o)),cCOMB,vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o))),bCOMB,vEQ(denota1663640101rp_ext(X2,X1,X0,product_unit))),freche229654227interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1128])).
% 3.31/0.90 thf(f1128,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((freche457001096interp(X2,X1,X0) = vAPP(sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(frechet_good_interp(X2,X1,X0),$o)),cCOMB,vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o))),bCOMB,vEQ(denota1663640101rp_ext(X2,X1,X0,product_unit))),freche229654227interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1127])).
% 3.31/0.90 thf(f1127,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((freche457001096interp(X2,X1,X0) = vAPP(sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(frechet_good_interp(X2,X1,X0),$o)),cCOMB,vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o))),bCOMB,vEQ(denota1663640101rp_ext(X2,X1,X0,product_unit))),freche229654227interp(X2,X1,X0)))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f627])).
% 3.31/0.90 thf(f627,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => (freche457001096interp(X2,X1,X0) = vAPP(sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(frechet_good_interp(X2,X1,X0),$o)),cCOMB,vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o)),sTfun(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(frechet_good_interp(X2,X1,X0),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o))),bCOMB,vEQ(denota1663640101rp_ext(X2,X1,X0,product_unit))),freche229654227interp(X2,X1,X0)))))),
% 3.31/0.90 inference(fool_elimination,[],[f626])).
% 3.31/0.90 thf(f626,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => (freche457001096interp(X2,X1,X0) = (^[X3 : denota1663640101rp_ext(X2,X1,X0,product_unit), X4 : frechet_good_interp(X2,X1,X0)] : ((vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X4) = X3)))))),
% 3.31/0.90 inference(rectify,[],[f32])).
% 3.31/0.90 thf(f32,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => (freche457001096interp(X0,X2,X1) = (^[X20 : denota1663640101rp_ext(X0,X2,X1,product_unit), X31 : frechet_good_interp(X0,X2,X1)] : ((vAPP(frechet_good_interp(X0,X2,X1),denota1663640101rp_ext(X0,X2,X1,product_unit),freche229654227interp(X0,X2,X1),X31) = X20)))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_cr__good__interp__def)).
% 3.31/0.90 thf(f6367,plain,(
% 3.31/0.90 spl132_228),
% 3.31/0.90 inference(avatar_split_clause,[],[f1655,f6365])).
% 3.31/0.90 thf(f6365,plain,(
% 3.31/0.90 spl132_228 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X5 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : set(sum_sum(X2,sum_sum(X1,X0))),X6 : denota1663640101rp_ext(X2,X1,X0,product_unit),X3 : set(sum_sum(X2,sum_sum(X1,X0)))] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X3)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X4)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(set(sum_sum(X2,sum_sum(X1,X0))),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),ord_less_eq(set(sum_sum(X2,sum_sum(X1,X0)))),X3),X4)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_228])])).
% 3.31/0.90 thf(f1655,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : set(sum_sum(X2,sum_sum(X1,X0))),X6 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : set(sum_sum(X2,sum_sum(X1,X0))),X5 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X3)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X4)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(set(sum_sum(X2,sum_sum(X1,X0))),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),ord_less_eq(set(sum_sum(X2,sum_sum(X1,X0)))),X3),X4)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1160])).
% 3.31/0.90 thf(f1160,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(sum_sum(X2,sum_sum(X1,X0))),X4 : set(sum_sum(X2,sum_sum(X1,X0))),X5 : denota1663640101rp_ext(X2,X1,X0,product_unit),X6 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X3)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X4)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(set(sum_sum(X2,sum_sum(X1,X0))),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),ord_less_eq(set(sum_sum(X2,sum_sum(X1,X0)))),X3),X4))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1159])).
% 3.31/0.90 thf(f1159,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(sum_sum(X2,sum_sum(X1,X0))),X4 : set(sum_sum(X2,sum_sum(X1,X0))),X5 : denota1663640101rp_ext(X2,X1,X0,product_unit),X6 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X3)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X4))) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(set(sum_sum(X2,sum_sum(X1,X0))),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),ord_less_eq(set(sum_sum(X2,sum_sum(X1,X0)))),X3),X4))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f659])).
% 3.31/0.90 thf(f659,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : set(sum_sum(X2,sum_sum(X1,X0))),X4 : set(sum_sum(X2,sum_sum(X1,X0))),X5 : denota1663640101rp_ext(X2,X1,X0,product_unit),X6 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(set(sum_sum(X2,sum_sum(X1,X0))),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),ord_less_eq(set(sum_sum(X2,sum_sum(X1,X0)))),X3),X4)) => (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X4)) => ($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X3)))))),
% 3.31/0.90 inference(fool_elimination,[],[f658])).
% 3.31/0.90 thf(f658,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : set(sum_sum(X2,sum_sum(X1,X0))),X4 : set(sum_sum(X2,sum_sum(X1,X0))),X5 : denota1663640101rp_ext(X2,X1,X0,product_unit),X6 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(set(sum_sum(X2,sum_sum(X1,X0))),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),ord_less_eq(set(sum_sum(X2,sum_sum(X1,X0)))),X3),X4) => (vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X4) => vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X5),X6),X3))))),
% 3.31/0.90 inference(rectify,[],[f91])).
% 3.31/0.90 thf(f91,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X11 : set(sum_sum(X0,sum_sum(X2,X1))),X12 : set(sum_sum(X0,sum_sum(X2,X1))),X26 : denota1663640101rp_ext(X0,X2,X1,product_unit),X84 : denota1663640101rp_ext(X0,X2,X1,product_unit)] : (vAPP(set(sum_sum(X0,sum_sum(X2,X1))),$o,vAPP(set(sum_sum(X0,sum_sum(X2,X1))),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o),ord_less_eq(set(sum_sum(X0,sum_sum(X2,X1)))),X11),X12) => (vAPP(set(sum_sum(X0,sum_sum(X2,X1))),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o),vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o)),denotational_Iagree(X0,X2,X1),X26),X84),X12) => vAPP(set(sum_sum(X0,sum_sum(X2,X1))),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o),vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o)),denotational_Iagree(X0,X2,X1),X26),X84),X11))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Iagree__sub)).
% 3.31/0.90 thf(f6349,plain,(
% 3.31/0.90 spl132_227),
% 3.31/0.90 inference(avatar_split_clause,[],[f1599,f6347])).
% 3.31/0.90 thf(f1599,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5)))) | (finite_finite(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1093])).
% 3.31/0.90 thf(f1093,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5))))) | (finite_finite(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f563])).
% 3.31/0.90 thf(f563,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X0) = $true) => ! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5)))) => ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5)))))),
% 3.31/0.90 inference(fool_elimination,[],[f562])).
% 3.31/0.90 thf(f562,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (finite_finite(X0) => ! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5))) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5))))),
% 3.31/0.90 inference(rectify,[],[f1])).
% 3.31/0.90 thf(f1,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType] : (finite_finite(X0) => ! [X7 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X8 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X9 : trm(X2,X0),X10 : trm(X2,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X8),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVDiff(X2,X0),vAPP(trm(X2,X0),trm(X2,X0),vAPP(trm(X2,X0),sTfun(trm(X2,X0),trm(X2,X0)),plus(X2,X0),X9),X10))) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X8),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVDiff(X2,X0),X10))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_agree__plus2)).
% 3.31/0.90 thf(f6345,plain,(
% 3.31/0.90 spl132_226),
% 3.31/0.90 inference(avatar_split_clause,[],[f1598,f6343])).
% 3.31/0.90 thf(f6343,plain,(
% 3.31/0.90 spl132_226 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5)))) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_226])])).
% 3.31/0.90 thf(f1598,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5)))) | (finite_finite(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1092])).
% 3.31/0.90 thf(f1092,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5))))) | (finite_finite(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f561])).
% 3.31/0.90 thf(f561,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X0) = $true) => ! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5)))) => ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4)))))),
% 3.31/0.90 inference(fool_elimination,[],[f560])).
% 3.31/0.90 thf(f560,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (finite_finite(X0) => ! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5))) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4))))),
% 3.31/0.90 inference(rectify,[],[f5])).
% 3.31/0.90 thf(f5,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType] : (finite_finite(X0) => ! [X7 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X8 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X9 : trm(X2,X0),X10 : trm(X2,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X8),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVDiff(X2,X0),vAPP(trm(X2,X0),trm(X2,X0),vAPP(trm(X2,X0),sTfun(trm(X2,X0),trm(X2,X0)),plus(X2,X0),X9),X10))) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X8),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVDiff(X2,X0),X9))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_agree__plus1)).
% 3.31/0.90 thf(f6305,plain,(
% 3.31/0.90 spl132_225),
% 3.31/0.90 inference(avatar_split_clause,[],[f1597,f6303])).
% 3.31/0.90 thf(f6303,plain,(
% 3.31/0.90 spl132_225 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5)))) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_225])])).
% 3.31/0.90 thf(f1597,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5)))) | (finite_finite(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1091])).
% 3.31/0.90 thf(f1091,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5))))) | (finite_finite(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f559])).
% 3.31/0.90 thf(f559,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X0) = $true) => ! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5)))) => ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5)))))),
% 3.31/0.90 inference(fool_elimination,[],[f558])).
% 3.31/0.90 thf(f558,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (finite_finite(X0) => ! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5))) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X5))))),
% 3.31/0.90 inference(rectify,[],[f12])).
% 3.31/0.90 thf(f12,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType] : (finite_finite(X0) => ! [X7 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X8 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X9 : trm(X2,X0),X10 : trm(X2,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X8),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVDiff(X2,X0),vAPP(trm(X2,X0),trm(X2,X0),vAPP(trm(X2,X0),sTfun(trm(X2,X0),trm(X2,X0)),times(X2,X0),X9),X10))) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X8),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVDiff(X2,X0),X10))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_agree__times2)).
% 3.31/0.90 thf(f6301,plain,(
% 3.31/0.90 spl132_224),
% 3.31/0.90 inference(avatar_split_clause,[],[f1596,f6299])).
% 3.31/0.90 thf(f6299,plain,(
% 3.31/0.90 spl132_224 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5)))) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_224])])).
% 3.31/0.90 thf(f1596,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5)))) | (finite_finite(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1090])).
% 3.31/0.90 thf(f1090,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5))))) | (finite_finite(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f557])).
% 3.31/0.90 thf(f557,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X0) = $true) => ! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5)))) => ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4)))))),
% 3.31/0.90 inference(fool_elimination,[],[f556])).
% 3.31/0.90 thf(f556,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (finite_finite(X0) => ! [X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5))) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X3),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X4))))),
% 3.31/0.90 inference(rectify,[],[f11])).
% 3.31/0.90 thf(f11,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType] : (finite_finite(X0) => ! [X7 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X8 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X9 : trm(X2,X0),X10 : trm(X2,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X8),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVDiff(X2,X0),vAPP(trm(X2,X0),trm(X2,X0),vAPP(trm(X2,X0),sTfun(trm(X2,X0),trm(X2,X0)),times(X2,X0),X9),X10))) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X8),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVDiff(X2,X0),X9))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_agree__times1)).
% 3.31/0.90 thf(f6268,plain,(
% 3.31/0.90 spl132_223),
% 3.31/0.90 inference(avatar_split_clause,[],[f1741,f6266])).
% 3.31/0.90 thf(f6266,plain,(
% 3.31/0.90 spl132_223 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X0,sK80(X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X1,sK81(X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X2,sK82(X0,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X3,sK83(X0,X1,X2,X3),X4)))) = X4)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_223])])).
% 3.31/0.90 thf(f1741,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ((vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X0,sK80(X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X1,sK81(X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X2,sK82(X0,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X3,sK83(X0,X1,X2,X3),X4)))) = X4)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1429])).
% 3.31/0.90 thf(f1429,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X0,sK80(X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X1,sK81(X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X2,sK82(X0,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X3,sK83(X0,X1,X2,X3),X4)))) = X4)),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK80,sK81,sK82,sK83])],[f1256,f1428])).
% 3.31/0.90 thf(f1428,plain,(
% 3.31/0.90 ! [X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (? [X5 : X0,X6 : X1,X7 : X2,X8 : X3] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),X5),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),X6),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X7),X8))) = X4) => (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X0,sK80(X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X1,sK81(X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X2,sK82(X0,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X3,sK83(X0,X1,X2,X3),X4)))) = X4))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1256,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ? [X5 : X0,X6 : X1,X7 : X2,X8 : X3] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),X5),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),X6),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X7),X8))) = X4)),
% 3.31/0.90 inference(ennf_transformation,[],[f943])).
% 3.31/0.90 thf(f943,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ~! [X5 : X0,X6 : X1,X7 : X2,X8 : X3] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),X5),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),X6),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X7),X8))) != X4)),
% 3.31/0.90 inference(rectify,[],[f65])).
% 3.31/0.90 thf(f65,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType,X1 : $tType,X63 : $tType,X15 : product_prod(X0,product_prod(X2,product_prod(X1,X63)))] : ~! [X57 : X0,X58 : X2,X64 : X1,X65 : X63] : (vAPP(product_prod(X2,product_prod(X1,X63)),product_prod(X0,product_prod(X2,product_prod(X1,X63))),vAPP(X0,sTfun(product_prod(X2,product_prod(X1,X63)),product_prod(X0,product_prod(X2,product_prod(X1,X63)))),product_Pair(X0,product_prod(X2,product_prod(X1,X63))),X57),vAPP(product_prod(X1,X63),product_prod(X2,product_prod(X1,X63)),vAPP(X2,sTfun(product_prod(X1,X63),product_prod(X2,product_prod(X1,X63))),product_Pair(X2,product_prod(X1,X63)),X58),vAPP(X63,product_prod(X1,X63),vAPP(X1,sTfun(X63,product_prod(X1,X63)),product_Pair(X1,X63),X64),X65))) != X15)),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_prod__cases4)).
% 3.31/0.90 thf(f6240,plain,(
% 3.31/0.90 spl132_222),
% 3.31/0.90 inference(avatar_split_clause,[],[f1527,f6238])).
% 3.31/0.90 thf(f6238,plain,(
% 3.31/0.90 spl132_222 <=> ! [X0 : $tType,X4 : finite_Cartesian_vec(real,X0),X3 : finite_Cartesian_vec(real,X0),X2 : finite_Cartesian_vec(real,X0),X1 : finite_Cartesian_vec(real,X0)] : ((X2 = X4) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1),X2)),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3),X4)),top_top(set(sum_sum(X0,X0))))) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_222])])).
% 3.31/0.90 thf(f1527,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : finite_Cartesian_vec(real,X0),X3 : finite_Cartesian_vec(real,X0),X1 : finite_Cartesian_vec(real,X0),X4 : finite_Cartesian_vec(real,X0)] : ((X2 = X4) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1),X2)),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3),X4)),top_top(set(sum_sum(X0,X0))))) | (finite_finite(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1006])).
% 3.31/0.90 thf(f1006,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : finite_Cartesian_vec(real,X0),X2 : finite_Cartesian_vec(real,X0),X3 : finite_Cartesian_vec(real,X0),X4 : finite_Cartesian_vec(real,X0)] : (((X2 = X4) & (X1 = X3)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1),X2)),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3),X4)),top_top(set(sum_sum(X0,X0)))))) | (finite_finite(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f433])).
% 3.31/0.90 thf(f433,plain,(
% 3.31/0.90 ! [X0 : $tType] : ((finite_finite(X0) = $true) => ! [X1 : finite_Cartesian_vec(real,X0),X2 : finite_Cartesian_vec(real,X0),X3 : finite_Cartesian_vec(real,X0),X4 : finite_Cartesian_vec(real,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1),X2)),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3),X4)),top_top(set(sum_sum(X0,X0))))) => ((X2 = X4) & (X1 = X3))))),
% 3.31/0.90 inference(fool_elimination,[],[f432])).
% 3.31/0.90 thf(f432,plain,(
% 3.31/0.90 ! [X0 : $tType] : (finite_finite(X0) => ! [X1 : finite_Cartesian_vec(real,X0),X2 : finite_Cartesian_vec(real,X0),X3 : finite_Cartesian_vec(real,X0),X4 : finite_Cartesian_vec(real,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1),X2)),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3),X4)),top_top(set(sum_sum(X0,X0)))) => ((X2 = X4) & (X1 = X3))))),
% 3.31/0.90 inference(rectify,[],[f203])).
% 3.31/0.90 thf(f203,axiom,(
% 3.31/0.90 ! [X0 : $tType] : (finite_finite(X0) => ! [X32 : finite_Cartesian_vec(real,X0),X33 : finite_Cartesian_vec(real,X0),X79 : finite_Cartesian_vec(real,X0),X80 : finite_Cartesian_vec(real,X0)] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X32),X33)),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X79),X80)),top_top(set(sum_sum(X0,X0)))) => ((X33 = X80) & (X32 = X79))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Vagree__univ)).
% 3.31/0.90 thf(f6236,plain,(
% 3.31/0.90 spl132_221),
% 3.31/0.90 inference(avatar_split_clause,[],[f1526,f6234])).
% 3.31/0.90 thf(f6234,plain,(
% 3.31/0.90 spl132_221 <=> ! [X0 : $tType,X2 : finite_Cartesian_vec(real,X0),X4 : finite_Cartesian_vec(real,X0),X3 : finite_Cartesian_vec(real,X0),X1 : finite_Cartesian_vec(real,X0)] : ((X1 = X3) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1),X2)),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3),X4)),top_top(set(sum_sum(X0,X0))))) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_221])])).
% 3.31/0.90 thf(f1526,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : finite_Cartesian_vec(real,X0),X3 : finite_Cartesian_vec(real,X0),X1 : finite_Cartesian_vec(real,X0),X4 : finite_Cartesian_vec(real,X0)] : ((X1 = X3) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1),X2)),vAPP(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),vAPP(finite_Cartesian_vec(real,X0),sTfun(finite_Cartesian_vec(real,X0),product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))),product_Pair(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3),X4)),top_top(set(sum_sum(X0,X0))))) | (finite_finite(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1006])).
% 3.31/0.90 thf(f6227,plain,(
% 3.31/0.90 spl132_220),
% 3.31/0.90 inference(avatar_split_clause,[],[f1603,f6225])).
% 3.31/0.90 thf(f6225,plain,(
% 3.31/0.90 spl132_220 <=> ! [X0 : denota1663640101rp_ext(sf,sc,sz,product_unit),X1 : trm(sf,sz)] : (($true = vAPP(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o,vAPP(set(finite_Cartesian_vec(real,sz)),sTfun(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),top_top(set(finite_Cartesian_vec(real,sz)))),vAPP(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),vAPP(frechet_good_interp(sf,sc,sz),sTfun(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real))),frechet_blin_frechet(sf,sc,sz),vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),frechet_good_interp(sf,sc,sz),freche227871258interp(sf,sc,sz),X0)),vAPP(trm(sf,sz),frechet_strm(sf,sz),frechet_simple_term(sf,sz),X1)))) | ($true != vAPP(trm(sf,sz),$o,dfree(sf,sz),X1)) | ($true != vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),$o,denota2077489681interp(sf,sc,sz),X0)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_220])])).
% 3.31/0.90 thf(f1603,plain,(
% 3.31/0.90 ( ! [X0 : denota1663640101rp_ext(sf,sc,sz,product_unit),X1 : trm(sf,sz)] : (($true = vAPP(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o,vAPP(set(finite_Cartesian_vec(real,sz)),sTfun(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),top_top(set(finite_Cartesian_vec(real,sz)))),vAPP(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),vAPP(frechet_good_interp(sf,sc,sz),sTfun(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real))),frechet_blin_frechet(sf,sc,sz),vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),frechet_good_interp(sf,sc,sz),freche227871258interp(sf,sc,sz),X0)),vAPP(trm(sf,sz),frechet_strm(sf,sz),frechet_simple_term(sf,sz),X1)))) | ($true != vAPP(trm(sf,sz),$o,dfree(sf,sz),X1)) | ($true != vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),$o,denota2077489681interp(sf,sc,sz),X0))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1099])).
% 3.31/0.90 thf(f1099,plain,(
% 3.31/0.90 ! [X0 : denota1663640101rp_ext(sf,sc,sz,product_unit),X1 : trm(sf,sz)] : (($true = vAPP(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o,vAPP(set(finite_Cartesian_vec(real,sz)),sTfun(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),top_top(set(finite_Cartesian_vec(real,sz)))),vAPP(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),vAPP(frechet_good_interp(sf,sc,sz),sTfun(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real))),frechet_blin_frechet(sf,sc,sz),vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),frechet_good_interp(sf,sc,sz),freche227871258interp(sf,sc,sz),X0)),vAPP(trm(sf,sz),frechet_strm(sf,sz),frechet_simple_term(sf,sz),X1)))) | ($true != vAPP(trm(sf,sz),$o,dfree(sf,sz),X1)) | ($true != vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),$o,denota2077489681interp(sf,sc,sz),X0)))),
% 3.31/0.90 inference(flattening,[],[f1098])).
% 3.31/0.90 thf(f1098,plain,(
% 3.31/0.90 ! [X0 : denota1663640101rp_ext(sf,sc,sz,product_unit),X1 : trm(sf,sz)] : ((($true = vAPP(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o,vAPP(set(finite_Cartesian_vec(real,sz)),sTfun(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),top_top(set(finite_Cartesian_vec(real,sz)))),vAPP(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),vAPP(frechet_good_interp(sf,sc,sz),sTfun(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real))),frechet_blin_frechet(sf,sc,sz),vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),frechet_good_interp(sf,sc,sz),freche227871258interp(sf,sc,sz),X0)),vAPP(trm(sf,sz),frechet_strm(sf,sz),frechet_simple_term(sf,sz),X1)))) | ($true != vAPP(trm(sf,sz),$o,dfree(sf,sz),X1))) | ($true != vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),$o,denota2077489681interp(sf,sc,sz),X0)))),
% 3.31/0.90 inference(ennf_transformation,[],[f571])).
% 3.31/0.90 thf(f571,plain,(
% 3.31/0.90 ! [X0 : denota1663640101rp_ext(sf,sc,sz,product_unit),X1 : trm(sf,sz)] : (($true = vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),$o,denota2077489681interp(sf,sc,sz),X0)) => (($true = vAPP(trm(sf,sz),$o,dfree(sf,sz),X1)) => ($true = vAPP(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o,vAPP(set(finite_Cartesian_vec(real,sz)),sTfun(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),top_top(set(finite_Cartesian_vec(real,sz)))),vAPP(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),vAPP(frechet_good_interp(sf,sc,sz),sTfun(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real))),frechet_blin_frechet(sf,sc,sz),vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),frechet_good_interp(sf,sc,sz),freche227871258interp(sf,sc,sz),X0)),vAPP(trm(sf,sz),frechet_strm(sf,sz),frechet_simple_term(sf,sz),X1))))))),
% 3.31/0.90 inference(fool_elimination,[],[f570])).
% 3.31/0.90 thf(f570,plain,(
% 3.31/0.90 ! [X0 : denota1663640101rp_ext(sf,sc,sz,product_unit),X1 : trm(sf,sz)] : (vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),$o,denota2077489681interp(sf,sc,sz),X0) => (vAPP(trm(sf,sz),$o,dfree(sf,sz),X1) => vAPP(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o,vAPP(set(finite_Cartesian_vec(real,sz)),sTfun(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),top_top(set(finite_Cartesian_vec(real,sz)))),vAPP(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),vAPP(frechet_good_interp(sf,sc,sz),sTfun(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real))),frechet_blin_frechet(sf,sc,sz),vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),frechet_good_interp(sf,sc,sz),freche227871258interp(sf,sc,sz),X0)),vAPP(trm(sf,sz),frechet_strm(sf,sz),frechet_simple_term(sf,sz),X1)))))),
% 3.31/0.90 inference(rectify,[],[f198])).
% 3.31/0.90 thf(f198,axiom,(
% 3.31/0.90 ! [X26 : denota1663640101rp_ext(sf,sc,sz,product_unit),X25 : trm(sf,sz)] : (vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),$o,denota2077489681interp(sf,sc,sz),X26) => (vAPP(trm(sf,sz),$o,dfree(sf,sz),X25) => vAPP(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o,vAPP(set(finite_Cartesian_vec(real,sz)),sTfun(sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),top_top(set(finite_Cartesian_vec(real,sz)))),vAPP(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real)),vAPP(frechet_good_interp(sf,sc,sz),sTfun(frechet_strm(sf,sz),sTfun(finite_Cartesian_vec(real,sz),bounde2145540817linfun(finite_Cartesian_vec(real,sz),real))),frechet_blin_frechet(sf,sc,sz),vAPP(denota1663640101rp_ext(sf,sc,sz,product_unit),frechet_good_interp(sf,sc,sz),freche227871258interp(sf,sc,sz),X26)),vAPP(trm(sf,sz),frechet_strm(sf,sz),frechet_simple_term(sf,sz),X25)))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_frechet__continuous)).
% 3.31/0.90 thf(f6171,plain,(
% 3.31/0.90 spl132_219),
% 3.31/0.90 inference(avatar_split_clause,[],[f1524,f6169])).
% 3.31/0.90 thf(f6169,plain,(
% 3.31/0.90 spl132_219 <=> ! [X0 : $tType,X2 : set(sum_sum(X0,X0)),X4 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1 : set(sum_sum(X0,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X1)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X2)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),X1),X2)) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_219])])).
% 3.31/0.90 thf(f1524,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : set(sum_sum(X0,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1 : set(sum_sum(X0,X0)),X4 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X1)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X2)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),X1),X2)) | (finite_finite(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1003])).
% 3.31/0.90 thf(f1003,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : set(sum_sum(X0,X0)),X2 : set(sum_sum(X0,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X1)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X2)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),X1),X2))) | (finite_finite(X0) != $true))),
% 3.31/0.90 inference(flattening,[],[f1002])).
% 3.31/0.90 thf(f1002,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : set(sum_sum(X0,X0)),X2 : set(sum_sum(X0,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : ((($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X1)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X2))) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),X1),X2))) | (finite_finite(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f429])).
% 3.31/0.90 thf(f429,plain,(
% 3.31/0.90 ! [X0 : $tType] : ((finite_finite(X0) = $true) => ! [X1 : set(sum_sum(X0,X0)),X2 : set(sum_sum(X0,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),X1),X2)) => (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X2)) => ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X1)))))),
% 3.31/0.90 inference(fool_elimination,[],[f428])).
% 3.31/0.90 thf(f428,plain,(
% 3.31/0.90 ! [X0 : $tType] : (finite_finite(X0) => ! [X1 : set(sum_sum(X0,X0)),X2 : set(sum_sum(X0,X0)),X3 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X4 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),X1),X2) => (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X2) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X3),X4),X1))))),
% 3.31/0.90 inference(rectify,[],[f50])).
% 3.31/0.90 thf(f50,axiom,(
% 3.31/0.90 ! [X0 : $tType] : (finite_finite(X0) => ! [X11 : set(sum_sum(X0,X0)),X12 : set(sum_sum(X0,X0)),X7 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X56 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),X11),X12) => (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X56),X12) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X56),X11))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_agree__sub)).
% 3.31/0.90 thf(f6157,plain,(
% 3.31/0.90 spl132_218),
% 3.31/0.90 inference(avatar_split_clause,[],[f1511,f6155])).
% 3.31/0.90 thf(f6155,plain,(
% 3.31/0.90 spl132_218 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_218])])).
% 3.31/0.90 thf(f1511,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1325])).
% 3.31/0.90 thf(f1325,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3))) | (linorder(X0) != $true))),
% 3.31/0.90 inference(definition_folding,[],[f992,f1324,f1323,f1322,f1321])).
% 3.31/0.90 thf(f1321,plain,(
% 3.31/0.90 ! [X3 : X0,X2 : X0,X0 : $tType,X1 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)))),
% 3.31/0.90 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 3.31/0.90 thf(f1322,plain,(
% 3.31/0.90 ! [X3 : X0,X1 : X0,X0 : $tType,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) | ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)))),
% 3.31/0.90 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 3.31/0.90 thf(f1323,plain,(
% 3.31/0.90 ! [X2 : X0,X3 : X0,X0 : $tType,X1 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) | ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)))),
% 3.31/0.90 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 3.31/0.90 thf(f1324,plain,(
% 3.31/0.90 ! [X1 : X0,X2 : X0,X0 : $tType,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) | ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)))),
% 3.31/0.90 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 3.31/0.90 thf(f992,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))) | (linorder(X0) != $true))),
% 3.31/0.90 inference(flattening,[],[f991])).
% 3.31/0.90 thf(f991,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((((((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))) | (linorder(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f918])).
% 3.31/0.90 thf(f918,plain,(
% 3.31/0.90 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) => ~(($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))))))))),
% 3.31/0.90 inference(flattening,[],[f411])).
% 3.31/0.90 thf(f411,plain,(
% 3.31/0.90 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) => ~(($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))))))))),
% 3.31/0.90 inference(fool_elimination,[],[f410])).
% 3.31/0.90 thf(f410,plain,(
% 3.31/0.90 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) => ~(vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))))))))),
% 3.31/0.90 inference(rectify,[],[f149])).
% 3.31/0.90 thf(f149,axiom,(
% 3.31/0.90 ! [X0 : $tType] : (linorder(X0) => ! [X14 : X0,X15 : X0,X106 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X14),X15) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X15),X106)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X15),X14) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X14),X106)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X14),X106) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X106),X15)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X106),X15) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X15),X14)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X15),X106) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X106),X14)) => ~(vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X106),X14) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X14),X15))))))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_le__cases3)).
% 3.31/0.90 thf(f6145,plain,(
% 3.31/0.90 spl132_217),
% 3.31/0.90 inference(avatar_split_clause,[],[f1649,f6143])).
% 3.31/0.90 thf(f6143,plain,(
% 3.31/0.90 spl132_217 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : denota1663640101rp_ext(X2,X1,X0,product_unit) > $o,X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,X3)) | ($true != vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),frechet_good_interp(X2,X1,X0),sK36(X0,X1,X2),X4)))) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_217])])).
% 3.31/0.90 thf(f1649,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit) > $o] : (($true = vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,X3)) | ($true != vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),frechet_good_interp(X2,X1,X0),sK36(X0,X1,X2),X4)))) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1371])).
% 3.31/0.90 thf(f1371,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit) > $o] : (($true = vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,X3)) | ($true != vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),frechet_good_interp(X2,X1,X0),sK36(X0,X1,X2),X4)))) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f1148,f1370])).
% 3.31/0.90 thf(f1370,plain,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType,X4 : denota1663640101rp_ext(X2,X1,X0,product_unit) > $o] : (? [X5 : frechet_good_interp(X2,X1,X0)] : ($true != vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X5))) => ($true != vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),frechet_good_interp(X2,X1,X0),sK36(X0,X1,X2),X4)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1148,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit) > $o] : (($true = vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,X3)) | ? [X5 : frechet_good_interp(X2,X1,X0)] : ($true != vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X5))) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1147])).
% 3.31/0.90 thf(f1147,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit) > $o] : ((($true = vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,X3)) | ? [X5 : frechet_good_interp(X2,X1,X0)] : ($true != vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X5)))) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f647])).
% 3.31/0.90 thf(f647,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit) > $o] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) => (! [X5 : frechet_good_interp(X2,X1,X0)] : ($true = vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X5))) => ($true = vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,X3)))))),
% 3.31/0.90 inference(fool_elimination,[],[f646])).
% 3.31/0.90 thf(f646,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit) > $o] : (vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))) => (! [X5 : frechet_good_interp(X2,X1,X0)] : vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X5)) => vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),$o,X4,X3))))),
% 3.31/0.90 inference(rectify,[],[f104])).
% 3.31/0.90 thf(f104,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X15 : denota1663640101rp_ext(X0,X2,X1,product_unit),X24 : denota1663640101rp_ext(X0,X2,X1,product_unit) > $o] : (vAPP(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o),member(denota1663640101rp_ext(X0,X2,X1,product_unit)),X15),vAPP(sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),$o),set(denota1663640101rp_ext(X0,X2,X1,product_unit)),collect(denota1663640101rp_ext(X0,X2,X1,product_unit)),denota2077489681interp(X0,X2,X1))) => (! [X23 : frechet_good_interp(X0,X2,X1)] : vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),$o,X24,vAPP(frechet_good_interp(X0,X2,X1),denota1663640101rp_ext(X0,X2,X1,product_unit),freche229654227interp(X0,X2,X1),X23)) => vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),$o,X24,X15))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_raw__interp__induct)).
% 3.31/0.90 thf(f6133,plain,(
% 3.31/0.90 spl132_216),
% 3.31/0.90 inference(avatar_split_clause,[],[f1653,f6131])).
% 3.31/0.90 thf(f6131,plain,(
% 3.31/0.90 spl132_216 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : denota1663640101rp_ext(X2,X1,X0,product_unit),X5 : set(sum_sum(X2,sum_sum(X1,X0))),X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X4),X3),X5)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X4),X5)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_216])])).
% 3.31/0.90 thf(f1653,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit),X5 : set(sum_sum(X2,sum_sum(X1,X0)))] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X4),X3),X5)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X4),X5)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1156])).
% 3.31/0.90 thf(f1156,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit),X5 : set(sum_sum(X2,sum_sum(X1,X0)))] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X4),X3),X5)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X4),X5))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1155])).
% 3.31/0.90 thf(f1155,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit),X5 : set(sum_sum(X2,sum_sum(X1,X0)))] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X4),X3),X5)) | ($true != vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X4),X5))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f655])).
% 3.31/0.90 thf(f655,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit),X5 : set(sum_sum(X2,sum_sum(X1,X0)))] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X4),X5)) => ($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X4),X3),X5))))),
% 3.31/0.90 inference(fool_elimination,[],[f654])).
% 3.31/0.90 thf(f654,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : denota1663640101rp_ext(X2,X1,X0,product_unit),X5 : set(sum_sum(X2,sum_sum(X1,X0)))] : (vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X4),X5) => vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X4),X3),X5)))),
% 3.31/0.90 inference(rectify,[],[f25])).
% 3.31/0.90 thf(f25,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X11 : denota1663640101rp_ext(X0,X2,X1,product_unit),X12 : denota1663640101rp_ext(X0,X2,X1,product_unit),X13 : set(sum_sum(X0,sum_sum(X2,X1)))] : (vAPP(set(sum_sum(X0,sum_sum(X2,X1))),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o),vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o)),denotational_Iagree(X0,X2,X1),X11),X12),X13) => vAPP(set(sum_sum(X0,sum_sum(X2,X1))),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o),vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o)),denotational_Iagree(X0,X2,X1),X12),X11),X13)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Iagree__comm)).
% 3.31/0.90 thf(f6107,plain,(
% 3.31/0.90 spl132_215),
% 3.31/0.90 inference(avatar_split_clause,[],[f1660,f6105])).
% 3.31/0.90 thf(f6105,plain,(
% 3.31/0.90 spl132_215 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o)),type_definition(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),freche229654227interp(X2,X1,X0)),freche227871258interp(X2,X1,X0)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_215])])).
% 3.31/0.90 thf(f1660,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o)),type_definition(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),freche229654227interp(X2,X1,X0)),freche227871258interp(X2,X1,X0)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1170])).
% 3.31/0.90 thf(f1170,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o)),type_definition(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),freche229654227interp(X2,X1,X0)),freche227871258interp(X2,X1,X0)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1169])).
% 3.31/0.90 thf(f1169,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o)),type_definition(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),freche229654227interp(X2,X1,X0)),freche227871258interp(X2,X1,X0)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f669])).
% 3.31/0.90 thf(f669,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o)),type_definition(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),freche229654227interp(X2,X1,X0)),freche227871258interp(X2,X1,X0)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))))),
% 3.31/0.90 inference(fool_elimination,[],[f668])).
% 3.31/0.90 thf(f668,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),vAPP(sTfun(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),sTfun(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0)),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o)),type_definition(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit)),freche229654227interp(X2,X1,X0)),freche227871258interp(X2,X1,X0)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))),
% 3.31/0.90 inference(rectify,[],[f128])).
% 3.31/0.90 thf(f128,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => vAPP(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o,vAPP(sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),frechet_good_interp(X0,X2,X1)),sTfun(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o),vAPP(sTfun(frechet_good_interp(X0,X2,X1),denota1663640101rp_ext(X0,X2,X1,product_unit)),sTfun(sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),frechet_good_interp(X0,X2,X1)),sTfun(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o)),type_definition(frechet_good_interp(X0,X2,X1),denota1663640101rp_ext(X0,X2,X1,product_unit)),freche229654227interp(X0,X2,X1)),freche227871258interp(X0,X2,X1)),vAPP(sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),$o),set(denota1663640101rp_ext(X0,X2,X1,product_unit)),collect(denota1663640101rp_ext(X0,X2,X1,product_unit)),denota2077489681interp(X0,X2,X1))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_type__definition__good__interp)).
% 3.31/0.90 thf(f5974,plain,(
% 3.31/0.90 spl132_214),
% 3.31/0.90 inference(avatar_split_clause,[],[f1702,f5972])).
% 3.31/0.90 thf(f5972,plain,(
% 3.31/0.90 spl132_214 <=> ! [X1 : $tType,X0 : $tType,X3 : set(product_prod(X1,X0)),X2 : set(product_prod(X1,X0))] : (($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),$o),ord_less_eq(set(product_prod(X1,X0))),X2),X3)) | ($true != vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(set(product_prod(X1,X0)),X1,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X1),sK60(X0,X1),X3),X2)),vAPP(set(product_prod(X1,X0)),X0,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X0),sK61(X0,X1),X3),X2))),X3)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_214])])).
% 3.31/0.90 thf(f1702,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : set(product_prod(X1,X0)),X3 : set(product_prod(X1,X0))] : (($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),$o),ord_less_eq(set(product_prod(X1,X0))),X2),X3)) | ($true != vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(set(product_prod(X1,X0)),X1,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X1),sK60(X0,X1),X3),X2)),vAPP(set(product_prod(X1,X0)),X0,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X0),sK61(X0,X1),X3),X2))),X3))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1405])).
% 3.31/0.90 thf(f1405,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : set(product_prod(X1,X0)),X3 : set(product_prod(X1,X0))] : (($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),$o),ord_less_eq(set(product_prod(X1,X0))),X2),X3)) | (($true != vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(set(product_prod(X1,X0)),X1,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X1),sK60(X0,X1),X3),X2)),vAPP(set(product_prod(X1,X0)),X0,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X0),sK61(X0,X1),X3),X2))),X3)) & ($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(set(product_prod(X1,X0)),X1,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X1),sK60(X0,X1),X3),X2)),vAPP(set(product_prod(X1,X0)),X0,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X0),sK61(X0,X1),X3),X2))),X2))))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61])],[f1198,f1404])).
% 3.31/0.90 thf(f1404,plain,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X2 : set(product_prod(X1,X0)),X3 : set(product_prod(X1,X0))] : (? [X4 : X1,X5 : X0] : (($true != vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3)) & ($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2))) => (($true != vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(set(product_prod(X1,X0)),X1,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X1),sK60(X0,X1),X3),X2)),vAPP(set(product_prod(X1,X0)),X0,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X0),sK61(X0,X1),X3),X2))),X3)) & ($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(set(product_prod(X1,X0)),X1,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X1),sK60(X0,X1),X3),X2)),vAPP(set(product_prod(X1,X0)),X0,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X0),sK61(X0,X1),X3),X2))),X2))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1198,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : set(product_prod(X1,X0)),X3 : set(product_prod(X1,X0))] : (($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),$o),ord_less_eq(set(product_prod(X1,X0))),X2),X3)) | ? [X4 : X1,X5 : X0] : (($true != vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3)) & ($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2))))),
% 3.31/0.90 inference(ennf_transformation,[],[f721])).
% 3.31/0.90 thf(f721,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : set(product_prod(X1,X0)),X3 : set(product_prod(X1,X0))] : (! [X4 : X1,X5 : X0] : (($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2)) => ($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3))) => ($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),$o),ord_less_eq(set(product_prod(X1,X0))),X2),X3)))),
% 3.31/0.90 inference(fool_elimination,[],[f720])).
% 3.31/0.90 thf(f720,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : set(product_prod(X1,X0)),X3 : set(product_prod(X1,X0))] : (! [X4 : X1,X5 : X0] : (vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2) => vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3)) => vAPP(set(product_prod(X1,X0)),$o,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),$o),ord_less_eq(set(product_prod(X1,X0))),X2),X3))),
% 3.31/0.90 inference(rectify,[],[f167])).
% 3.31/0.90 thf(f167,axiom,(
% 3.31/0.90 ! [X2 : $tType,X0 : $tType,X110 : set(product_prod(X0,X2)),X111 : set(product_prod(X0,X2))] : (! [X23 : X0,X34 : X2] : (vAPP(set(product_prod(X0,X2)),$o,vAPP(product_prod(X0,X2),sTfun(set(product_prod(X0,X2)),$o),member(product_prod(X0,X2)),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X23),X34)),X110) => vAPP(set(product_prod(X0,X2)),$o,vAPP(product_prod(X0,X2),sTfun(set(product_prod(X0,X2)),$o),member(product_prod(X0,X2)),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X23),X34)),X111)) => vAPP(set(product_prod(X0,X2)),$o,vAPP(set(product_prod(X0,X2)),sTfun(set(product_prod(X0,X2)),$o),ord_less_eq(set(product_prod(X0,X2))),X110),X111))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_subrelI)).
% 3.31/0.90 thf(f5970,plain,(
% 3.31/0.90 spl132_213),
% 3.31/0.90 inference(avatar_split_clause,[],[f1701,f5968])).
% 3.31/0.90 thf(f5968,plain,(
% 3.31/0.90 spl132_213 <=> ! [X1 : $tType,X0 : $tType,X3 : set(product_prod(X1,X0)),X2 : set(product_prod(X1,X0))] : (($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),$o),ord_less_eq(set(product_prod(X1,X0))),X2),X3)) | ($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(set(product_prod(X1,X0)),X1,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X1),sK60(X0,X1),X3),X2)),vAPP(set(product_prod(X1,X0)),X0,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X0),sK61(X0,X1),X3),X2))),X2)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_213])])).
% 3.31/0.90 thf(f1701,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : set(product_prod(X1,X0)),X3 : set(product_prod(X1,X0))] : (($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),$o),ord_less_eq(set(product_prod(X1,X0))),X2),X3)) | ($true = vAPP(set(product_prod(X1,X0)),$o,vAPP(product_prod(X1,X0),sTfun(set(product_prod(X1,X0)),$o),member(product_prod(X1,X0)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(set(product_prod(X1,X0)),X1,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X1),sK60(X0,X1),X3),X2)),vAPP(set(product_prod(X1,X0)),X0,vAPP(set(product_prod(X1,X0)),sTfun(set(product_prod(X1,X0)),X0),sK61(X0,X1),X3),X2))),X2))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1405])).
% 3.31/0.90 thf(f5966,plain,(
% 3.31/0.90 spl132_212),
% 3.31/0.90 inference(avatar_split_clause,[],[f1679,f5964])).
% 3.31/0.90 thf(f5964,plain,(
% 3.31/0.90 spl132_212 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o)),sCOMB,vAPP(sTfun(X0,$o),sTfun(X0,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1))),X2))),X1))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_212])])).
% 3.31/0.90 thf(f1679,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : X0 > $o,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o)),sCOMB,vAPP(sTfun(X0,$o),sTfun(X0,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1))),X2))),X1))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f693])).
% 3.31/0.90 thf(f693,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : set(X0),X2 : X0 > $o] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o)),sCOMB,vAPP(sTfun(X0,$o),sTfun(X0,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1))),X2))),X1))),
% 3.31/0.90 inference(fool_elimination,[],[f692])).
% 3.31/0.90 thf(f692,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : set(X0),X2 : X0 > $o] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X3 : X0] : (vAPP(X0,$o,X2,X3) & vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))))),X1)),
% 3.31/0.90 inference(rectify,[],[f125])).
% 3.31/0.90 thf(f125,axiom,(
% 3.31/0.90 ! [X0 : $tType,X11 : set(X0),X24 : X0 > $o] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X20 : X0] : (vAPP(X0,$o,X24,X20) & vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X20),X11))))),X11)),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Collect__subset)).
% 3.31/0.90 thf(f5952,plain,(
% 3.31/0.90 spl132_211),
% 3.31/0.90 inference(avatar_split_clause,[],[f2021,f5950])).
% 3.31/0.90 thf(f5950,plain,(
% 3.31/0.90 spl132_211 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_211])])).
% 3.31/0.90 thf(f2021,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true)) )),
% 3.31/0.90 inference(duplicate_literal_removal,[],[f1510])).
% 3.31/0.90 thf(f1510,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1325])).
% 3.31/0.90 thf(f5917,plain,(
% 3.31/0.90 spl132_210),
% 3.31/0.90 inference(avatar_split_clause,[],[f1735,f5915])).
% 3.31/0.90 thf(f5915,plain,(
% 3.31/0.90 spl132_210 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : product_prod(X2,product_prod(X1,X0)),X3 : product_prod(X2,product_prod(X1,X0)) > $o] : (($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)) | ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK76(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK77(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK78(X0,X1,X2),X3))))))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_210])])).
% 3.31/0.90 thf(f1735,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)) | ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK76(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK77(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK78(X0,X1,X2),X3)))))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1425])).
% 3.31/0.90 thf(f1425,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)) | ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK76(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK77(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK78(X0,X1,X2),X3))))))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK76,sK77,sK78])],[f1250,f1424])).
% 3.31/0.90 thf(f1424,plain,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o] : (? [X5 : X2,X6 : X1,X7 : X0] : ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)))) => ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK76(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK77(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK78(X0,X1,X2),X3))))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1250,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)) | ? [X5 : X2,X6 : X1,X7 : X0] : ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)))))),
% 3.31/0.90 inference(ennf_transformation,[],[f777])).
% 3.31/0.90 thf(f777,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (! [X5 : X2,X6 : X1,X7 : X0] : ($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)))) => ($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)))),
% 3.31/0.90 inference(fool_elimination,[],[f776])).
% 3.31/0.90 thf(f776,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (! [X5 : X2,X6 : X1,X7 : X0] : vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7))) => vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4))),
% 3.31/0.90 inference(rectify,[],[f61])).
% 3.31/0.90 thf(f61,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType,X24 : product_prod(X0,product_prod(X2,X1)) > $o,X14 : product_prod(X0,product_prod(X2,X1))] : (! [X57 : X0,X58 : X2,X64 : X1] : vAPP(product_prod(X0,product_prod(X2,X1)),$o,X24,vAPP(product_prod(X2,X1),product_prod(X0,product_prod(X2,X1)),vAPP(X0,sTfun(product_prod(X2,X1),product_prod(X0,product_prod(X2,X1))),product_Pair(X0,product_prod(X2,X1)),X57),vAPP(X1,product_prod(X2,X1),vAPP(X2,sTfun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X58),X64))) => vAPP(product_prod(X0,product_prod(X2,X1)),$o,X24,X14))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_prod__induct3)).
% 3.31/0.90 thf(f5849,plain,(
% 3.31/0.90 spl132_209),
% 3.31/0.90 inference(avatar_split_clause,[],[f1640,f5847])).
% 3.31/0.90 thf(f5847,plain,(
% 3.31/0.90 spl132_209 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),sK31(X0,X1,X2),X3)) = X3) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_209])])).
% 3.31/0.90 thf(f1640,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),sK31(X0,X1,X2),X3)) = X3) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1363])).
% 3.31/0.90 thf(f1363,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),sK31(X0,X1,X2),X3)) = X3) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f1134,f1362])).
% 3.31/0.90 thf(f1362,plain,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (? [X4 : frechet_good_interp(X2,X1,X0)] : (vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X4) = X3) => (vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),sK31(X0,X1,X2),X3)) = X3))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1134,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (? [X4 : frechet_good_interp(X2,X1,X0)] : (vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X4) = X3) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1133])).
% 3.31/0.90 thf(f1133,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (? [X4 : frechet_good_interp(X2,X1,X0)] : (vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X4) = X3) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f633])).
% 3.31/0.90 thf(f633,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) => ~! [X4 : frechet_good_interp(X2,X1,X0)] : (vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X4) != X3)))),
% 3.31/0.90 inference(fool_elimination,[],[f632])).
% 3.31/0.90 thf(f632,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))) => ~! [X4 : frechet_good_interp(X2,X1,X0)] : (vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X4) != X3)))),
% 3.31/0.90 inference(rectify,[],[f105])).
% 3.31/0.90 thf(f105,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X15 : denota1663640101rp_ext(X0,X2,X1,product_unit)] : (vAPP(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o),member(denota1663640101rp_ext(X0,X2,X1,product_unit)),X15),vAPP(sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),$o),set(denota1663640101rp_ext(X0,X2,X1,product_unit)),collect(denota1663640101rp_ext(X0,X2,X1,product_unit)),denota2077489681interp(X0,X2,X1))) => ~! [X23 : frechet_good_interp(X0,X2,X1)] : (vAPP(frechet_good_interp(X0,X2,X1),denota1663640101rp_ext(X0,X2,X1,product_unit),freche229654227interp(X0,X2,X1),X23) != X15)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_raw__interp__cases)).
% 3.31/0.90 thf(f5845,plain,(
% 3.31/0.90 spl132_208),
% 3.31/0.90 inference(avatar_split_clause,[],[f1639,f5843])).
% 3.31/0.90 thf(f5843,plain,(
% 3.31/0.90 spl132_208 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X3)) = X3) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_208])])).
% 3.31/0.90 thf(f1639,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X3)) = X3) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1132])).
% 3.31/0.90 thf(f1132,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X3)) = X3) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1131])).
% 3.31/0.90 thf(f1131,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X3)) = X3) | ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f631])).
% 3.31/0.90 thf(f631,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) => (vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X3)) = X3)))),
% 3.31/0.90 inference(fool_elimination,[],[f630])).
% 3.31/0.90 thf(f630,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X3),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))) => (vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X3)) = X3)))),
% 3.31/0.90 inference(rectify,[],[f101])).
% 3.31/0.90 thf(f101,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X15 : denota1663640101rp_ext(X0,X2,X1,product_unit)] : (vAPP(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o),member(denota1663640101rp_ext(X0,X2,X1,product_unit)),X15),vAPP(sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),$o),set(denota1663640101rp_ext(X0,X2,X1,product_unit)),collect(denota1663640101rp_ext(X0,X2,X1,product_unit)),denota2077489681interp(X0,X2,X1))) => (vAPP(frechet_good_interp(X0,X2,X1),denota1663640101rp_ext(X0,X2,X1,product_unit),freche229654227interp(X0,X2,X1),vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),frechet_good_interp(X0,X2,X1),freche227871258interp(X0,X2,X1),X15)) = X15)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_good__interp__inverse)).
% 3.31/0.90 thf(f5841,plain,(
% 3.31/0.90 spl132_207),
% 3.31/0.90 inference(avatar_split_clause,[],[f1523,f5839])).
% 3.31/0.90 thf(f5839,plain,(
% 3.31/0.90 spl132_207 <=> ! [X0 : $tType,X3 : set(sum_sum(X0,X0)),X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X1),X3)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),X3)) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_207])])).
% 3.31/0.90 thf(f1523,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : set(sum_sum(X0,X0)),X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X1),X3)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),X3)) | (finite_finite(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1001])).
% 3.31/0.90 thf(f1001,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : set(sum_sum(X0,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X1),X3)) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),X3))) | (finite_finite(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f427])).
% 3.31/0.90 thf(f427,plain,(
% 3.31/0.90 ! [X0 : $tType] : ((finite_finite(X0) = $true) => ! [X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : set(sum_sum(X0,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),X3)) => ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X1),X3))))),
% 3.31/0.90 inference(fool_elimination,[],[f426])).
% 3.31/0.90 thf(f426,plain,(
% 3.31/0.90 ! [X0 : $tType] : (finite_finite(X0) => ! [X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X3 : set(sum_sum(X0,X0))] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),X3) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X2),X1),X3)))),
% 3.31/0.90 inference(rectify,[],[f6])).
% 3.31/0.90 thf(f6,axiom,(
% 3.31/0.90 ! [X0 : $tType] : (finite_finite(X0) => ! [X11 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X12 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X13 : set(sum_sum(X0,X0))] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X11),X12),X13) => vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X12),X11),X13)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_agree__comm)).
% 3.31/0.90 thf(f5499,plain,(
% 3.31/0.90 spl132_206),
% 3.31/0.90 inference(avatar_split_clause,[],[f1557,f5497])).
% 3.31/0.90 thf(f5497,plain,(
% 3.31/0.90 spl132_206 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK21(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK22(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | (order(X1) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_206])])).
% 3.31/0.90 thf(f1557,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK21(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK22(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | (order(X1) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1349])).
% 3.31/0.90 thf(f1349,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK21(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK22(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK21(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK22(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4)))) | (order(X0) != $true) | (order(X1) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f1033,f1348])).
% 3.31/0.90 thf(f1348,plain,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X3 : X1 > X0] : (? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK21(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK22(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK21(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK22(X0,X1),X3)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1033,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4)))) | (order(X0) != $true) | (order(X1) != $true))),
% 3.31/0.90 inference(flattening,[],[f1032])).
% 3.31/0.90 thf(f1032,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4)))) | ((order(X0) != $true) | (order(X1) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f487])).
% 3.31/0.90 thf(f487,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (((order(X0) = $true) & (order(X1) = $true)) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) => (! [X6 : X1,X7 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7)))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5)))))))),
% 3.31/0.90 inference(fool_elimination,[],[f486])).
% 3.31/0.90 thf(f486,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((order(X0) & order(X1)) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4)) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5) => (! [X6 : X1,X7 : X1] : (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))))))),
% 3.31/0.90 inference(rectify,[],[f139])).
% 3.31/0.90 thf(f139,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType] : ((order(X0) & order(X2)) => ! [X32 : X0,X54 : X2 > X0,X33 : X2,X79 : X2] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X32),vAPP(X2,X0,X54,X33)) => (vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X33),X79) => (! [X23 : X2,X34 : X2] : (vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X23),X34) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X2,X0,X54,X23)),vAPP(X2,X0,X54,X34))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X32),vAPP(X2,X0,X54,X79))))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order__subst1)).
% 3.31/0.90 thf(f5495,plain,(
% 3.31/0.90 spl132_205),
% 3.31/0.90 inference(avatar_split_clause,[],[f1555,f5493])).
% 3.31/0.90 thf(f5493,plain,(
% 3.31/0.90 spl132_205 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X4 : X0 > X1,X5 : X1,X2 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK19(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK20(X0,X1),X4)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | (order(X1) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_205])])).
% 3.31/0.90 thf(f1555,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK19(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK20(X0,X1),X4)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | (order(X1) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1347])).
% 3.31/0.90 thf(f1347,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK19(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK20(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK19(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK20(X0,X1),X4)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (order(X0) != $true) | (order(X1) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f1031,f1346])).
% 3.31/0.90 thf(f1346,plain,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X4 : X0 > X1] : (? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7))) => (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK19(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK20(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK19(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK20(X0,X1),X4)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1031,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (order(X0) != $true) | (order(X1) != $true))),
% 3.31/0.90 inference(flattening,[],[f1030])).
% 3.31/0.90 thf(f1030,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (((($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | ((order(X0) != $true) | (order(X1) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f485])).
% 3.31/0.90 thf(f485,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (((order(X0) = $true) & (order(X1) = $true)) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) => (! [X6 : X0,X7 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7)) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7)))) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5))))))),
% 3.31/0.90 inference(fool_elimination,[],[f484])).
% 3.31/0.90 thf(f484,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((order(X0) & order(X1)) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5) => (! [X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)))))),
% 3.31/0.90 inference(rectify,[],[f140])).
% 3.31/0.90 thf(f140,axiom,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((order(X0) & order(X1)) => ! [X32 : X0,X33 : X0,X54 : X0 > X1,X79 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X32),X33) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X54,X33)),X79) => (! [X23 : X0,X34 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X23),X34) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X54,X23)),vAPP(X0,X1,X54,X34))) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X54,X32)),X79)))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_order__subst2)).
% 3.31/0.90 thf(f5491,plain,(
% 3.31/0.90 spl132_204 | ~spl132_7 | ~spl132_42),
% 3.31/0.90 inference(avatar_split_clause,[],[f2335,f2317,f2067,f5488])).
% 3.31/0.90 thf(f5488,plain,(
% 3.31/0.90 spl132_204 <=> ($true = finite_finite(set(a)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_204])])).
% 3.31/0.90 thf(f2067,plain,(
% 3.31/0.90 spl132_7 <=> (finite_finite(a) = $true)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_7])])).
% 3.31/0.90 thf(f2317,plain,(
% 3.31/0.90 spl132_42 <=> ! [X0 : $tType] : (($true = finite_finite(set(X0))) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_42])])).
% 3.31/0.90 thf(f2335,plain,(
% 3.31/0.90 ($true = finite_finite(set(a))) | (~spl132_7 | ~spl132_42)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f2322])).
% 3.31/0.90 thf(f2322,plain,(
% 3.31/0.90 ($true != $true) | ($true = finite_finite(set(a))) | (~spl132_7 | ~spl132_42)),
% 3.31/0.90 inference(superposition,[],[f2318,f2069])).
% 3.31/0.90 thf(f2069,plain,(
% 3.31/0.90 (finite_finite(a) = $true) | ~spl132_7),
% 3.31/0.90 inference(avatar_component_clause,[],[f2067])).
% 3.31/0.90 thf(f2318,plain,(
% 3.31/0.90 ( ! [X0 : $tType] : ((finite_finite(X0) != $true) | ($true = finite_finite(set(X0)))) ) | ~spl132_42),
% 3.31/0.90 inference(avatar_component_clause,[],[f2317])).
% 3.31/0.90 thf(f5468,plain,(
% 3.31/0.90 spl132_203),
% 3.31/0.90 inference(avatar_split_clause,[],[f1652,f5466])).
% 3.31/0.90 thf(f5466,plain,(
% 3.31/0.90 spl132_203 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : trm(X2,X1),X3 : denota1663640101rp_ext(X2,X0,X1,product_unit),X5 : set(finite_Cartesian_vec(real,X1))] : (($true = vAPP(sTfun(finite_Cartesian_vec(real,X1),real),$o,vAPP(set(finite_Cartesian_vec(real,X1)),sTfun(sTfun(finite_Cartesian_vec(real,X1),real),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,X1),real),X5),vAPP(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real)),denota126604975rm_sem(X2,X0,X1),X3),X4))) | ($true != vAPP(trm(X2,X1),$o,dfree(X2,X1),X4)) | ($true != vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),$o,denota2077489681interp(X2,X0,X1),X3)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_203])])).
% 3.31/0.90 thf(f1652,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : denota1663640101rp_ext(X2,X0,X1,product_unit),X4 : trm(X2,X1),X5 : set(finite_Cartesian_vec(real,X1))] : (($true = vAPP(sTfun(finite_Cartesian_vec(real,X1),real),$o,vAPP(set(finite_Cartesian_vec(real,X1)),sTfun(sTfun(finite_Cartesian_vec(real,X1),real),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,X1),real),X5),vAPP(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real)),denota126604975rm_sem(X2,X0,X1),X3),X4))) | ($true != vAPP(trm(X2,X1),$o,dfree(X2,X1),X4)) | ($true != vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),$o,denota2077489681interp(X2,X0,X1),X3)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1154])).
% 3.31/0.90 thf(f1154,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X0,X1,product_unit),X4 : trm(X2,X1),X5 : set(finite_Cartesian_vec(real,X1))] : (($true = vAPP(sTfun(finite_Cartesian_vec(real,X1),real),$o,vAPP(set(finite_Cartesian_vec(real,X1)),sTfun(sTfun(finite_Cartesian_vec(real,X1),real),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,X1),real),X5),vAPP(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real)),denota126604975rm_sem(X2,X0,X1),X3),X4))) | ($true != vAPP(trm(X2,X1),$o,dfree(X2,X1),X4)) | ($true != vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),$o,denota2077489681interp(X2,X0,X1),X3))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1153])).
% 3.31/0.90 thf(f1153,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X0,X1,product_unit),X4 : trm(X2,X1),X5 : set(finite_Cartesian_vec(real,X1))] : ((($true = vAPP(sTfun(finite_Cartesian_vec(real,X1),real),$o,vAPP(set(finite_Cartesian_vec(real,X1)),sTfun(sTfun(finite_Cartesian_vec(real,X1),real),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,X1),real),X5),vAPP(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real)),denota126604975rm_sem(X2,X0,X1),X3),X4))) | ($true != vAPP(trm(X2,X1),$o,dfree(X2,X1),X4))) | ($true != vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),$o,denota2077489681interp(X2,X0,X1),X3))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f653])).
% 3.31/0.90 thf(f653,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : denota1663640101rp_ext(X2,X0,X1,product_unit),X4 : trm(X2,X1),X5 : set(finite_Cartesian_vec(real,X1))] : (($true = vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),$o,denota2077489681interp(X2,X0,X1),X3)) => (($true = vAPP(trm(X2,X1),$o,dfree(X2,X1),X4)) => ($true = vAPP(sTfun(finite_Cartesian_vec(real,X1),real),$o,vAPP(set(finite_Cartesian_vec(real,X1)),sTfun(sTfun(finite_Cartesian_vec(real,X1),real),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,X1),real),X5),vAPP(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real)),denota126604975rm_sem(X2,X0,X1),X3),X4))))))),
% 3.31/0.90 inference(fool_elimination,[],[f652])).
% 3.31/0.90 thf(f652,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : denota1663640101rp_ext(X2,X0,X1,product_unit),X4 : trm(X2,X1),X5 : set(finite_Cartesian_vec(real,X1))] : (vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),$o,denota2077489681interp(X2,X0,X1),X3) => (vAPP(trm(X2,X1),$o,dfree(X2,X1),X4) => vAPP(sTfun(finite_Cartesian_vec(real,X1),real),$o,vAPP(set(finite_Cartesian_vec(real,X1)),sTfun(sTfun(finite_Cartesian_vec(real,X1),real),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,X1),real),X5),vAPP(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(trm(X2,X1),sTfun(finite_Cartesian_vec(real,X1),real)),denota126604975rm_sem(X2,X0,X1),X3),X4)))))),
% 3.31/0.90 inference(rectify,[],[f165])).
% 3.31/0.90 thf(f165,axiom,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType] : ((finite_finite(X2) & finite_finite(X1) & finite_finite(X0)) => ! [X26 : denota1663640101rp_ext(X0,X2,X1,product_unit),X25 : trm(X0,X1),X109 : set(finite_Cartesian_vec(real,X1))] : (vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),$o,denota2077489681interp(X0,X2,X1),X26) => (vAPP(trm(X0,X1),$o,dfree(X0,X1),X25) => vAPP(sTfun(finite_Cartesian_vec(real,X1),real),$o,vAPP(set(finite_Cartesian_vec(real,X1)),sTfun(sTfun(finite_Cartesian_vec(real,X1),real),$o),topolo2071040574ous_on(finite_Cartesian_vec(real,X1),real),X109),vAPP(trm(X0,X1),sTfun(finite_Cartesian_vec(real,X1),real),vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(trm(X0,X1),sTfun(finite_Cartesian_vec(real,X1),real)),denota126604975rm_sem(X0,X2,X1),X26),X25)))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_sterm__continuous_H)).
% 3.31/0.90 thf(f5464,plain,(
% 3.31/0.90 spl132_202),
% 3.31/0.90 inference(avatar_split_clause,[],[f1625,f5462])).
% 3.31/0.90 thf(f5462,plain,(
% 3.31/0.90 spl132_202 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : X2 > X1 > X0,X3 : set(X2)] : (($true = vAPP(sTfun(X2,sTfun(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X1,X0)),$o),topolo2071040574ous_on(X2,sTfun(X1,X0)),X3),X4)) | ($true != vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(X1,sTfun(X2,X0),vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(X1,sTfun(X2,X0)),cCOMB,X4),vAPP(set(X2),X1,vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(set(X2),X1),sK30(X0,X1,X2),X4),X3)))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_202])])).
% 3.31/0.90 thf(f1625,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : set(X2),X4 : X2 > X1 > X0] : (($true = vAPP(sTfun(X2,sTfun(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X1,X0)),$o),topolo2071040574ous_on(X2,sTfun(X1,X0)),X3),X4)) | ($true != vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(X1,sTfun(X2,X0),vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(X1,sTfun(X2,X0)),cCOMB,X4),vAPP(set(X2),X1,vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(set(X2),X1),sK30(X0,X1,X2),X4),X3)))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1361])).
% 3.31/0.90 thf(f1361,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(X2),X4 : X2 > X1 > X0] : (($true = vAPP(sTfun(X2,sTfun(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X1,X0)),$o),topolo2071040574ous_on(X2,sTfun(X1,X0)),X3),X4)) | ($true != vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(X1,sTfun(X2,X0),vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(X1,sTfun(X2,X0)),cCOMB,X4),vAPP(set(X2),X1,vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(set(X2),X1),sK30(X0,X1,X2),X4),X3))))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X2) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f1104,f1360])).
% 3.31/0.90 thf(f1360,plain,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : set(X2),X4 : X2 > X1 > X0] : (? [X5 : X1] : ($true != vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(X1,sTfun(X2,X0),vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(X1,sTfun(X2,X0)),cCOMB,X4),X5))) => ($true != vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(X1,sTfun(X2,X0),vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(X1,sTfun(X2,X0)),cCOMB,X4),vAPP(set(X2),X1,vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(set(X2),X1),sK30(X0,X1,X2),X4),X3)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1104,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(X2),X4 : X2 > X1 > X0] : (($true = vAPP(sTfun(X2,sTfun(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X1,X0)),$o),topolo2071040574ous_on(X2,sTfun(X1,X0)),X3),X4)) | ? [X5 : X1] : ($true != vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(X1,sTfun(X2,X0),vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(X1,sTfun(X2,X0)),cCOMB,X4),X5)))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1103])).
% 3.31/0.90 thf(f1103,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(X2),X4 : X2 > X1 > X0] : (($true = vAPP(sTfun(X2,sTfun(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X1,X0)),$o),topolo2071040574ous_on(X2,sTfun(X1,X0)),X3),X4)) | ? [X5 : X1] : ($true != vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(X1,sTfun(X2,X0),vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(X1,sTfun(X2,X0)),cCOMB,X4),X5)))) | ((topolo503727757_space(X0) != $true) | (topolo503727757_space(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f603])).
% 3.31/0.90 thf(f603,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((topolo503727757_space(X0) = $true) & (topolo503727757_space(X2) = $true)) => ! [X3 : set(X2),X4 : X2 > X1 > X0] : (! [X5 : X1] : ($true = vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(X1,sTfun(X2,X0),vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(X1,sTfun(X2,X0)),cCOMB,X4),X5))) => ($true = vAPP(sTfun(X2,sTfun(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X1,X0)),$o),topolo2071040574ous_on(X2,sTfun(X1,X0)),X3),X4))))),
% 3.31/0.90 inference(fool_elimination,[],[f602])).
% 3.31/0.90 thf(f602,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((topolo503727757_space(X0) & topolo503727757_space(X2)) => ! [X3 : set(X2),X4 : X2 > X1 > X0] : (! [X5 : X1] : vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),(^[X6 : X2] : (vAPP(X1,X0,vAPP(X2,sTfun(X1,X0),X4,X6),X5)))) => vAPP(sTfun(X2,sTfun(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X1,X0)),$o),topolo2071040574ous_on(X2,sTfun(X1,X0)),X3),X4)))),
% 3.31/0.90 inference(rectify,[],[f242])).
% 3.31/0.90 thf(f242,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((topolo503727757_space(X1) & topolo503727757_space(X0)) => ! [X109 : set(X0),X54 : X0 > X2 > X1] : (! [X27 : X2] : vAPP(sTfun(X0,X1),$o,vAPP(set(X0),sTfun(sTfun(X0,X1),$o),topolo2071040574ous_on(X0,X1),X109),(^[X20 : X0] : (vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X54,X20),X27)))) => vAPP(sTfun(X0,sTfun(X2,X1)),$o,vAPP(set(X0),sTfun(sTfun(X0,sTfun(X2,X1)),$o),topolo2071040574ous_on(X0,sTfun(X2,X1)),X109),X54)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_continuous__on__coordinatewise__then__product)).
% 3.31/0.90 thf(f5442,plain,(
% 3.31/0.90 spl132_201),
% 3.31/0.90 inference(avatar_split_clause,[],[f1646,f5440])).
% 3.31/0.90 thf(f5440,plain,(
% 3.31/0.90 spl132_201 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : frechet_good_interp(X2,X1,X0),X3 : frechet_good_interp(X2,X1,X0) > $o] : (($true = vAPP(frechet_good_interp(X2,X1,X0),$o,X3,X4)) | ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(sTfun(frechet_good_interp(X2,X1,X0),$o),denota1663640101rp_ext(X2,X1,X0,product_unit),sK35(X0,X1,X2),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_201])])).
% 3.31/0.90 thf(f1646,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : frechet_good_interp(X2,X1,X0) > $o,X4 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(frechet_good_interp(X2,X1,X0),$o,X3,X4)) | ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(sTfun(frechet_good_interp(X2,X1,X0),$o),denota1663640101rp_ext(X2,X1,X0,product_unit),sK35(X0,X1,X2),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1369])).
% 3.31/0.90 thf(f1369,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0) > $o,X4 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(frechet_good_interp(X2,X1,X0),$o,X3,X4)) | (($true != vAPP(frechet_good_interp(X2,X1,X0),$o,X3,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(sTfun(frechet_good_interp(X2,X1,X0),$o),denota1663640101rp_ext(X2,X1,X0,product_unit),sK35(X0,X1,X2),X3)))) & ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(sTfun(frechet_good_interp(X2,X1,X0),$o),denota1663640101rp_ext(X2,X1,X0,product_unit),sK35(X0,X1,X2),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f1144,f1368])).
% 3.31/0.90 thf(f1368,plain,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : frechet_good_interp(X2,X1,X0) > $o] : (? [X5 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true != vAPP(frechet_good_interp(X2,X1,X0),$o,X3,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X5))) & ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X5),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))) => (($true != vAPP(frechet_good_interp(X2,X1,X0),$o,X3,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(sTfun(frechet_good_interp(X2,X1,X0),$o),denota1663640101rp_ext(X2,X1,X0,product_unit),sK35(X0,X1,X2),X3)))) & ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(sTfun(frechet_good_interp(X2,X1,X0),$o),denota1663640101rp_ext(X2,X1,X0,product_unit),sK35(X0,X1,X2),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1144,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0) > $o,X4 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(frechet_good_interp(X2,X1,X0),$o,X3,X4)) | ? [X5 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true != vAPP(frechet_good_interp(X2,X1,X0),$o,X3,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X5))) & ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X5),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1143])).
% 3.31/0.90 thf(f1143,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0) > $o,X4 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(frechet_good_interp(X2,X1,X0),$o,X3,X4)) | ? [X5 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true != vAPP(frechet_good_interp(X2,X1,X0),$o,X3,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X5))) & ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X5),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f643])).
% 3.31/0.90 thf(f643,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : frechet_good_interp(X2,X1,X0) > $o,X4 : frechet_good_interp(X2,X1,X0)] : (! [X5 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X5),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) => ($true = vAPP(frechet_good_interp(X2,X1,X0),$o,X3,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X5)))) => ($true = vAPP(frechet_good_interp(X2,X1,X0),$o,X3,X4))))),
% 3.31/0.90 inference(fool_elimination,[],[f642])).
% 3.31/0.90 thf(f642,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : frechet_good_interp(X2,X1,X0) > $o,X4 : frechet_good_interp(X2,X1,X0)] : (! [X5 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X5),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))) => vAPP(frechet_good_interp(X2,X1,X0),$o,X3,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X5))) => vAPP(frechet_good_interp(X2,X1,X0),$o,X3,X4)))),
% 3.31/0.90 inference(rectify,[],[f108])).
% 3.31/0.90 thf(f108,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X24 : frechet_good_interp(X0,X2,X1) > $o,X14 : frechet_good_interp(X0,X2,X1)] : (! [X34 : denota1663640101rp_ext(X0,X2,X1,product_unit)] : (vAPP(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o),member(denota1663640101rp_ext(X0,X2,X1,product_unit)),X34),vAPP(sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),$o),set(denota1663640101rp_ext(X0,X2,X1,product_unit)),collect(denota1663640101rp_ext(X0,X2,X1,product_unit)),denota2077489681interp(X0,X2,X1))) => vAPP(frechet_good_interp(X0,X2,X1),$o,X24,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),frechet_good_interp(X0,X2,X1),freche227871258interp(X0,X2,X1),X34))) => vAPP(frechet_good_interp(X0,X2,X1),$o,X24,X14)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_good__interp__induct)).
% 3.31/0.90 thf(f5245,plain,(
% 3.31/0.90 spl132_200 | ~spl132_4 | ~spl132_42),
% 3.31/0.90 inference(avatar_split_clause,[],[f2334,f2317,f2052,f5242])).
% 3.31/0.90 thf(f5242,plain,(
% 3.31/0.90 spl132_200 <=> ($true = finite_finite(set(b)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_200])])).
% 3.31/0.90 thf(f2052,plain,(
% 3.31/0.90 spl132_4 <=> (finite_finite(b) = $true)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_4])])).
% 3.31/0.90 thf(f2334,plain,(
% 3.31/0.90 ($true = finite_finite(set(b))) | (~spl132_4 | ~spl132_42)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f2323])).
% 3.31/0.90 thf(f2323,plain,(
% 3.31/0.90 ($true != $true) | ($true = finite_finite(set(b))) | (~spl132_4 | ~spl132_42)),
% 3.31/0.90 inference(superposition,[],[f2318,f2054])).
% 3.31/0.90 thf(f2054,plain,(
% 3.31/0.90 (finite_finite(b) = $true) | ~spl132_4),
% 3.31/0.90 inference(avatar_component_clause,[],[f2052])).
% 3.31/0.90 thf(f5240,plain,(
% 3.31/0.90 spl132_199),
% 3.31/0.90 inference(avatar_split_clause,[],[f1700,f5238])).
% 3.31/0.90 thf(f5238,plain,(
% 3.31/0.90 spl132_199 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0 > $o,X2 : X1 > X0 > $o] : (($true = vAPP(sTfun(X1,sTfun(X0,$o)),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X1,sTfun(X0,$o))),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X3,vAPP(sTfun(X1,sTfun(X0,$o)),X1,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X1),sK58(X0,X1),X3),X2)),vAPP(sTfun(X1,sTfun(X0,$o)),X0,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X0),sK59(X0,X1),X3),X2))))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_199])])).
% 3.31/0.90 thf(f1700,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0 > $o,X3 : X1 > X0 > $o] : (($true = vAPP(sTfun(X1,sTfun(X0,$o)),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X1,sTfun(X0,$o))),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X3,vAPP(sTfun(X1,sTfun(X0,$o)),X1,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X1),sK58(X0,X1),X3),X2)),vAPP(sTfun(X1,sTfun(X0,$o)),X0,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X0),sK59(X0,X1),X3),X2)))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1403])).
% 3.31/0.90 thf(f1403,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0 > $o,X3 : X1 > X0 > $o] : (($true = vAPP(sTfun(X1,sTfun(X0,$o)),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X1,sTfun(X0,$o))),X2),X3)) | (($true != vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X3,vAPP(sTfun(X1,sTfun(X0,$o)),X1,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X1),sK58(X0,X1),X3),X2)),vAPP(sTfun(X1,sTfun(X0,$o)),X0,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X0),sK59(X0,X1),X3),X2))) & ($true = vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X2,vAPP(sTfun(X1,sTfun(X0,$o)),X1,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X1),sK58(X0,X1),X3),X2)),vAPP(sTfun(X1,sTfun(X0,$o)),X0,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X0),sK59(X0,X1),X3),X2)))))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59])],[f1197,f1402])).
% 3.31/0.90 thf(f1402,plain,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0 > $o,X3 : X1 > X0 > $o] : (? [X4 : X1,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X3,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X2,X4),X5))) => (($true != vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X3,vAPP(sTfun(X1,sTfun(X0,$o)),X1,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X1),sK58(X0,X1),X3),X2)),vAPP(sTfun(X1,sTfun(X0,$o)),X0,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X0),sK59(X0,X1),X3),X2))) & ($true = vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X2,vAPP(sTfun(X1,sTfun(X0,$o)),X1,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X1),sK58(X0,X1),X3),X2)),vAPP(sTfun(X1,sTfun(X0,$o)),X0,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X0),sK59(X0,X1),X3),X2)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1197,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0 > $o,X3 : X1 > X0 > $o] : (($true = vAPP(sTfun(X1,sTfun(X0,$o)),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X1,sTfun(X0,$o))),X2),X3)) | ? [X4 : X1,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X3,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X2,X4),X5))))),
% 3.31/0.90 inference(ennf_transformation,[],[f719])).
% 3.31/0.90 thf(f719,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0 > $o,X3 : X1 > X0 > $o] : (! [X4 : X1,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X2,X4),X5)) => ($true = vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X3,X4),X5))) => ($true = vAPP(sTfun(X1,sTfun(X0,$o)),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X1,sTfun(X0,$o))),X2),X3)))),
% 3.31/0.90 inference(fool_elimination,[],[f718])).
% 3.31/0.90 thf(f718,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0 > $o,X3 : X1 > X0 > $o] : (! [X4 : X1,X5 : X0] : (vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X2,X4),X5) => vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X3,X4),X5)) => vAPP(sTfun(X1,sTfun(X0,$o)),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X1,sTfun(X0,$o))),X2),X3))),
% 3.31/0.90 inference(rectify,[],[f176])).
% 3.31/0.90 thf(f176,axiom,(
% 3.31/0.90 ! [X2 : $tType,X0 : $tType,X24 : X0 > X2 > $o,X53 : X0 > X2 > $o] : (! [X23 : X0,X34 : X2] : (vAPP(X2,$o,vAPP(X0,sTfun(X2,$o),X24,X23),X34) => vAPP(X2,$o,vAPP(X0,sTfun(X2,$o),X53,X23),X34)) => vAPP(sTfun(X0,sTfun(X2,$o)),$o,vAPP(sTfun(X0,sTfun(X2,$o)),sTfun(sTfun(X0,sTfun(X2,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X2,$o))),X24),X53))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_predicate2I)).
% 3.31/0.90 thf(f5236,plain,(
% 3.31/0.90 spl132_198),
% 3.31/0.90 inference(avatar_split_clause,[],[f1699,f5234])).
% 3.31/0.90 thf(f5234,plain,(
% 3.31/0.90 spl132_198 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0 > $o,X2 : X1 > X0 > $o] : (($true = vAPP(sTfun(X1,sTfun(X0,$o)),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X1,sTfun(X0,$o))),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X2,vAPP(sTfun(X1,sTfun(X0,$o)),X1,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X1),sK58(X0,X1),X3),X2)),vAPP(sTfun(X1,sTfun(X0,$o)),X0,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X0),sK59(X0,X1),X3),X2))))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_198])])).
% 3.31/0.90 thf(f1699,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0 > $o,X3 : X1 > X0 > $o] : (($true = vAPP(sTfun(X1,sTfun(X0,$o)),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X1,sTfun(X0,$o))),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X1,sTfun(X0,$o),X2,vAPP(sTfun(X1,sTfun(X0,$o)),X1,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X1),sK58(X0,X1),X3),X2)),vAPP(sTfun(X1,sTfun(X0,$o)),X0,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,sTfun(X0,$o)),X0),sK59(X0,X1),X3),X2)))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1403])).
% 3.31/0.90 thf(f5232,plain,(
% 3.31/0.90 spl132_197),
% 3.31/0.90 inference(avatar_split_clause,[],[f1629,f5230])).
% 3.31/0.90 thf(f5230,plain,(
% 3.31/0.90 spl132_197 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : X2 > product_prod(X1,X0),X3 : set(X2)] : (($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1),vAPP(sTfun(product_prod(X1,X0),X1),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1)),bCOMB,product_fst(X1,X0)),X4))) | ($true != vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4)) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_197])])).
% 3.31/0.90 thf(f1629,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1),vAPP(sTfun(product_prod(X1,X0),X1),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1)),bCOMB,product_fst(X1,X0)),X4))) | ($true != vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4)) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1112])).
% 3.31/0.90 thf(f1112,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1),vAPP(sTfun(product_prod(X1,X0),X1),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1)),bCOMB,product_fst(X1,X0)),X4))) | ($true != vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1111])).
% 3.31/0.90 thf(f1111,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1),vAPP(sTfun(product_prod(X1,X0),X1),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1)),bCOMB,product_fst(X1,X0)),X4))) | ($true != vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4))) | ((topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f611])).
% 3.31/0.90 thf(f611,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((topolo503727757_space(X0) = $true) & (topolo503727757_space(X1) = $true) & (topolo503727757_space(X2) = $true)) => ! [X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (($true = vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4)) => ($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1),vAPP(sTfun(product_prod(X1,X0),X1),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X1)),bCOMB,product_fst(X1,X0)),X4)))))),
% 3.31/0.90 inference(fool_elimination,[],[f610])).
% 3.31/0.90 thf(f610,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((topolo503727757_space(X0) & topolo503727757_space(X1) & topolo503727757_space(X2)) => ! [X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4) => vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),(^[X5 : X2] : (vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),vAPP(X2,product_prod(X1,X0),X4,X5)))))))),
% 3.31/0.90 inference(rectify,[],[f238])).
% 3.31/0.90 thf(f238,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((topolo503727757_space(X1) & topolo503727757_space(X2) & topolo503727757_space(X0)) => ! [X111 : set(X0),X54 : X0 > product_prod(X2,X1)] : (vAPP(sTfun(X0,product_prod(X2,X1)),$o,vAPP(set(X0),sTfun(sTfun(X0,product_prod(X2,X1)),$o),topolo2071040574ous_on(X0,product_prod(X2,X1)),X111),X54) => vAPP(sTfun(X0,X2),$o,vAPP(set(X0),sTfun(sTfun(X0,X2),$o),topolo2071040574ous_on(X0,X2),X111),(^[X20 : X0] : (vAPP(product_prod(X2,X1),X2,product_fst(X2,X1),vAPP(X0,product_prod(X2,X1),X54,X20)))))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_continuous__on__fst)).
% 3.31/0.90 thf(f5228,plain,(
% 3.31/0.90 spl132_196),
% 3.31/0.90 inference(avatar_split_clause,[],[f1628,f5226])).
% 3.31/0.90 thf(f5226,plain,(
% 3.31/0.90 spl132_196 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : X2 > product_prod(X1,X0),X3 : set(X2)] : (($true = vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0),vAPP(sTfun(product_prod(X1,X0),X0),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0)),bCOMB,product_snd(X1,X0)),X4))) | ($true != vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4)) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_196])])).
% 3.31/0.90 thf(f1628,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (($true = vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0),vAPP(sTfun(product_prod(X1,X0),X0),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0)),bCOMB,product_snd(X1,X0)),X4))) | ($true != vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4)) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1110])).
% 3.31/0.90 thf(f1110,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (($true = vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0),vAPP(sTfun(product_prod(X1,X0),X0),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0)),bCOMB,product_snd(X1,X0)),X4))) | ($true != vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1109])).
% 3.31/0.90 thf(f1109,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (($true = vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0),vAPP(sTfun(product_prod(X1,X0),X0),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0)),bCOMB,product_snd(X1,X0)),X4))) | ($true != vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4))) | ((topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f609])).
% 3.31/0.90 thf(f609,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((topolo503727757_space(X0) = $true) & (topolo503727757_space(X1) = $true) & (topolo503727757_space(X2) = $true)) => ! [X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (($true = vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4)) => ($true = vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),vAPP(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0),vAPP(sTfun(product_prod(X1,X0),X0),sTfun(sTfun(X2,product_prod(X1,X0)),sTfun(X2,X0)),bCOMB,product_snd(X1,X0)),X4)))))),
% 3.31/0.90 inference(fool_elimination,[],[f608])).
% 3.31/0.90 thf(f608,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((topolo503727757_space(X0) & topolo503727757_space(X1) & topolo503727757_space(X2)) => ! [X3 : set(X2),X4 : X2 > product_prod(X1,X0)] : (vAPP(sTfun(X2,product_prod(X1,X0)),$o,vAPP(set(X2),sTfun(sTfun(X2,product_prod(X1,X0)),$o),topolo2071040574ous_on(X2,product_prod(X1,X0)),X3),X4) => vAPP(sTfun(X2,X0),$o,vAPP(set(X2),sTfun(sTfun(X2,X0),$o),topolo2071040574ous_on(X2,X0),X3),(^[X5 : X2] : (vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),vAPP(X2,product_prod(X1,X0),X4,X5)))))))),
% 3.31/0.90 inference(rectify,[],[f230])).
% 3.31/0.90 thf(f230,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((topolo503727757_space(X1) & topolo503727757_space(X2) & topolo503727757_space(X0)) => ! [X111 : set(X0),X54 : X0 > product_prod(X2,X1)] : (vAPP(sTfun(X0,product_prod(X2,X1)),$o,vAPP(set(X0),sTfun(sTfun(X0,product_prod(X2,X1)),$o),topolo2071040574ous_on(X0,product_prod(X2,X1)),X111),X54) => vAPP(sTfun(X0,X1),$o,vAPP(set(X0),sTfun(sTfun(X0,X1),$o),topolo2071040574ous_on(X0,X1),X111),(^[X20 : X0] : (vAPP(product_prod(X2,X1),X1,product_snd(X2,X1),vAPP(X0,product_prod(X2,X1),X54,X20)))))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_continuous__on__snd)).
% 3.31/0.90 thf(f5198,plain,(
% 3.31/0.90 spl132_195),
% 3.31/0.90 inference(avatar_split_clause,[],[f1569,f5196])).
% 3.31/0.90 thf(f5196,plain,(
% 3.31/0.90 spl132_195 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X1,X5 : X1] : (($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),ord_less_eq(product_prod(X0,X1)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X4)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X5))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_195])])).
% 3.31/0.90 thf(f1569,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X1,X5 : X1] : (($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),ord_less_eq(product_prod(X0,X1)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X4)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X5))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1053])).
% 3.31/0.90 thf(f1053,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X1,X5 : X1] : (($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),ord_less_eq(product_prod(X0,X1)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X4)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X5))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 inference(flattening,[],[f1052])).
% 3.31/0.90 thf(f1052,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X1,X5 : X1] : ((($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),ord_less_eq(product_prod(X0,X1)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X4)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X5))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | ((ord(X0) != $true) | ($true != ord(X1))))),
% 3.31/0.90 inference(ennf_transformation,[],[f507])).
% 3.31/0.90 thf(f507,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (((ord(X0) = $true) & ($true = ord(X1))) => ! [X2 : X0,X3 : X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) => ($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),ord_less_eq(product_prod(X0,X1)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X4)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X5))))))),
% 3.31/0.90 inference(fool_elimination,[],[f506])).
% 3.31/0.90 thf(f506,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((ord(X0) & ord(X1)) => ! [X2 : X0,X3 : X0,X4 : X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5) => vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),ord_less_eq(product_prod(X0,X1)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X4)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X5)))))),
% 3.31/0.90 inference(rectify,[],[f94])).
% 3.31/0.90 thf(f94,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType] : ((ord(X0) & ord(X2)) => ! [X14 : X0,X85 : X0,X15 : X2,X86 : X2] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X14),X85) => (vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X15),X86) => vAPP(product_prod(X0,X2),$o,vAPP(product_prod(X0,X2),sTfun(product_prod(X0,X2),$o),ord_less_eq(product_prod(X0,X2)),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X14),X15)),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X85),X86)))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Pair__mono)).
% 3.31/0.90 thf(f4897,plain,(
% 3.31/0.90 spl132_194),
% 3.31/0.90 inference(avatar_split_clause,[],[f1556,f4895])).
% 3.31/0.90 thf(f4895,plain,(
% 3.31/0.90 spl132_194 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK21(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK22(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | (order(X1) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_194])])).
% 3.31/0.90 thf(f1556,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK21(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK22(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | (order(X1) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1349])).
% 3.31/0.90 thf(f4893,plain,(
% 3.31/0.90 spl132_193),
% 3.31/0.90 inference(avatar_split_clause,[],[f1554,f4891])).
% 3.31/0.90 thf(f4891,plain,(
% 3.31/0.90 spl132_193 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X4 : X0 > X1,X5 : X1,X2 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK19(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK20(X0,X1),X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | (order(X1) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_193])])).
% 3.31/0.90 thf(f1554,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK19(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK20(X0,X1),X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | (order(X1) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1347])).
% 3.31/0.90 thf(f4889,plain,(
% 3.31/0.90 spl132_192 | ~spl132_8 | ~spl132_42),
% 3.31/0.90 inference(avatar_split_clause,[],[f2333,f2317,f2072,f4886])).
% 3.31/0.90 thf(f4886,plain,(
% 3.31/0.90 spl132_192 <=> ($true = finite_finite(set(c)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_192])])).
% 3.31/0.90 thf(f2333,plain,(
% 3.31/0.90 ($true = finite_finite(set(c))) | (~spl132_8 | ~spl132_42)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f2324])).
% 3.31/0.90 thf(f2324,plain,(
% 3.31/0.90 ($true != $true) | ($true = finite_finite(set(c))) | (~spl132_8 | ~spl132_42)),
% 3.31/0.90 inference(superposition,[],[f2318,f2074])).
% 3.31/0.90 thf(f2074,plain,(
% 3.31/0.90 (finite_finite(c) = $true) | ~spl132_8),
% 3.31/0.90 inference(avatar_component_clause,[],[f2072])).
% 3.31/0.90 thf(f4762,plain,(
% 3.31/0.90 spl132_191),
% 3.31/0.90 inference(avatar_split_clause,[],[f1591,f4760])).
% 3.31/0.90 thf(f4760,plain,(
% 3.31/0.90 spl132_191 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X2 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK29(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK29(X0,X1),X3),X2)))) | (ord(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_191])])).
% 3.31/0.90 thf(f1591,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK29(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK29(X0,X1),X3),X2)))) | (ord(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1359])).
% 3.31/0.90 thf(f1359,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK29(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK29(X0,X1),X3),X2))))) | (ord(X0) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f1085,f1358])).
% 3.31/0.90 thf(f1358,plain,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (? [X4 : X1] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK29(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK29(X0,X1),X3),X2)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1085,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | ? [X4 : X1] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4)))) | (ord(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f547])).
% 3.31/0.90 thf(f547,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((ord(X0) = $true) => ! [X2 : X1 > X0,X3 : X1 > X0] : (! [X4 : X1] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) => ($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3))))),
% 3.31/0.90 inference(fool_elimination,[],[f546])).
% 3.31/0.90 thf(f546,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (ord(X0) => ! [X2 : X1 > X0,X3 : X1 > X0] : (! [X4 : X1] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4)) => vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)))),
% 3.31/0.90 inference(rectify,[],[f137])).
% 3.31/0.90 thf(f137,axiom,(
% 3.31/0.90 ! [X2 : $tType,X0 : $tType] : (ord(X2) => ! [X54 : X0 > X2,X55 : X0 > X2] : (! [X23 : X0] : vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(X0,X2,X54,X23)),vAPP(X0,X2,X55,X23)) => vAPP(sTfun(X0,X2),$o,vAPP(sTfun(X0,X2),sTfun(sTfun(X0,X2),$o),ord_less_eq(sTfun(X0,X2)),X54),X55)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_le__funI)).
% 3.31/0.90 thf(f4740,plain,(
% 3.31/0.90 spl132_190),
% 3.31/0.90 inference(avatar_split_clause,[],[f1643,f4738])).
% 3.31/0.90 thf(f4738,plain,(
% 3.31/0.90 spl132_190 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)] : ((vAPP(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)),product_Pair(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),denota1663640101rp_ext(X2,X0,X1,product_unit),sK33(X0,X1,X2),X3)),vAPP(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),X2,sK34(X0,X1,X2),X3)) = X3) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_190])])).
% 3.31/0.90 thf(f1643,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)] : ((vAPP(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)),product_Pair(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),denota1663640101rp_ext(X2,X0,X1,product_unit),sK33(X0,X1,X2),X3)),vAPP(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),X2,sK34(X0,X1,X2),X3)) = X3) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1367])).
% 3.31/0.90 thf(f1367,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)] : (vAPP(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)),product_Pair(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),denota1663640101rp_ext(X2,X0,X1,product_unit),sK33(X0,X1,X2),X3)),vAPP(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),X2,sK34(X0,X1,X2),X3)) = X3) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f1138,f1366])).
% 3.31/0.90 thf(f1366,plain,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)] : (? [X4 : denota1663640101rp_ext(X2,X0,X1,product_unit),X5 : X2] : (vAPP(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)),product_Pair(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),X4),X5) = X3) => (vAPP(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)),product_Pair(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),denota1663640101rp_ext(X2,X0,X1,product_unit),sK33(X0,X1,X2),X3)),vAPP(product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),X2,sK34(X0,X1,X2),X3)) = X3))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1138,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)] : ? [X4 : denota1663640101rp_ext(X2,X0,X1,product_unit),X5 : X2] : (vAPP(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)),product_Pair(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),X4),X5) = X3) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1137])).
% 3.31/0.90 thf(f1137,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)] : ? [X4 : denota1663640101rp_ext(X2,X0,X1,product_unit),X5 : X2] : (vAPP(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)),product_Pair(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),X4),X5) = X3) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f637])).
% 3.31/0.90 thf(f637,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)] : ~! [X4 : denota1663640101rp_ext(X2,X0,X1,product_unit),X5 : X2] : (vAPP(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)),product_Pair(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),X4),X5) != X3))),
% 3.31/0.90 inference(fool_elimination,[],[f636])).
% 3.31/0.90 thf(f636,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)] : ~! [X4 : denota1663640101rp_ext(X2,X0,X1,product_unit),X5 : X2] : (vAPP(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),vAPP(denota1663640101rp_ext(X2,X0,X1,product_unit),sTfun(X2,product_prod(denota1663640101rp_ext(X2,X0,X1,product_unit),X2)),product_Pair(denota1663640101rp_ext(X2,X0,X1,product_unit),X2),X4),X5) != X3))),
% 3.31/0.90 inference(rectify,[],[f27])).
% 3.31/0.90 thf(f27,axiom,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType] : ((finite_finite(X2) & finite_finite(X1) & finite_finite(X0)) => ! [X14 : product_prod(denota1663640101rp_ext(X0,X2,X1,product_unit),X0)] : ~! [X21 : denota1663640101rp_ext(X0,X2,X1,product_unit),X27 : X0] : (vAPP(X0,product_prod(denota1663640101rp_ext(X0,X2,X1,product_unit),X0),vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(X0,product_prod(denota1663640101rp_ext(X0,X2,X1,product_unit),X0)),product_Pair(denota1663640101rp_ext(X0,X2,X1,product_unit),X0),X21),X27) != X14))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_FunctionFrechet_Ocases)).
% 3.31/0.90 thf(f4401,plain,(
% 3.31/0.90 spl132_189),
% 3.31/0.90 inference(avatar_split_clause,[],[f1839,f4399])).
% 3.31/0.90 thf(f4399,plain,(
% 3.31/0.90 spl132_189 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X4 : X0 > X1,X3 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_189])])).
% 3.31/0.90 thf(f1839,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.90 inference(equality_resolution,[],[f1568])).
% 3.31/0.90 thf(f1568,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4)))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1353])).
% 3.31/0.90 thf(f1353,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4)))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f1051,f1352])).
% 3.31/0.90 thf(f1352,plain,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X4 : X0 > X1] : (? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7))) => (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1051,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 inference(flattening,[],[f1050])).
% 3.31/0.90 thf(f1050,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (((($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7)))) | (vAPP(X0,X1,X4,X3) != X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | ((ord(X0) != $true) | ($true != ord(X1))))),
% 3.31/0.90 inference(ennf_transformation,[],[f505])).
% 3.31/0.90 thf(f505,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (((ord(X0) = $true) & ($true = ord(X1))) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ((vAPP(X0,X1,X4,X3) = X5) => (! [X6 : X0,X7 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7)) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7)))) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5))))))),
% 3.31/0.90 inference(fool_elimination,[],[f504])).
% 3.31/0.90 thf(f504,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((ord(X0) & ord(X1)) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => ((vAPP(X0,X1,X4,X3) = X5) => (! [X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)))))),
% 3.31/0.90 inference(rectify,[],[f142])).
% 3.31/0.90 thf(f142,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType] : ((ord(X0) & ord(X2)) => ! [X32 : X0,X33 : X0,X54 : X0 > X2,X79 : X2] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X32),X33) => ((vAPP(X0,X2,X54,X33) = X79) => (! [X23 : X0,X34 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X23),X34) => vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(X0,X2,X54,X23)),vAPP(X0,X2,X54,X34))) => vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(X0,X2,X54,X32)),X79)))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_ord__le__eq__subst)).
% 3.31/0.90 thf(f4397,plain,(
% 3.31/0.90 spl132_188),
% 3.31/0.90 inference(avatar_split_clause,[],[f1837,f4395])).
% 3.31/0.90 thf(f4395,plain,(
% 3.31/0.90 spl132_188 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_188])])).
% 3.31/0.90 thf(f1837,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.90 inference(equality_resolution,[],[f1566])).
% 3.31/0.90 thf(f1566,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1351])).
% 3.31/0.90 thf(f1351,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f1049,f1350])).
% 3.31/0.90 thf(f1350,plain,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X3 : X1 > X0] : (? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1049,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 inference(flattening,[],[f1048])).
% 3.31/0.90 thf(f1048,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5))) | (vAPP(X1,X0,X3,X4) != X2)) | ((ord(X0) != $true) | ($true != ord(X1))))),
% 3.31/0.90 inference(ennf_transformation,[],[f503])).
% 3.31/0.90 thf(f503,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (((ord(X0) = $true) & ($true = ord(X1))) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : ((vAPP(X1,X0,X3,X4) = X2) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) => (! [X6 : X1,X7 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7)))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5)))))))),
% 3.31/0.90 inference(fool_elimination,[],[f502])).
% 3.31/0.90 thf(f502,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((ord(X0) & ord(X1)) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : ((vAPP(X1,X0,X3,X4) = X2) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5) => (! [X6 : X1,X7 : X1] : (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))))))),
% 3.31/0.90 inference(rectify,[],[f141])).
% 3.31/0.90 thf(f141,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType] : ((ord(X0) & ord(X2)) => ! [X32 : X0,X54 : X2 > X0,X33 : X2,X79 : X2] : ((vAPP(X2,X0,X54,X33) = X32) => (vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X33),X79) => (! [X23 : X2,X34 : X2] : (vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X23),X34) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X2,X0,X54,X23)),vAPP(X2,X0,X54,X34))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X32),vAPP(X2,X0,X54,X79))))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_ord__eq__le__subst)).
% 3.31/0.90 thf(f4393,plain,(
% 3.31/0.90 spl132_187 | ~spl132_3 | ~spl132_42),
% 3.31/0.90 inference(avatar_split_clause,[],[f2332,f2317,f2047,f4390])).
% 3.31/0.90 thf(f4390,plain,(
% 3.31/0.90 spl132_187 <=> ($true = finite_finite(set(sc)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_187])])).
% 3.31/0.90 thf(f2047,plain,(
% 3.31/0.90 spl132_3 <=> (finite_finite(sc) = $true)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_3])])).
% 3.31/0.90 thf(f2332,plain,(
% 3.31/0.90 ($true = finite_finite(set(sc))) | (~spl132_3 | ~spl132_42)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f2325])).
% 3.31/0.90 thf(f2325,plain,(
% 3.31/0.90 ($true != $true) | ($true = finite_finite(set(sc))) | (~spl132_3 | ~spl132_42)),
% 3.31/0.90 inference(superposition,[],[f2318,f2049])).
% 3.31/0.90 thf(f2049,plain,(
% 3.31/0.90 (finite_finite(sc) = $true) | ~spl132_3),
% 3.31/0.90 inference(avatar_component_clause,[],[f2047])).
% 3.31/0.90 thf(f4388,plain,(
% 3.31/0.90 spl132_186),
% 3.31/0.90 inference(avatar_split_clause,[],[f1817,f4385])).
% 3.31/0.90 thf(f1817,plain,(
% 3.31/0.90 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),vAPP(trm(a,c),trm(a,c),vAPP(trm(a,c),sTfun(trm(a,c),trm(a,c)),plus(a,c),t1),t2))) = $true)),
% 3.31/0.90 inference(cnf_transformation,[],[f909])).
% 3.31/0.90 thf(f909,plain,(
% 3.31/0.90 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),vAPP(trm(a,c),trm(a,c),vAPP(trm(a,c),sTfun(trm(a,c),trm(a,c)),plus(a,c),t1),t2))) = $true)),
% 3.31/0.90 inference(fool_elimination,[],[f908])).
% 3.31/0.90 thf(f908,plain,(
% 3.31/0.90 vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),vAPP(trm(a,c),trm(a,c),vAPP(trm(a,c),sTfun(trm(a,c),trm(a,c)),plus(a,c),t1),t2)))),
% 3.31/0.90 inference(rectify,[],[f2])).
% 3.31/0.90 thf(f2,axiom,(
% 3.31/0.90 vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),vAPP(trm(a,c),trm(a,c),vAPP(trm(a,c),sTfun(trm(a,c),trm(a,c)),plus(a,c),t1),t2)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_agree)).
% 3.31/0.90 thf(f4383,plain,(
% 3.31/0.90 spl132_185),
% 3.31/0.90 inference(avatar_split_clause,[],[f1716,f4381])).
% 3.31/0.90 thf(f4381,plain,(
% 3.31/0.90 spl132_185 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK69(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK70(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK71(X0,X1,X2),X3))) = X3)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_185])])).
% 3.31/0.90 thf(f1716,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : ((vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK69(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK70(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK71(X0,X1,X2),X3))) = X3)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1415])).
% 3.31/0.90 thf(f1415,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK69(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK70(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK71(X0,X1,X2),X3))) = X3)),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70,sK71])],[f1221,f1414])).
% 3.31/0.90 thf(f1414,plain,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : (? [X4 : X0,X5 : X1,X6 : X2] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = X3) => (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK69(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK70(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK71(X0,X1,X2),X3))) = X3))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1221,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : ? [X4 : X0,X5 : X1,X6 : X2] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = X3)),
% 3.31/0.90 inference(ennf_transformation,[],[f939])).
% 3.31/0.90 thf(f939,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : ~! [X4 : X0,X5 : X1,X6 : X2] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) != X3)),
% 3.31/0.90 inference(rectify,[],[f66])).
% 3.31/0.90 thf(f66,axiom,(
% 3.31/0.90 ! [X0 : $tType,X2 : $tType,X1 : $tType,X15 : product_prod(X0,product_prod(X2,X1))] : ~! [X57 : X0,X58 : X2,X64 : X1] : (vAPP(product_prod(X2,X1),product_prod(X0,product_prod(X2,X1)),vAPP(X0,sTfun(product_prod(X2,X1),product_prod(X0,product_prod(X2,X1))),product_Pair(X0,product_prod(X2,X1)),X57),vAPP(X1,product_prod(X2,X1),vAPP(X2,sTfun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X58),X64)) != X15)),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_prod__cases3)).
% 3.31/0.90 thf(f4343,plain,(
% 3.31/0.90 spl132_184),
% 3.31/0.90 inference(avatar_split_clause,[],[f1644,f4341])).
% 3.31/0.90 thf(f4341,plain,(
% 3.31/0.90 spl132_184 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_184])])).
% 3.31/0.90 thf(f1644,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1140])).
% 3.31/0.90 thf(f1140,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0)] : ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1139])).
% 3.31/0.90 thf(f1139,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0)] : ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f639])).
% 3.31/0.90 thf(f639,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : frechet_good_interp(X2,X1,X0)] : ($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))))),
% 3.31/0.90 inference(fool_elimination,[],[f638])).
% 3.31/0.90 thf(f638,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : frechet_good_interp(X2,X1,X0)] : vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))),
% 3.31/0.90 inference(rectify,[],[f106])).
% 3.31/0.90 thf(f106,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X14 : frechet_good_interp(X0,X2,X1)] : vAPP(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o),member(denota1663640101rp_ext(X0,X2,X1,product_unit)),vAPP(frechet_good_interp(X0,X2,X1),denota1663640101rp_ext(X0,X2,X1,product_unit),freche229654227interp(X0,X2,X1),X14)),vAPP(sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),$o),set(denota1663640101rp_ext(X0,X2,X1,product_unit)),collect(denota1663640101rp_ext(X0,X2,X1,product_unit)),denota2077489681interp(X0,X2,X1))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_raw__interp)).
% 3.31/0.90 thf(f4339,plain,(
% 3.31/0.90 spl132_183),
% 3.31/0.90 inference(avatar_split_clause,[],[f1642,f4337])).
% 3.31/0.90 thf(f4337,plain,(
% 3.31/0.90 spl132_183 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),sK32(X0,X1,X2),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_183])])).
% 3.31/0.90 thf(f1642,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),sK32(X0,X1,X2),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1365])).
% 3.31/0.90 thf(f1365,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),sK32(X0,X1,X2),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) & (vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),sK32(X0,X1,X2),X3)) = X3)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f1136,f1364])).
% 3.31/0.90 thf(f1364,plain,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : frechet_good_interp(X2,X1,X0)] : (? [X4 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X4),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) & (vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X4) = X3)) => (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),sK32(X0,X1,X2),X3)),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) & (vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),sK32(X0,X1,X2),X3)) = X3)))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1136,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0)] : ? [X4 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X4),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) & (vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X4) = X3)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1135])).
% 3.31/0.90 thf(f1135,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0)] : ? [X4 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X4),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))) & (vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X4) = X3)) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f927])).
% 3.31/0.90 thf(f927,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : frechet_good_interp(X2,X1,X0)] : ~! [X4 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X4) = X3) => ($true != vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X4),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))))),
% 3.31/0.90 inference(flattening,[],[f635])).
% 3.31/0.90 thf(f635,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : frechet_good_interp(X2,X1,X0)] : ~! [X4 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X4) = X3) => ~($true = vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X4),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0))))))),
% 3.31/0.90 inference(fool_elimination,[],[f634])).
% 3.31/0.90 thf(f634,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : frechet_good_interp(X2,X1,X0)] : ~! [X4 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : ((vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),X4) = X3) => ~vAPP(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(denota1663640101rp_ext(X2,X1,X0,product_unit)),$o),member(denota1663640101rp_ext(X2,X1,X0,product_unit)),X4),vAPP(sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),$o),set(denota1663640101rp_ext(X2,X1,X0,product_unit)),collect(denota1663640101rp_ext(X2,X1,X0,product_unit)),denota2077489681interp(X2,X1,X0)))))),
% 3.31/0.90 inference(rectify,[],[f107])).
% 3.31/0.90 thf(f107,axiom,(
% 3.31/0.90 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X14 : frechet_good_interp(X0,X2,X1)] : ~! [X34 : denota1663640101rp_ext(X0,X2,X1,product_unit)] : ((vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),frechet_good_interp(X0,X2,X1),freche227871258interp(X0,X2,X1),X34) = X14) => ~vAPP(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(denota1663640101rp_ext(X0,X2,X1,product_unit)),$o),member(denota1663640101rp_ext(X0,X2,X1,product_unit)),X34),vAPP(sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),$o),set(denota1663640101rp_ext(X0,X2,X1,product_unit)),collect(denota1663640101rp_ext(X0,X2,X1,product_unit)),denota2077489681interp(X0,X2,X1)))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_good__interp__cases)).
% 3.31/0.90 thf(f4320,plain,(
% 3.31/0.90 spl132_182 | ~spl132_98 | ~spl132_136 | ~spl132_167 | ~spl132_180),
% 3.31/0.90 inference(avatar_split_clause,[],[f4240,f4237,f3930,f3354,f2896,f4318])).
% 3.31/0.90 thf(f4318,plain,(
% 3.31/0.90 spl132_182 <=> ! [X1 : $tType,X0 : $tType,X3 : trm(X1,X0) > $o,X2 : trm(X1,X0)] : (($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),vAPP(sTfun(trm(X1,X0),$o),frechet_strm(X1,X0),sK68(X0,X1),X3)))) | ($true = vAPP(trm(X1,X0),$o,X3,X2)) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_182])])).
% 3.31/0.90 thf(f2896,plain,(
% 3.31/0.90 spl132_98 <=> ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : (vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)) = X2)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_98])])).
% 3.31/0.90 thf(f3354,plain,(
% 3.31/0.90 spl132_136 <=> ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : ($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_136])])).
% 3.31/0.90 thf(f3930,plain,(
% 3.31/0.90 spl132_167 <=> ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0)] : ((vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X2)) = X2) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_167])])).
% 3.31/0.90 thf(f4237,plain,(
% 3.31/0.90 spl132_180 <=> ! [X1 : $tType,X0 : $tType,X3 : trm(X1,X0) > $o,X2 : trm(X1,X0)] : (($true = vAPP(trm(X1,X0),$o,X3,X2)) | ($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(sTfun(trm(X1,X0),$o),frechet_strm(X1,X0),sK68(X0,X1),X3)))) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_180])])).
% 3.31/0.90 thf(f4240,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0) > $o] : (($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),vAPP(sTfun(trm(X1,X0),$o),frechet_strm(X1,X0),sK68(X0,X1),X3)))) | ($true = vAPP(trm(X1,X0),$o,X3,X2)) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) ) | (~spl132_98 | ~spl132_136 | ~spl132_167 | ~spl132_180)),
% 3.31/0.90 inference(forward_demodulation,[],[f4238,f3950])).
% 3.31/0.90 thf(f3950,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X0,X1)] : ((vAPP(frechet_strm(X0,X1),trm(X0,X1),frechet_raw_term(X0,X1),X2) = vAPP(frechet_strm(X0,X1),trm(X0,X1),sK46(X1,X0),X2))) ) | (~spl132_98 | ~spl132_136 | ~spl132_167)),
% 3.31/0.90 inference(forward_demodulation,[],[f3949,f2897])).
% 3.31/0.90 thf(f2897,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : ((vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)) = X2)) ) | ~spl132_98),
% 3.31/0.90 inference(avatar_component_clause,[],[f2896])).
% 3.31/0.90 thf(f3949,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X0,X1)] : ((vAPP(frechet_strm(X0,X1),trm(X0,X1),sK46(X1,X0),X2) = vAPP(frechet_strm(X0,X1),trm(X0,X1),frechet_raw_term(X0,X1),vAPP(trm(X0,X1),frechet_strm(X0,X1),frechet_simple_term(X0,X1),vAPP(frechet_strm(X0,X1),trm(X0,X1),sK46(X1,X0),X2))))) ) | (~spl132_136 | ~spl132_167)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f3940])).
% 3.31/0.90 thf(f3940,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X0,X1)] : (($true != $true) | (vAPP(frechet_strm(X0,X1),trm(X0,X1),sK46(X1,X0),X2) = vAPP(frechet_strm(X0,X1),trm(X0,X1),frechet_raw_term(X0,X1),vAPP(trm(X0,X1),frechet_strm(X0,X1),frechet_simple_term(X0,X1),vAPP(frechet_strm(X0,X1),trm(X0,X1),sK46(X1,X0),X2)))) | (dfree(X0,X1) != dfree(X0,X1))) ) | (~spl132_136 | ~spl132_167)),
% 3.31/0.90 inference(constrained_superposition,[],[f3931,f3355])).
% 3.31/0.90 thf(f3355,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) ) | ~spl132_136),
% 3.31/0.90 inference(avatar_component_clause,[],[f3354])).
% 3.31/0.90 thf(f3931,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0)] : (($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))) | (vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X2)) = X2)) ) | ~spl132_167),
% 3.31/0.90 inference(avatar_component_clause,[],[f3930])).
% 3.31/0.90 thf(f4238,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0) > $o] : (($true = vAPP(trm(X1,X0),$o,X3,X2)) | ($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(sTfun(trm(X1,X0),$o),frechet_strm(X1,X0),sK68(X0,X1),X3)))) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) ) | ~spl132_180),
% 3.31/0.90 inference(avatar_component_clause,[],[f4237])).
% 3.31/0.90 thf(f4245,plain,(
% 3.31/0.90 spl132_181 | ~spl132_5 | ~spl132_42),
% 3.31/0.90 inference(avatar_split_clause,[],[f2331,f2317,f2057,f4242])).
% 3.31/0.90 thf(f4242,plain,(
% 3.31/0.90 spl132_181 <=> ($true = finite_finite(set(sf)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_181])])).
% 3.31/0.90 thf(f2057,plain,(
% 3.31/0.90 spl132_5 <=> (finite_finite(sf) = $true)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_5])])).
% 3.31/0.90 thf(f2331,plain,(
% 3.31/0.90 ($true = finite_finite(set(sf))) | (~spl132_5 | ~spl132_42)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f2326])).
% 3.31/0.90 thf(f2326,plain,(
% 3.31/0.90 ($true != $true) | ($true = finite_finite(set(sf))) | (~spl132_5 | ~spl132_42)),
% 3.31/0.90 inference(superposition,[],[f2318,f2059])).
% 3.31/0.90 thf(f2059,plain,(
% 3.31/0.90 (finite_finite(sf) = $true) | ~spl132_5),
% 3.31/0.90 inference(avatar_component_clause,[],[f2057])).
% 3.31/0.90 thf(f4239,plain,(
% 3.31/0.90 spl132_180),
% 3.31/0.90 inference(avatar_split_clause,[],[f1714,f4237])).
% 3.31/0.90 thf(f1714,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0) > $o] : (($true = vAPP(trm(X1,X0),$o,X3,X2)) | ($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(sTfun(trm(X1,X0),$o),frechet_strm(X1,X0),sK68(X0,X1),X3)))) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1413])).
% 3.31/0.90 thf(f1413,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0) > $o] : (($true = vAPP(trm(X1,X0),$o,X3,X2)) | ($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(sTfun(trm(X1,X0),$o),frechet_strm(X1,X0),sK68(X0,X1),X3)))) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f1218,f1412])).
% 3.31/0.90 thf(f1412,plain,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X3 : trm(X1,X0) > $o] : (? [X4 : frechet_strm(X1,X0)] : ($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X4))) => ($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(sTfun(trm(X1,X0),$o),frechet_strm(X1,X0),sK68(X0,X1),X3)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1218,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0) > $o] : (($true = vAPP(trm(X1,X0),$o,X3,X2)) | ? [X4 : frechet_strm(X1,X0)] : ($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X4))) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 inference(flattening,[],[f1217])).
% 3.31/0.90 thf(f1217,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0) > $o] : ((($true = vAPP(trm(X1,X0),$o,X3,X2)) | ? [X4 : frechet_strm(X1,X0)] : ($true != vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X4)))) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 inference(ennf_transformation,[],[f745])).
% 3.31/0.90 thf(f745,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0) > $o] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))) => (! [X4 : frechet_strm(X1,X0)] : ($true = vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X4))) => ($true = vAPP(trm(X1,X0),$o,X3,X2))))),
% 3.31/0.90 inference(fool_elimination,[],[f744])).
% 3.31/0.90 thf(f744,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0) > $o] : (vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))) => (! [X4 : frechet_strm(X1,X0)] : vAPP(trm(X1,X0),$o,X3,vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X4)) => vAPP(trm(X1,X0),$o,X3,X2)))),
% 3.31/0.90 inference(rectify,[],[f19])).
% 3.31/0.90 thf(f19,axiom,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X15 : trm(X0,X1),X24 : trm(X0,X1) > $o] : (vAPP(set(trm(X0,X1)),$o,vAPP(trm(X0,X1),sTfun(set(trm(X0,X1)),$o),member(trm(X0,X1)),X15),vAPP(sTfun(trm(X0,X1),$o),set(trm(X0,X1)),collect(trm(X0,X1)),dfree(X0,X1))) => (! [X23 : frechet_strm(X0,X1)] : vAPP(trm(X0,X1),$o,X24,vAPP(frechet_strm(X0,X1),trm(X0,X1),frechet_raw_term(X0,X1),X23)) => vAPP(trm(X0,X1),$o,X24,X15)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_raw__term__induct)).
% 3.31/0.90 thf(f4235,plain,(
% 3.31/0.90 spl132_179),
% 3.31/0.90 inference(avatar_split_clause,[],[f1515,f4233])).
% 3.31/0.90 thf(f4233,plain,(
% 3.31/0.90 spl132_179 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($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,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_179])])).
% 3.31/0.90 thf(f1515,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($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,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1341])).
% 3.31/0.90 thf(f1341,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($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,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))))) | (linorder(X0) != $true))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f1338,f1340,f1339])).
% 3.31/0.90 thf(f1339,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1340,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X6 : X0,X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1)))))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1338,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7)))) | (linorder(X0) != $true))),
% 3.31/0.90 inference(rectify,[],[f994])).
% 3.31/0.90 thf(f994,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X6))) | ? [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),ord_less_eq(X0),X4),X5)))) | (linorder(X0) != $true))),
% 3.31/0.90 inference(flattening,[],[f993])).
% 3.31/0.90 thf(f993,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X6)))) | ? [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),ord_less_eq(X0),X4),X5)))) | (linorder(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f413])).
% 3.31/0.90 thf(f413,plain,(
% 3.31/0.90 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (! [X4 : X0,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X5)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) => (! [X6 : X0,X7 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X6)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))))),
% 3.31/0.90 inference(fool_elimination,[],[f412])).
% 3.31/0.90 thf(f412,plain,(
% 3.31/0.90 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (! [X4 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X5) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) => (! [X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X6) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 3.31/0.90 inference(rectify,[],[f157])).
% 3.31/0.90 thf(f157,axiom,(
% 3.31/0.90 ! [X0 : $tType] : (linorder(X0) => ! [X24 : X0 > X0 > $o,X32 : X0,X33 : X0] : (! [X57 : X0,X58 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X57),X58) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X24,X57),X58)) => (! [X57 : X0,X58 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X24,X58),X57) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X24,X57),X58)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X24,X32),X33))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_linorder__wlog)).
% 3.31/0.90 thf(f4231,plain,(
% 3.31/0.90 spl132_178),
% 3.31/0.90 inference(avatar_split_clause,[],[f1513,f4229])).
% 3.31/0.90 thf(f4229,plain,(
% 3.31/0.90 spl132_178 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($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,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_178])])).
% 3.31/0.90 thf(f1513,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($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,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1341])).
% 3.31/0.90 thf(f4072,plain,(
% 3.31/0.90 spl132_177),
% 3.31/0.90 inference(avatar_split_clause,[],[f1516,f4070])).
% 3.31/0.90 thf(f4070,plain,(
% 3.31/0.90 spl132_177 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($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,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_177])])).
% 3.31/0.90 thf(f1516,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($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,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1341])).
% 3.31/0.90 thf(f4068,plain,(
% 3.31/0.90 spl132_176),
% 3.31/0.90 inference(avatar_split_clause,[],[f1514,f4066])).
% 3.31/0.90 thf(f4066,plain,(
% 3.31/0.90 spl132_176 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($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,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_176])])).
% 3.31/0.90 thf(f1514,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($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,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1341])).
% 3.31/0.90 thf(f4058,plain,(
% 3.31/0.90 spl132_175),
% 3.31/0.90 inference(avatar_split_clause,[],[f1627,f4056])).
% 3.31/0.90 thf(f4056,plain,(
% 3.31/0.90 spl132_175 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : set(X2),X4 : X2 > X0 > X1,X5 : X0] : (($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(X0,sTfun(X2,X1),vAPP(sTfun(X2,sTfun(X0,X1)),sTfun(X0,sTfun(X2,X1)),cCOMB,X4),X5))) | ($true != vAPP(sTfun(X2,sTfun(X0,X1)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X0,X1)),$o),topolo2071040574ous_on(X2,sTfun(X0,X1)),X3),X4)) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_175])])).
% 3.31/0.90 thf(f1627,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : set(X2),X4 : X2 > X0 > X1,X5 : X0] : (($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(X0,sTfun(X2,X1),vAPP(sTfun(X2,sTfun(X0,X1)),sTfun(X0,sTfun(X2,X1)),cCOMB,X4),X5))) | ($true != vAPP(sTfun(X2,sTfun(X0,X1)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X0,X1)),$o),topolo2071040574ous_on(X2,sTfun(X0,X1)),X3),X4)) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1108])).
% 3.31/0.90 thf(f1108,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(X2),X4 : X2 > X0 > X1,X5 : X0] : (($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(X0,sTfun(X2,X1),vAPP(sTfun(X2,sTfun(X0,X1)),sTfun(X0,sTfun(X2,X1)),cCOMB,X4),X5))) | ($true != vAPP(sTfun(X2,sTfun(X0,X1)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X0,X1)),$o),topolo2071040574ous_on(X2,sTfun(X0,X1)),X3),X4))) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1107])).
% 3.31/0.90 thf(f1107,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : set(X2),X4 : X2 > X0 > X1,X5 : X0] : (($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(X0,sTfun(X2,X1),vAPP(sTfun(X2,sTfun(X0,X1)),sTfun(X0,sTfun(X2,X1)),cCOMB,X4),X5))) | ($true != vAPP(sTfun(X2,sTfun(X0,X1)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X0,X1)),$o),topolo2071040574ous_on(X2,sTfun(X0,X1)),X3),X4))) | ((topolo503727757_space(X1) != $true) | (topolo503727757_space(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f607])).
% 3.31/0.90 thf(f607,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((topolo503727757_space(X1) = $true) & (topolo503727757_space(X2) = $true)) => ! [X3 : set(X2),X4 : X2 > X0 > X1,X5 : X0] : (($true = vAPP(sTfun(X2,sTfun(X0,X1)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X0,X1)),$o),topolo2071040574ous_on(X2,sTfun(X0,X1)),X3),X4)) => ($true = vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),vAPP(X0,sTfun(X2,X1),vAPP(sTfun(X2,sTfun(X0,X1)),sTfun(X0,sTfun(X2,X1)),cCOMB,X4),X5)))))),
% 3.31/0.90 inference(fool_elimination,[],[f606])).
% 3.31/0.90 thf(f606,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((topolo503727757_space(X1) & topolo503727757_space(X2)) => ! [X3 : set(X2),X4 : X2 > X0 > X1,X5 : X0] : (vAPP(sTfun(X2,sTfun(X0,X1)),$o,vAPP(set(X2),sTfun(sTfun(X2,sTfun(X0,X1)),$o),topolo2071040574ous_on(X2,sTfun(X0,X1)),X3),X4) => vAPP(sTfun(X2,X1),$o,vAPP(set(X2),sTfun(sTfun(X2,X1),$o),topolo2071040574ous_on(X2,X1),X3),(^[X6 : X2] : (vAPP(X0,X1,vAPP(X2,sTfun(X0,X1),X4,X6),X5))))))),
% 3.31/0.90 inference(rectify,[],[f243])).
% 3.31/0.90 thf(f243,axiom,(
% 3.31/0.90 ! [X2 : $tType,X1 : $tType,X0 : $tType] : ((topolo503727757_space(X1) & topolo503727757_space(X0)) => ! [X109 : set(X0),X54 : X0 > X2 > X1,X18 : X2] : (vAPP(sTfun(X0,sTfun(X2,X1)),$o,vAPP(set(X0),sTfun(sTfun(X0,sTfun(X2,X1)),$o),topolo2071040574ous_on(X0,sTfun(X2,X1)),X109),X54) => vAPP(sTfun(X0,X1),$o,vAPP(set(X0),sTfun(sTfun(X0,X1),$o),topolo2071040574ous_on(X0,X1),X109),(^[X20 : X0] : (vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X54,X20),X18))))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_continuous__on__product__then__coordinatewise)).
% 3.31/0.90 thf(f4028,plain,(
% 3.31/0.90 spl132_174 | ~spl132_6 | ~spl132_42),
% 3.31/0.90 inference(avatar_split_clause,[],[f2330,f2317,f2062,f4025])).
% 3.31/0.90 thf(f4025,plain,(
% 3.31/0.90 spl132_174 <=> ($true = finite_finite(set(sz)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_174])])).
% 3.31/0.90 thf(f2062,plain,(
% 3.31/0.90 spl132_6 <=> (finite_finite(sz) = $true)),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_6])])).
% 3.31/0.90 thf(f2330,plain,(
% 3.31/0.90 ($true = finite_finite(set(sz))) | (~spl132_6 | ~spl132_42)),
% 3.31/0.90 inference(trivial_inequality_removal,[],[f2327])).
% 3.31/0.90 thf(f2327,plain,(
% 3.31/0.90 ($true != $true) | ($true = finite_finite(set(sz))) | (~spl132_6 | ~spl132_42)),
% 3.31/0.90 inference(superposition,[],[f2318,f2064])).
% 3.31/0.90 thf(f2064,plain,(
% 3.31/0.90 (finite_finite(sz) = $true) | ~spl132_6),
% 3.31/0.90 inference(avatar_component_clause,[],[f2062])).
% 3.31/0.90 thf(f3994,plain,(
% 3.31/0.90 spl132_173),
% 3.31/0.90 inference(avatar_split_clause,[],[f1840,f3992])).
% 3.31/0.90 thf(f3992,plain,(
% 3.31/0.90 spl132_173 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X4 : X0 > X1,X3 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_173])])).
% 3.31/0.90 thf(f1840,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.90 inference(equality_resolution,[],[f1567])).
% 3.31/0.90 thf(f1567,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK25(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK26(X0,X1),X4))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1353])).
% 3.31/0.90 thf(f3990,plain,(
% 3.31/0.90 spl132_172),
% 3.31/0.90 inference(avatar_split_clause,[],[f1838,f3988])).
% 3.31/0.90 thf(f3988,plain,(
% 3.31/0.90 spl132_172 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_172])])).
% 3.31/0.90 thf(f1838,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.90 inference(equality_resolution,[],[f1565])).
% 3.31/0.90 thf(f1565,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK23(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK24(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1351])).
% 3.31/0.90 thf(f3986,plain,(
% 3.31/0.90 spl132_171),
% 3.31/0.90 inference(avatar_split_clause,[],[f1608,f3984])).
% 3.31/0.90 thf(f3984,plain,(
% 3.31/0.90 spl132_171 <=> ! [X1 : $tType,X0 : $tType] : ($true = vAPP(set(trm(X1,X0)),$o,vAPP(sTfun(trm(X1,X0),frechet_strm(X1,X0)),sTfun(set(trm(X1,X0)),$o),vAPP(sTfun(frechet_strm(X1,X0),trm(X1,X0)),sTfun(sTfun(trm(X1,X0),frechet_strm(X1,X0)),sTfun(set(trm(X1,X0)),$o)),type_definition(frechet_strm(X1,X0),trm(X1,X0)),frechet_raw_term(X1,X0)),frechet_simple_term(X1,X0)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_171])])).
% 3.31/0.90 thf(f1608,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(sTfun(trm(X1,X0),frechet_strm(X1,X0)),sTfun(set(trm(X1,X0)),$o),vAPP(sTfun(frechet_strm(X1,X0),trm(X1,X0)),sTfun(sTfun(trm(X1,X0),frechet_strm(X1,X0)),sTfun(set(trm(X1,X0)),$o)),type_definition(frechet_strm(X1,X0),trm(X1,X0)),frechet_raw_term(X1,X0)),frechet_simple_term(X1,X0)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f581])).
% 3.31/0.90 thf(f581,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ($true = vAPP(set(trm(X1,X0)),$o,vAPP(sTfun(trm(X1,X0),frechet_strm(X1,X0)),sTfun(set(trm(X1,X0)),$o),vAPP(sTfun(frechet_strm(X1,X0),trm(X1,X0)),sTfun(sTfun(trm(X1,X0),frechet_strm(X1,X0)),sTfun(set(trm(X1,X0)),$o)),type_definition(frechet_strm(X1,X0),trm(X1,X0)),frechet_raw_term(X1,X0)),frechet_simple_term(X1,X0)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))),
% 3.31/0.90 inference(fool_elimination,[],[f580])).
% 3.31/0.90 thf(f580,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : vAPP(set(trm(X1,X0)),$o,vAPP(sTfun(trm(X1,X0),frechet_strm(X1,X0)),sTfun(set(trm(X1,X0)),$o),vAPP(sTfun(frechet_strm(X1,X0),trm(X1,X0)),sTfun(sTfun(trm(X1,X0),frechet_strm(X1,X0)),sTfun(set(trm(X1,X0)),$o)),type_definition(frechet_strm(X1,X0),trm(X1,X0)),frechet_raw_term(X1,X0)),frechet_simple_term(X1,X0)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))),
% 3.31/0.90 inference(rectify,[],[f86])).
% 3.31/0.90 thf(f86,axiom,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType] : vAPP(set(trm(X0,X1)),$o,vAPP(sTfun(trm(X0,X1),frechet_strm(X0,X1)),sTfun(set(trm(X0,X1)),$o),vAPP(sTfun(frechet_strm(X0,X1),trm(X0,X1)),sTfun(sTfun(trm(X0,X1),frechet_strm(X0,X1)),sTfun(set(trm(X0,X1)),$o)),type_definition(frechet_strm(X0,X1),trm(X0,X1)),frechet_raw_term(X0,X1)),frechet_simple_term(X0,X1)),vAPP(sTfun(trm(X0,X1),$o),set(trm(X0,X1)),collect(trm(X0,X1)),dfree(X0,X1)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_type__definition__strm)).
% 3.31/0.90 thf(f3974,plain,(
% 3.31/0.90 spl132_170),
% 3.31/0.90 inference(avatar_split_clause,[],[f1573,f3972])).
% 3.31/0.90 thf(f3972,plain,(
% 3.31/0.90 spl132_170 <=> ! [X1 : $tType,X0 : $tType,X2 : set(X1),X4 : set(X1),X3 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(set(X1),sTfun(set(X1),$o),ord_less_eq(set(X1)),X4),X2)) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),X3)) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_170])])).
% 3.31/0.90 thf(f1573,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : set(X1),X3 : X1 > X0,X4 : set(X1)] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(set(X1),sTfun(set(X1),$o),ord_less_eq(set(X1)),X4),X2)) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),X3)) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1061])).
% 3.31/0.90 thf(f1061,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : set(X1),X3 : X1 > X0,X4 : set(X1)] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(set(X1),sTfun(set(X1),$o),ord_less_eq(set(X1)),X4),X2)) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),X3))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true))),
% 3.31/0.90 inference(flattening,[],[f1060])).
% 3.31/0.90 thf(f1060,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : set(X1),X3 : X1 > X0,X4 : set(X1)] : ((($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(set(X1),sTfun(set(X1),$o),ord_less_eq(set(X1)),X4),X2))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),X3))) | ((topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f515])).
% 3.31/0.90 thf(f515,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : (((topolo503727757_space(X0) = $true) & (topolo503727757_space(X1) = $true)) => ! [X2 : set(X1),X3 : X1 > X0,X4 : set(X1)] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),X3)) => (($true = vAPP(set(X1),$o,vAPP(set(X1),sTfun(set(X1),$o),ord_less_eq(set(X1)),X4),X2)) => ($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X4),X3)))))),
% 3.31/0.90 inference(fool_elimination,[],[f514])).
% 3.31/0.90 thf(f514,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType] : ((topolo503727757_space(X0) & topolo503727757_space(X1)) => ! [X2 : set(X1),X3 : X1 > X0,X4 : set(X1)] : (vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),X3) => (vAPP(set(X1),$o,vAPP(set(X1),sTfun(set(X1),$o),ord_less_eq(set(X1)),X4),X2) => vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X4),X3))))),
% 3.31/0.90 inference(rectify,[],[f235])).
% 3.31/0.90 thf(f235,axiom,(
% 3.31/0.90 ! [X2 : $tType,X0 : $tType] : ((topolo503727757_space(X2) & topolo503727757_space(X0)) => ! [X111 : set(X0),X54 : X0 > X2,X78 : set(X0)] : (vAPP(sTfun(X0,X2),$o,vAPP(set(X0),sTfun(sTfun(X0,X2),$o),topolo2071040574ous_on(X0,X2),X111),X54) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X78),X111) => vAPP(sTfun(X0,X2),$o,vAPP(set(X0),sTfun(sTfun(X0,X2),$o),topolo2071040574ous_on(X0,X2),X78),X54))))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_continuous__on__subset)).
% 3.31/0.90 thf(f3970,plain,(
% 3.31/0.90 spl132_169),
% 3.31/0.90 inference(avatar_split_clause,[],[f1521,f3968])).
% 3.31/0.90 thf(f3968,plain,(
% 3.31/0.90 spl132_169 <=> ! [X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : ((X1 = X2) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),top_top(set(sum_sum(X0,X0))))) | (finite_finite(X0) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_169])])).
% 3.31/0.90 thf(f1521,plain,(
% 3.31/0.90 ( ! [X0 : $tType,X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : ((X1 = X2) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),top_top(set(sum_sum(X0,X0))))) | (finite_finite(X0) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f999])).
% 3.31/0.90 thf(f999,plain,(
% 3.31/0.90 ! [X0 : $tType] : (! [X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : ((X1 = X2) | ($true != vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),top_top(set(sum_sum(X0,X0)))))) | (finite_finite(X0) != $true))),
% 3.31/0.90 inference(ennf_transformation,[],[f423])).
% 3.31/0.90 thf(f423,plain,(
% 3.31/0.90 ! [X0 : $tType] : ((finite_finite(X0) = $true) => ! [X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),top_top(set(sum_sum(X0,X0))))) => (X1 = X2)))),
% 3.31/0.90 inference(fool_elimination,[],[f422])).
% 3.31/0.90 thf(f422,plain,(
% 3.31/0.90 ! [X0 : $tType] : (finite_finite(X0) => ! [X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X2 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X2),top_top(set(sum_sum(X0,X0)))) => (X1 = X2)))),
% 3.31/0.90 inference(rectify,[],[f204])).
% 3.31/0.90 thf(f204,axiom,(
% 3.31/0.90 ! [X0 : $tType] : (finite_finite(X0) => ! [X7 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X56 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X56),top_top(set(sum_sum(X0,X0)))) => (X7 = X56)))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_agree__UNIV__eq)).
% 3.31/0.90 thf(f3936,plain,(
% 3.31/0.90 spl132_168),
% 3.31/0.90 inference(avatar_split_clause,[],[f1671,f3934])).
% 3.31/0.90 thf(f3934,plain,(
% 3.31/0.90 spl132_168 <=> ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0)] : ((vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),sK45(X0,X1),X2)) = X2) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_168])])).
% 3.31/0.90 thf(f1671,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0)] : ((vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),sK45(X0,X1),X2)) = X2) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1385])).
% 3.31/0.90 thf(f1385,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0)] : ((vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),sK45(X0,X1),X2)) = X2) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f1180,f1384])).
% 3.31/0.90 thf(f1384,plain,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0)] : (? [X3 : frechet_strm(X1,X0)] : (vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X3) = X2) => (vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),sK45(X0,X1),X2)) = X2))),
% 3.31/0.90 introduced(choice_axiom,[])).
% 3.31/0.90 thf(f1180,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0)] : (? [X3 : frechet_strm(X1,X0)] : (vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X3) = X2) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 inference(ennf_transformation,[],[f683])).
% 3.31/0.90 thf(f683,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0)] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))) => ~! [X3 : frechet_strm(X1,X0)] : (vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X3) != X2))),
% 3.31/0.90 inference(fool_elimination,[],[f682])).
% 3.31/0.90 thf(f682,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0)] : (vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))) => ~! [X3 : frechet_strm(X1,X0)] : (vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X3) != X2))),
% 3.31/0.90 inference(rectify,[],[f18])).
% 3.31/0.90 thf(f18,axiom,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X15 : trm(X0,X1)] : (vAPP(set(trm(X0,X1)),$o,vAPP(trm(X0,X1),sTfun(set(trm(X0,X1)),$o),member(trm(X0,X1)),X15),vAPP(sTfun(trm(X0,X1),$o),set(trm(X0,X1)),collect(trm(X0,X1)),dfree(X0,X1))) => ~! [X23 : frechet_strm(X0,X1)] : (vAPP(frechet_strm(X0,X1),trm(X0,X1),frechet_raw_term(X0,X1),X23) != X15))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_raw__term__cases)).
% 3.31/0.90 thf(f3932,plain,(
% 3.31/0.90 spl132_167),
% 3.31/0.90 inference(avatar_split_clause,[],[f1670,f3930])).
% 3.31/0.90 thf(f1670,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0)] : ((vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X2)) = X2) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1179])).
% 3.31/0.90 thf(f1179,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0)] : ((vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X2)) = X2) | ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.90 inference(ennf_transformation,[],[f681])).
% 3.31/0.90 thf(f681,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0)] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))) => (vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X2)) = X2))),
% 3.31/0.90 inference(fool_elimination,[],[f680])).
% 3.31/0.90 thf(f680,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0)] : (vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X2),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))) => (vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X2)) = X2))),
% 3.31/0.90 inference(rectify,[],[f30])).
% 3.31/0.90 thf(f30,axiom,(
% 3.31/0.90 ! [X1 : $tType,X0 : $tType,X15 : trm(X0,X1)] : (vAPP(set(trm(X0,X1)),$o,vAPP(trm(X0,X1),sTfun(set(trm(X0,X1)),$o),member(trm(X0,X1)),X15),vAPP(sTfun(trm(X0,X1),$o),set(trm(X0,X1)),collect(trm(X0,X1)),dfree(X0,X1))) => (vAPP(frechet_strm(X0,X1),trm(X0,X1),frechet_raw_term(X0,X1),vAPP(trm(X0,X1),frechet_strm(X0,X1),frechet_simple_term(X0,X1),X15)) = X15))),
% 3.31/0.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_simple__term__inverse)).
% 3.31/0.90 thf(f3910,plain,(
% 3.31/0.90 spl132_166),
% 3.31/0.90 inference(avatar_split_clause,[],[f1651,f3908])).
% 3.31/0.90 thf(f3908,plain,(
% 3.31/0.90 spl132_166 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : set(sum_sum(X2,sum_sum(X1,X0))),X3 : denota1663640101rp_ext(X2,X1,X0,product_unit)] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X3),X4)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 introduced(avatar_definition,[new_symbols(naming,[spl132_166])])).
% 3.31/0.90 thf(f1651,plain,(
% 3.31/0.90 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : set(sum_sum(X2,sum_sum(X1,X0)))] : (($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X3),X4)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.90 inference(cnf_transformation,[],[f1152])).
% 3.31/0.90 thf(f1152,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : set(sum_sum(X2,sum_sum(X1,X0)))] : ($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X3),X4)) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.90 inference(flattening,[],[f1151])).
% 3.31/0.90 thf(f1151,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : set(sum_sum(X2,sum_sum(X1,X0)))] : ($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X3),X4)) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.90 inference(ennf_transformation,[],[f651])).
% 3.31/0.90 thf(f651,plain,(
% 3.31/0.90 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : set(sum_sum(X2,sum_sum(X1,X0)))] : ($true = vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X3),X4)))),
% 3.31/0.90 inference(fool_elimination,[],[f650])).
% 3.31/0.91 thf(f650,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : denota1663640101rp_ext(X2,X1,X0,product_unit),X4 : set(sum_sum(X2,sum_sum(X1,X0)))] : vAPP(set(sum_sum(X2,sum_sum(X1,X0))),$o,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o),vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(denota1663640101rp_ext(X2,X1,X0,product_unit),sTfun(set(sum_sum(X2,sum_sum(X1,X0))),$o)),denotational_Iagree(X2,X1,X0),X3),X3),X4))),
% 3.31/0.91 inference(rectify,[],[f26])).
% 3.31/0.91 thf(f26,axiom,(
% 3.31/0.91 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X26 : denota1663640101rp_ext(X0,X2,X1,product_unit),X11 : set(sum_sum(X0,sum_sum(X2,X1)))] : vAPP(set(sum_sum(X0,sum_sum(X2,X1))),$o,vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o),vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(denota1663640101rp_ext(X0,X2,X1,product_unit),sTfun(set(sum_sum(X0,sum_sum(X2,X1))),$o)),denotational_Iagree(X0,X2,X1),X26),X26),X11))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Iagree__refl)).
% 3.31/0.91 thf(f3861,plain,(
% 3.31/0.91 spl132_165 | ~spl132_99 | ~spl132_100 | ~spl132_116 | ~spl132_164),
% 3.31/0.91 inference(avatar_split_clause,[],[f3840,f3836,f3045,f2916,f2912,f3859])).
% 3.31/0.91 thf(f3859,plain,(
% 3.31/0.91 spl132_165 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : X0 > X1 > $o] : (($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,sK48(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,sK47(X1,X0),X3))) | ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK67(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X1,$o)),X1,sK66(X0,X1),X2))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_165])])).
% 3.31/0.91 thf(f2912,plain,(
% 3.31/0.91 spl132_99 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : X0] : (vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3)) = X3)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_99])])).
% 3.31/0.91 thf(f2916,plain,(
% 3.31/0.91 spl132_100 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X2 : X1] : (vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X2),X3)) = X2)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_100])])).
% 3.31/0.91 thf(f3045,plain,(
% 3.31/0.91 spl132_116 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK47(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK48(X0,X1),X2)) = X2)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_116])])).
% 3.31/0.91 thf(f3836,plain,(
% 3.31/0.91 spl132_164 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK67(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X1,$o)),X1,sK66(X0,X1),X2))) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_164])])).
% 3.31/0.91 thf(f3840,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X1,X0)] : (($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,sK48(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,sK47(X1,X0),X3))) | ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK67(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X1,$o)),X1,sK66(X0,X1),X2)))) ) | (~spl132_99 | ~spl132_100 | ~spl132_116 | ~spl132_164)),
% 3.31/0.91 inference(forward_demodulation,[],[f3839,f3062])).
% 3.31/0.91 thf(f3062,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2) = vAPP(product_prod(X1,X0),X0,sK48(X1,X0),X2))) ) | (~spl132_99 | ~spl132_116)),
% 3.31/0.91 inference(superposition,[],[f2913,f3046])).
% 3.31/0.91 thf(f3046,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK47(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK48(X0,X1),X2)) = X2)) ) | ~spl132_116),
% 3.31/0.91 inference(avatar_component_clause,[],[f3045])).
% 3.31/0.91 thf(f2913,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : ((vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3)) = X3)) ) | ~spl132_99),
% 3.31/0.91 inference(avatar_component_clause,[],[f2912])).
% 3.31/0.91 thf(f3839,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X1,X0)] : (($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,sK47(X1,X0),X3))) | ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK67(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X1,$o)),X1,sK66(X0,X1),X2)))) ) | (~spl132_100 | ~spl132_116 | ~spl132_164)),
% 3.31/0.91 inference(forward_demodulation,[],[f3837,f3061])).
% 3.31/0.91 thf(f3061,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2) = vAPP(product_prod(X1,X0),X1,sK47(X1,X0),X2))) ) | (~spl132_100 | ~spl132_116)),
% 3.31/0.91 inference(superposition,[],[f2917,f3046])).
% 3.31/0.91 thf(f2917,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0] : ((vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X2),X3)) = X2)) ) | ~spl132_100),
% 3.31/0.91 inference(avatar_component_clause,[],[f2916])).
% 3.31/0.91 thf(f3837,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK67(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X1,$o)),X1,sK66(X0,X1),X2))) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3)))) ) | ~spl132_164),
% 3.31/0.91 inference(avatar_component_clause,[],[f3836])).
% 3.31/0.91 thf(f3838,plain,(
% 3.31/0.91 spl132_164),
% 3.31/0.91 inference(avatar_split_clause,[],[f1713,f3836])).
% 3.31/0.91 thf(f1713,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK67(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X1,$o)),X1,sK66(X0,X1),X2))) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1411])).
% 3.31/0.91 thf(f1411,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK67(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X1,$o)),X1,sK66(X0,X1),X2))) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK66,sK67])],[f1216,f1410])).
% 3.31/0.91 thf(f1410,plain,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o] : (? [X4 : X1,X5 : X0] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X5),X4)) => ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK67(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X1,$o)),X1,sK66(X0,X1),X2))))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1216,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X1,X0)] : (? [X4 : X1,X5 : X0] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X5),X4)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))))),
% 3.31/0.91 inference(ennf_transformation,[],[f938])).
% 3.31/0.91 thf(f938,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))) => ~! [X4 : X1,X5 : X0] : ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X5),X4)))),
% 3.31/0.91 inference(flattening,[],[f743])).
% 3.31/0.91 thf(f743,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))) => ~! [X4 : X1,X5 : X0] : ~($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X5),X4)))),
% 3.31/0.91 inference(fool_elimination,[],[f742])).
% 3.31/0.91 thf(f742,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X1,X0)] : (vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3)) => ~! [X4 : X1,X5 : X0] : ~vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X5),X4))),
% 3.31/0.91 inference(rectify,[],[f97])).
% 3.31/0.91 thf(f97,axiom,(
% 3.31/0.91 ! [X0 : $tType,X2 : $tType,X24 : X0 > X2 > $o,X59 : product_prod(X2,X0)] : (vAPP(X2,$o,vAPP(X0,sTfun(X2,$o),X24,vAPP(product_prod(X2,X0),X0,product_snd(X2,X0),X59)),vAPP(product_prod(X2,X0),X2,product_fst(X2,X0),X59)) => ~! [X23 : X2,X34 : X0] : ~vAPP(X2,$o,vAPP(X0,sTfun(X2,$o),X24,X34),X23))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_exE__realizer_H)).
% 3.31/0.91 thf(f3834,plain,(
% 3.31/0.91 spl132_163),
% 3.31/0.91 inference(avatar_split_clause,[],[f1698,f3832])).
% 3.31/0.91 thf(f3832,plain,(
% 3.31/0.91 spl132_163 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X2 : X1 > trm(X0,X1)] : (($true = vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(sTfun(X1,trm(X0,X1)),trm(X0,X1),vAPP(X0,sTfun(sTfun(X1,trm(X0,X1)),trm(X0,X1)),function(X0,X1),X3),X2))) | ($true != vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(X1,trm(X0,X1),X2,vAPP(sTfun(X1,trm(X0,X1)),X1,sK57(X0,X1),X2)))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_163])])).
% 3.31/0.91 thf(f1698,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > trm(X0,X1),X3 : X0] : (($true = vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(sTfun(X1,trm(X0,X1)),trm(X0,X1),vAPP(X0,sTfun(sTfun(X1,trm(X0,X1)),trm(X0,X1)),function(X0,X1),X3),X2))) | ($true != vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(X1,trm(X0,X1),X2,vAPP(sTfun(X1,trm(X0,X1)),X1,sK57(X0,X1),X2))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1401])).
% 3.31/0.91 thf(f1401,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1 > trm(X0,X1),X3 : X0] : (($true = vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(sTfun(X1,trm(X0,X1)),trm(X0,X1),vAPP(X0,sTfun(sTfun(X1,trm(X0,X1)),trm(X0,X1)),function(X0,X1),X3),X2))) | ($true != vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(X1,trm(X0,X1),X2,vAPP(sTfun(X1,trm(X0,X1)),X1,sK57(X0,X1),X2)))))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f1196,f1400])).
% 3.31/0.91 thf(f1400,plain,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X2 : X1 > trm(X0,X1)] : (? [X4 : X1] : ($true != vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(X1,trm(X0,X1),X2,X4))) => ($true != vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(X1,trm(X0,X1),X2,vAPP(sTfun(X1,trm(X0,X1)),X1,sK57(X0,X1),X2)))))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1196,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1 > trm(X0,X1),X3 : X0] : (($true = vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(sTfun(X1,trm(X0,X1)),trm(X0,X1),vAPP(X0,sTfun(sTfun(X1,trm(X0,X1)),trm(X0,X1)),function(X0,X1),X3),X2))) | ? [X4 : X1] : ($true != vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(X1,trm(X0,X1),X2,X4))))),
% 3.31/0.91 inference(ennf_transformation,[],[f717])).
% 3.31/0.91 thf(f717,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1 > trm(X0,X1),X3 : X0] : (! [X4 : X1] : ($true = vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(X1,trm(X0,X1),X2,X4))) => ($true = vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(sTfun(X1,trm(X0,X1)),trm(X0,X1),vAPP(X0,sTfun(sTfun(X1,trm(X0,X1)),trm(X0,X1)),function(X0,X1),X3),X2))))),
% 3.31/0.91 inference(fool_elimination,[],[f716])).
% 3.31/0.91 thf(f716,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1 > trm(X0,X1),X3 : X0] : (! [X4 : X1] : vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(X1,trm(X0,X1),X2,X4)) => vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(sTfun(X1,trm(X0,X1)),trm(X0,X1),vAPP(X0,sTfun(sTfun(X1,trm(X0,X1)),trm(X0,X1)),function(X0,X1),X3),X2)))),
% 3.31/0.91 inference(rectify,[],[f74])).
% 3.31/0.91 thf(f74,axiom,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X17 : X1 > trm(X0,X1),X18 : X0] : (! [X27 : X1] : vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(X1,trm(X0,X1),X17,X27)) => vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(sTfun(X1,trm(X0,X1)),trm(X0,X1),vAPP(X0,sTfun(sTfun(X1,trm(X0,X1)),trm(X0,X1)),function(X0,X1),X18),X17)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_dfree__Fun)).
% 3.31/0.91 thf(f3830,plain,(
% 3.31/0.91 spl132_162),
% 3.31/0.91 inference(avatar_split_clause,[],[f1647,f3828])).
% 3.31/0.91 thf(f3828,plain,(
% 3.31/0.91 spl132_162 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : frechet_good_interp(X2,X1,X0),X3 : frechet_good_interp(X2,X1,X0) > $o] : (($true = vAPP(frechet_good_interp(X2,X1,X0),$o,X3,X4)) | ($true != vAPP(frechet_good_interp(X2,X1,X0),$o,X3,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(sTfun(frechet_good_interp(X2,X1,X0),$o),denota1663640101rp_ext(X2,X1,X0,product_unit),sK35(X0,X1,X2),X3)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_162])])).
% 3.31/0.91 thf(f1647,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : frechet_good_interp(X2,X1,X0) > $o,X4 : frechet_good_interp(X2,X1,X0)] : (($true = vAPP(frechet_good_interp(X2,X1,X0),$o,X3,X4)) | ($true != vAPP(frechet_good_interp(X2,X1,X0),$o,X3,vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(sTfun(frechet_good_interp(X2,X1,X0),$o),denota1663640101rp_ext(X2,X1,X0,product_unit),sK35(X0,X1,X2),X3)))) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1369])).
% 3.31/0.91 thf(f3787,plain,(
% 3.31/0.91 spl132_161),
% 3.31/0.91 inference(avatar_split_clause,[],[f1696,f3785])).
% 3.31/0.91 thf(f3785,plain,(
% 3.31/0.91 spl132_161 <=> ! [X1 : $tType,X0 : $tType,X3 : frechet_strm(X1,X0),X2 : frechet_strm(X1,X0) > $o] : (($true = vAPP(frechet_strm(X1,X0),$o,X2,X3)) | ($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(sTfun(frechet_strm(X1,X0),$o),trm(X1,X0),sK56(X0,X1),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_161])])).
% 3.31/0.91 thf(f1696,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0) > $o,X3 : frechet_strm(X1,X0)] : (($true = vAPP(frechet_strm(X1,X0),$o,X2,X3)) | ($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(sTfun(frechet_strm(X1,X0),$o),trm(X1,X0),sK56(X0,X1),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1399])).
% 3.31/0.91 thf(f1399,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0) > $o,X3 : frechet_strm(X1,X0)] : (($true = vAPP(frechet_strm(X1,X0),$o,X2,X3)) | (($true != vAPP(frechet_strm(X1,X0),$o,X2,vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(sTfun(frechet_strm(X1,X0),$o),trm(X1,X0),sK56(X0,X1),X2)))) & ($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(sTfun(frechet_strm(X1,X0),$o),trm(X1,X0),sK56(X0,X1),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f1195,f1398])).
% 3.31/0.91 thf(f1398,plain,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0) > $o] : (? [X4 : trm(X1,X0)] : (($true != vAPP(frechet_strm(X1,X0),$o,X2,vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X4))) & ($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X4),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) => (($true != vAPP(frechet_strm(X1,X0),$o,X2,vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(sTfun(frechet_strm(X1,X0),$o),trm(X1,X0),sK56(X0,X1),X2)))) & ($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(sTfun(frechet_strm(X1,X0),$o),trm(X1,X0),sK56(X0,X1),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1195,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0) > $o,X3 : frechet_strm(X1,X0)] : (($true = vAPP(frechet_strm(X1,X0),$o,X2,X3)) | ? [X4 : trm(X1,X0)] : (($true != vAPP(frechet_strm(X1,X0),$o,X2,vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X4))) & ($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X4),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))))),
% 3.31/0.91 inference(ennf_transformation,[],[f715])).
% 3.31/0.91 thf(f715,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0) > $o,X3 : frechet_strm(X1,X0)] : (! [X4 : trm(X1,X0)] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X4),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))) => ($true = vAPP(frechet_strm(X1,X0),$o,X2,vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X4)))) => ($true = vAPP(frechet_strm(X1,X0),$o,X2,X3)))),
% 3.31/0.91 inference(fool_elimination,[],[f714])).
% 3.31/0.91 thf(f714,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0) > $o,X3 : frechet_strm(X1,X0)] : (! [X4 : trm(X1,X0)] : (vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X4),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))) => vAPP(frechet_strm(X1,X0),$o,X2,vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X4))) => vAPP(frechet_strm(X1,X0),$o,X2,X3))),
% 3.31/0.91 inference(rectify,[],[f40])).
% 3.31/0.91 thf(f40,axiom,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X24 : frechet_strm(X0,X1) > $o,X14 : frechet_strm(X0,X1)] : (! [X34 : trm(X0,X1)] : (vAPP(set(trm(X0,X1)),$o,vAPP(trm(X0,X1),sTfun(set(trm(X0,X1)),$o),member(trm(X0,X1)),X34),vAPP(sTfun(trm(X0,X1),$o),set(trm(X0,X1)),collect(trm(X0,X1)),dfree(X0,X1))) => vAPP(frechet_strm(X0,X1),$o,X24,vAPP(trm(X0,X1),frechet_strm(X0,X1),frechet_simple_term(X0,X1),X34))) => vAPP(frechet_strm(X0,X1),$o,X24,X14))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_simple__term__induct)).
% 3.31/0.91 thf(f3771,plain,(
% 3.31/0.91 spl132_160 | ~spl132_100 | ~spl132_116 | ~spl132_157),
% 3.31/0.91 inference(avatar_split_clause,[],[f3758,f3754,f3045,f2916,f3769])).
% 3.31/0.91 thf(f3769,plain,(
% 3.31/0.91 spl132_160 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,sK47(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,sK47(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_160])])).
% 3.31/0.91 thf(f3754,plain,(
% 3.31/0.91 spl132_157 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_157])])).
% 3.31/0.91 thf(f3758,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,sK47(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,sK47(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) ) | (~spl132_100 | ~spl132_116 | ~spl132_157)),
% 3.31/0.91 inference(forward_demodulation,[],[f3757,f3061])).
% 3.31/0.91 thf(f3757,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,sK47(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) ) | (~spl132_100 | ~spl132_116 | ~spl132_157)),
% 3.31/0.91 inference(forward_demodulation,[],[f3755,f3061])).
% 3.31/0.91 thf(f3755,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl132_157),
% 3.31/0.91 inference(avatar_component_clause,[],[f3754])).
% 3.31/0.91 thf(f3767,plain,(
% 3.31/0.91 spl132_159 | ~spl132_99 | ~spl132_116 | ~spl132_156),
% 3.31/0.91 inference(avatar_split_clause,[],[f3752,f3748,f3045,f2912,f3765])).
% 3.31/0.91 thf(f3765,plain,(
% 3.31/0.91 spl132_159 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0)] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,sK48(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,sK48(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_159])])).
% 3.31/0.91 thf(f3748,plain,(
% 3.31/0.91 spl132_156 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0)] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_156])])).
% 3.31/0.91 thf(f3752,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,sK48(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,sK48(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) ) | (~spl132_99 | ~spl132_116 | ~spl132_156)),
% 3.31/0.91 inference(forward_demodulation,[],[f3751,f3062])).
% 3.31/0.91 thf(f3751,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,sK48(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) ) | (~spl132_99 | ~spl132_116 | ~spl132_156)),
% 3.31/0.91 inference(forward_demodulation,[],[f3749,f3062])).
% 3.31/0.91 thf(f3749,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl132_156),
% 3.31/0.91 inference(avatar_component_clause,[],[f3748])).
% 3.31/0.91 thf(f3763,plain,(
% 3.31/0.91 spl132_158),
% 3.31/0.91 inference(avatar_split_clause,[],[f1816,f3760])).
% 3.31/0.91 thf(f3760,plain,(
% 3.31/0.91 spl132_158 <=> (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t1)) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_158])])).
% 3.31/0.91 thf(f1816,plain,(
% 3.31/0.91 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t1)) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f907])).
% 3.31/0.91 thf(f907,plain,(
% 3.31/0.91 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t1)) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f906])).
% 3.31/0.91 thf(f906,plain,(
% 3.31/0.91 vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t1))),
% 3.31/0.91 inference(rectify,[],[f3])).
% 3.31/0.91 thf(f3,axiom,(
% 3.31/0.91 vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t1))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_agree1)).
% 3.31/0.91 thf(f3756,plain,(
% 3.31/0.91 spl132_157),
% 3.31/0.91 inference(avatar_split_clause,[],[f1563,f3754])).
% 3.31/0.91 thf(f1563,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1045])).
% 3.31/0.91 thf(f1045,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (! [X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3))) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.91 inference(flattening,[],[f1044])).
% 3.31/0.91 thf(f1044,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (! [X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3))) | ((ord(X0) != $true) | ($true != ord(X1))))),
% 3.31/0.91 inference(ennf_transformation,[],[f499])).
% 3.31/0.91 thf(f499,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((ord(X0) = $true) & ($true = ord(X1))) => ! [X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3)))))),
% 3.31/0.91 inference(fool_elimination,[],[f498])).
% 3.31/0.91 thf(f498,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((ord(X0) & ord(X1)) => ! [X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))))),
% 3.31/0.91 inference(rectify,[],[f95])).
% 3.31/0.91 thf(f95,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType] : ((ord(X2) & ord(X0)) => ! [X14 : product_prod(X0,X2),X15 : product_prod(X0,X2)] : (vAPP(product_prod(X0,X2),$o,vAPP(product_prod(X0,X2),sTfun(product_prod(X0,X2),$o),ord_less_eq(product_prod(X0,X2)),X14),X15) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X0,X2),X0,product_fst(X0,X2),X14)),vAPP(product_prod(X0,X2),X0,product_fst(X0,X2),X15))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_fst__mono)).
% 3.31/0.91 thf(f3750,plain,(
% 3.31/0.91 spl132_156),
% 3.31/0.91 inference(avatar_split_clause,[],[f1562,f3748])).
% 3.31/0.91 thf(f1562,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1043])).
% 3.31/0.91 thf(f1043,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (! [X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3))) | (ord(X0) != $true) | ($true != ord(X1)))),
% 3.31/0.91 inference(flattening,[],[f1042])).
% 3.31/0.91 thf(f1042,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (! [X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3))) | ($true != vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3))) | ((ord(X0) != $true) | ($true != ord(X1))))),
% 3.31/0.91 inference(ennf_transformation,[],[f497])).
% 3.31/0.91 thf(f497,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((ord(X0) = $true) & ($true = ord(X1))) => ! [X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)))))),
% 3.31/0.91 inference(fool_elimination,[],[f496])).
% 3.31/0.91 thf(f496,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((ord(X0) & ord(X1)) => ! [X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (vAPP(product_prod(X1,X0),$o,vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),ord_less_eq(product_prod(X1,X0)),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3))))),
% 3.31/0.91 inference(rectify,[],[f96])).
% 3.31/0.91 thf(f96,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType] : ((ord(X2) & ord(X0)) => ! [X14 : product_prod(X0,X2),X15 : product_prod(X0,X2)] : (vAPP(product_prod(X0,X2),$o,vAPP(product_prod(X0,X2),sTfun(product_prod(X0,X2),$o),ord_less_eq(product_prod(X0,X2)),X14),X15) => vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(product_prod(X0,X2),X2,product_snd(X0,X2),X14)),vAPP(product_prod(X0,X2),X2,product_snd(X0,X2),X15))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_snd__mono)).
% 3.31/0.91 thf(f3610,plain,(
% 3.31/0.91 spl132_155),
% 3.31/0.91 inference(avatar_split_clause,[],[f1666,f3608])).
% 3.31/0.91 thf(f3608,plain,(
% 3.31/0.91 spl132_155 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK43(X0),X2),X1))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_155])])).
% 3.31/0.91 thf(f1666,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK43(X0),X2),X1)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1381])).
% 3.31/0.91 thf(f1381,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK43(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK43(X0),X2),X1)))))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f1175,f1380])).
% 3.31/0.91 thf(f1380,plain,(
% 3.31/0.91 ! [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),sK43(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK43(X0),X2),X1)))))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1175,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))))),
% 3.31/0.91 inference(ennf_transformation,[],[f675])).
% 3.31/0.91 thf(f675,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) => ($true = vAPP(X0,$o,X2,X3))) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))))),
% 3.31/0.91 inference(fool_elimination,[],[f674])).
% 3.31/0.91 thf(f674,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (vAPP(X0,$o,X1,X3) => vAPP(X0,$o,X2,X3)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2)))),
% 3.31/0.91 inference(rectify,[],[f115])).
% 3.31/0.91 thf(f115,axiom,(
% 3.31/0.91 ! [X0 : $tType,X24 : X0 > $o,X53 : X0 > $o] : (! [X23 : X0] : (vAPP(X0,$o,X24,X23) => vAPP(X0,$o,X53,X23)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X24)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X53)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Collect__mono)).
% 3.31/0.91 thf(f3606,plain,(
% 3.31/0.91 spl132_154),
% 3.31/0.91 inference(avatar_split_clause,[],[f1665,f3604])).
% 3.31/0.91 thf(f3604,plain,(
% 3.31/0.91 spl132_154 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK43(X0),X2),X1))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_154])])).
% 3.31/0.91 thf(f1665,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK43(X0),X2),X1)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1381])).
% 3.31/0.91 thf(f3602,plain,(
% 3.31/0.91 spl132_153),
% 3.31/0.91 inference(avatar_split_clause,[],[f1466,f3599])).
% 3.31/0.91 thf(f3599,plain,(
% 3.31/0.91 spl132_153 <=> (f0(sf,sz) = vAPP(sTfun(sz,trm(sf,sz)),sTfun(sf,trm(sf,sz)),vAPP(sTfun(sf,sTfun(sTfun(sz,trm(sf,sz)),trm(sf,sz))),sTfun(sTfun(sz,trm(sf,sz)),sTfun(sf,trm(sf,sz))),cCOMB,function(sf,sz)),empty(sz,sf)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_153])])).
% 3.31/0.91 thf(f1466,plain,(
% 3.31/0.91 (f0(sf,sz) = vAPP(sTfun(sz,trm(sf,sz)),sTfun(sf,trm(sf,sz)),vAPP(sTfun(sf,sTfun(sTfun(sz,trm(sf,sz)),trm(sf,sz))),sTfun(sTfun(sz,trm(sf,sz)),sTfun(sf,trm(sf,sz))),cCOMB,function(sf,sz)),empty(sz,sf)))),
% 3.31/0.91 inference(cnf_transformation,[],[f345])).
% 3.31/0.91 thf(f345,plain,(
% 3.31/0.91 (f0(sf,sz) = vAPP(sTfun(sz,trm(sf,sz)),sTfun(sf,trm(sf,sz)),vAPP(sTfun(sf,sTfun(sTfun(sz,trm(sf,sz)),trm(sf,sz))),sTfun(sTfun(sz,trm(sf,sz)),sTfun(sf,trm(sf,sz))),cCOMB,function(sf,sz)),empty(sz,sf)))),
% 3.31/0.91 inference(fool_elimination,[],[f344])).
% 3.31/0.91 thf(f344,plain,(
% 3.31/0.91 (f0(sf,sz) = (^[X0 : sf] : (vAPP(sTfun(sz,trm(sf,sz)),trm(sf,sz),vAPP(sf,sTfun(sTfun(sz,trm(sf,sz)),trm(sf,sz)),function(sf,sz),X0),empty(sz,sf)))))),
% 3.31/0.91 inference(rectify,[],[f102])).
% 3.31/0.91 thf(f102,axiom,(
% 3.31/0.91 (f0(sf,sz) = (^[X93 : sf] : (vAPP(sTfun(sz,trm(sf,sz)),trm(sf,sz),vAPP(sf,sTfun(sTfun(sz,trm(sf,sz)),trm(sf,sz)),function(sf,sz),X93),empty(sz,sf)))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_f0__def)).
% 3.31/0.91 thf(f3590,plain,(
% 3.31/0.91 spl132_152),
% 3.31/0.91 inference(avatar_split_clause,[],[f1778,f3588])).
% 3.31/0.91 thf(f3588,plain,(
% 3.31/0.91 spl132_152 <=> ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_152])])).
% 3.31/0.91 thf(f1778,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1300])).
% 3.31/0.91 thf(f1300,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 3.31/0.91 inference(flattening,[],[f1299])).
% 3.31/0.91 thf(f1299,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : ((($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5))) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 3.31/0.91 inference(ennf_transformation,[],[f837])).
% 3.31/0.91 thf(f837,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)) => (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5)) => ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4))))),
% 3.31/0.91 inference(fool_elimination,[],[f836])).
% 3.31/0.91 thf(f836,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4) => (vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5) => vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)))),
% 3.31/0.91 inference(rectify,[],[f183])).
% 3.31/0.91 thf(f183,axiom,(
% 3.31/0.91 ! [X0 : $tType,X2 : $tType,X24 : X0 > X2 > $o,X14 : X0,X15 : X2,X53 : X0 > X2 > $o] : (vAPP(X2,$o,vAPP(X0,sTfun(X2,$o),X24,X14),X15) => (vAPP(sTfun(X0,sTfun(X2,$o)),$o,vAPP(sTfun(X0,sTfun(X2,$o)),sTfun(sTfun(X0,sTfun(X2,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X2,$o))),X24),X53) => vAPP(X2,$o,vAPP(X0,sTfun(X2,$o),X53,X14),X15)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_rev__predicate2D)).
% 3.31/0.91 thf(f3586,plain,(
% 3.31/0.91 spl132_151 | ~spl132_27 | ~spl132_36),
% 3.31/0.91 inference(avatar_split_clause,[],[f2262,f2234,f2167,f3583])).
% 3.31/0.91 thf(f3583,plain,(
% 3.31/0.91 spl132_151 <=> ($true = type($o))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_151])])).
% 3.31/0.91 thf(f2167,plain,(
% 3.31/0.91 spl132_27 <=> (linorder($o) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_27])])).
% 3.31/0.91 thf(f2234,plain,(
% 3.31/0.91 spl132_36 <=> ! [X0 : $tType] : ((type(X0) = $true) | (linorder(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_36])])).
% 3.31/0.91 thf(f2262,plain,(
% 3.31/0.91 ($true = type($o)) | (~spl132_27 | ~spl132_36)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2253])).
% 3.31/0.91 thf(f2253,plain,(
% 3.31/0.91 ($true != $true) | ($true = type($o)) | (~spl132_27 | ~spl132_36)),
% 3.31/0.91 inference(superposition,[],[f2235,f2169])).
% 3.31/0.91 thf(f2169,plain,(
% 3.31/0.91 (linorder($o) = $true) | ~spl132_27),
% 3.31/0.91 inference(avatar_component_clause,[],[f2167])).
% 3.31/0.91 thf(f2235,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((linorder(X0) != $true) | (type(X0) = $true)) ) | ~spl132_36),
% 3.31/0.91 inference(avatar_component_clause,[],[f2234])).
% 3.31/0.91 thf(f3565,plain,(
% 3.31/0.91 spl132_150),
% 3.31/0.91 inference(avatar_split_clause,[],[f1707,f3563])).
% 3.31/0.91 thf(f3563,plain,(
% 3.31/0.91 spl132_150 <=> ! [X1 : $tType,X0 : $tType,X3 : trm(X1,X0),X2 : trm(X1,X0)] : (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X2),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X3)) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X2)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_150])])).
% 3.31/0.91 thf(f1707,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X2),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X3)) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X2))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1206])).
% 3.31/0.91 thf(f1206,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X2),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X3)) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X2)))),
% 3.31/0.91 inference(flattening,[],[f1205])).
% 3.31/0.91 thf(f1205,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : ((($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X2),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X2)))),
% 3.31/0.91 inference(ennf_transformation,[],[f731])).
% 3.31/0.91 thf(f731,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),X2)) => (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),X3)) => ($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X2),X3)))))),
% 3.31/0.91 inference(fool_elimination,[],[f730])).
% 3.31/0.91 thf(f730,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : (vAPP(trm(X1,X0),$o,dfree(X1,X0),X2) => (vAPP(trm(X1,X0),$o,dfree(X1,X0),X3) => vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X2),X3))))),
% 3.31/0.91 inference(rectify,[],[f75])).
% 3.31/0.91 thf(f75,axiom,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X76 : trm(X0,X1),X77 : trm(X0,X1)] : (vAPP(trm(X0,X1),$o,dfree(X0,X1),X76) => (vAPP(trm(X0,X1),$o,dfree(X0,X1),X77) => vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(trm(X0,X1),trm(X0,X1),vAPP(trm(X0,X1),sTfun(trm(X0,X1),trm(X0,X1)),plus(X0,X1),X76),X77))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_dfree_Odfree__Plus)).
% 3.31/0.91 thf(f3561,plain,(
% 3.31/0.91 spl132_149),
% 3.31/0.91 inference(avatar_split_clause,[],[f1706,f3559])).
% 3.31/0.91 thf(f3559,plain,(
% 3.31/0.91 spl132_149 <=> ! [X1 : $tType,X0 : $tType,X3 : trm(X1,X0),X2 : trm(X1,X0)] : (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X2),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X3)) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X2)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_149])])).
% 3.31/0.91 thf(f1706,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X2),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X3)) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X2))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1204])).
% 3.31/0.91 thf(f1204,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X2),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X3)) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X2)))),
% 3.31/0.91 inference(flattening,[],[f1203])).
% 3.31/0.91 thf(f1203,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : ((($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X2),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X3))) | ($true != vAPP(trm(X1,X0),$o,dfree(X1,X0),X2)))),
% 3.31/0.91 inference(ennf_transformation,[],[f729])).
% 3.31/0.91 thf(f729,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),X2)) => (($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),X3)) => ($true = vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X2),X3)))))),
% 3.31/0.91 inference(fool_elimination,[],[f728])).
% 3.31/0.91 thf(f728,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0)] : (vAPP(trm(X1,X0),$o,dfree(X1,X0),X2) => (vAPP(trm(X1,X0),$o,dfree(X1,X0),X3) => vAPP(trm(X1,X0),$o,dfree(X1,X0),vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X2),X3))))),
% 3.31/0.91 inference(rectify,[],[f76])).
% 3.31/0.91 thf(f76,axiom,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X76 : trm(X0,X1),X77 : trm(X0,X1)] : (vAPP(trm(X0,X1),$o,dfree(X0,X1),X76) => (vAPP(trm(X0,X1),$o,dfree(X0,X1),X77) => vAPP(trm(X0,X1),$o,dfree(X0,X1),vAPP(trm(X0,X1),trm(X0,X1),vAPP(trm(X0,X1),sTfun(trm(X0,X1),trm(X0,X1)),times(X0,X1),X76),X77))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_dfree__Times)).
% 3.31/0.91 thf(f3504,plain,(
% 3.31/0.91 spl132_148),
% 3.31/0.91 inference(avatar_split_clause,[],[f1711,f3502])).
% 3.31/0.91 thf(f3502,plain,(
% 3.31/0.91 spl132_148 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_148])])).
% 3.31/0.91 thf(f1711,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1213])).
% 3.31/0.91 thf(f1213,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 inference(flattening,[],[f1212])).
% 3.31/0.91 thf(f1212,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : ((($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 inference(ennf_transformation,[],[f739])).
% 3.31/0.91 thf(f739,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3))))),
% 3.31/0.91 inference(fool_elimination,[],[f738])).
% 3.31/0.91 thf(f738,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)))),
% 3.31/0.91 inference(rectify,[],[f114])).
% 3.31/0.91 thf(f114,axiom,(
% 3.31/0.91 ! [X0 : $tType,X11 : set(X0),X12 : set(X0),X96 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X11),X12) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X12),X96) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X11),X96)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_subset__trans)).
% 3.31/0.91 thf(f3500,plain,(
% 3.31/0.91 spl132_147),
% 3.31/0.91 inference(avatar_split_clause,[],[f1704,f3498])).
% 3.31/0.91 thf(f3498,plain,(
% 3.31/0.91 spl132_147 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0) > $o] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK64(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK65(X0,X1),X2)))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_147])])).
% 3.31/0.91 thf(f1704,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK64(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK65(X0,X1),X2))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1409])).
% 3.31/0.91 thf(f1409,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK64(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK65(X0,X1),X2)))))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f1200,f1408])).
% 3.31/0.91 thf(f1408,plain,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o] : (? [X4 : X1,X5 : X0] : ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))) => ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK64(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK65(X0,X1),X2)))))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1200,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ? [X4 : X1,X5 : X0] : ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))))),
% 3.31/0.91 inference(ennf_transformation,[],[f725])).
% 3.31/0.91 thf(f725,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (! [X4 : X1,X5 : X0] : ($true = vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))) => ($true = vAPP(product_prod(X1,X0),$o,X2,X3)))),
% 3.31/0.91 inference(fool_elimination,[],[f724])).
% 3.31/0.91 thf(f724,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (! [X4 : X1,X5 : X0] : vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) => vAPP(product_prod(X1,X0),$o,X2,X3))),
% 3.31/0.91 inference(rectify,[],[f55])).
% 3.31/0.91 thf(f55,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType,X24 : product_prod(X0,X2) > $o,X59 : product_prod(X0,X2)] : (! [X57 : X0,X58 : X2] : vAPP(product_prod(X0,X2),$o,X24,vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X57),X58)) => vAPP(product_prod(X0,X2),$o,X24,X59))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_prod__cases)).
% 3.31/0.91 thf(f3496,plain,(
% 3.31/0.91 spl132_146),
% 3.31/0.91 inference(avatar_split_clause,[],[f1703,f3494])).
% 3.31/0.91 thf(f3494,plain,(
% 3.31/0.91 spl132_146 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0) > $o] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK62(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK63(X0,X1),X2)))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_146])])).
% 3.31/0.91 thf(f1703,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK62(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK63(X0,X1),X2))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1407])).
% 3.31/0.91 thf(f1407,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK62(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK63(X0,X1),X2)))))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63])],[f1199,f1406])).
% 3.31/0.91 thf(f1406,plain,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o] : (? [X4 : X1,X5 : X0] : ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))) => ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK62(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK63(X0,X1),X2)))))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1199,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ? [X4 : X1,X5 : X0] : ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))))),
% 3.31/0.91 inference(ennf_transformation,[],[f723])).
% 3.31/0.91 thf(f723,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (! [X4 : X1,X5 : X0] : ($true = vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))) => ($true = vAPP(product_prod(X1,X0),$o,X2,X3)))),
% 3.31/0.91 inference(fool_elimination,[],[f722])).
% 3.31/0.91 thf(f722,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (! [X4 : X1,X5 : X0] : vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) => vAPP(product_prod(X1,X0),$o,X2,X3))),
% 3.31/0.91 inference(rectify,[],[f52])).
% 3.31/0.91 thf(f52,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType,X24 : product_prod(X0,X2) > $o,X30 : product_prod(X0,X2)] : (! [X57 : X0,X58 : X2] : vAPP(product_prod(X0,X2),$o,X24,vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X57),X58)) => vAPP(product_prod(X0,X2),$o,X24,X30))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_old_Oprod_Oinducts)).
% 3.31/0.91 thf(f3492,plain,(
% 3.31/0.91 spl132_145 | ~spl132_25 | ~spl132_36),
% 3.31/0.91 inference(avatar_split_clause,[],[f2261,f2234,f2157,f3489])).
% 3.31/0.91 thf(f3489,plain,(
% 3.31/0.91 spl132_145 <=> ($true = type(product_unit))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_145])])).
% 3.31/0.91 thf(f2157,plain,(
% 3.31/0.91 spl132_25 <=> (linorder(product_unit) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_25])])).
% 3.31/0.91 thf(f2261,plain,(
% 3.31/0.91 ($true = type(product_unit)) | (~spl132_25 | ~spl132_36)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2254])).
% 3.31/0.91 thf(f2254,plain,(
% 3.31/0.91 ($true != $true) | ($true = type(product_unit)) | (~spl132_25 | ~spl132_36)),
% 3.31/0.91 inference(superposition,[],[f2235,f2159])).
% 3.31/0.91 thf(f2159,plain,(
% 3.31/0.91 (linorder(product_unit) = $true) | ~spl132_25),
% 3.31/0.91 inference(avatar_component_clause,[],[f2157])).
% 3.31/0.91 thf(f3469,plain,(
% 3.31/0.91 spl132_144),
% 3.31/0.91 inference(avatar_split_clause,[],[f1522,f3467])).
% 3.31/0.91 thf(f3467,plain,(
% 3.31/0.91 spl132_144 <=> ! [X0 : $tType,X2 : set(sum_sum(X0,X0)),X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X1),X2)) | (finite_finite(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_144])])).
% 3.31/0.91 thf(f1522,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : set(sum_sum(X0,X0)),X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0))] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X1),X2)) | (finite_finite(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1000])).
% 3.31/0.91 thf(f1000,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X2 : set(sum_sum(X0,X0))] : ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X1),X2)) | (finite_finite(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f425])).
% 3.31/0.91 thf(f425,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((finite_finite(X0) = $true) => ! [X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X2 : set(sum_sum(X0,X0))] : ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X1),X2)))),
% 3.31/0.91 inference(fool_elimination,[],[f424])).
% 3.31/0.91 thf(f424,plain,(
% 3.31/0.91 ! [X0 : $tType] : (finite_finite(X0) => ! [X1 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X2 : set(sum_sum(X0,X0))] : vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X1),X1),X2))),
% 3.31/0.91 inference(rectify,[],[f7])).
% 3.31/0.91 thf(f7,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (finite_finite(X0) => ! [X7 : product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),X11 : set(sum_sum(X0,X0))] : vAPP(set(sum_sum(X0,X0)),$o,vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o),vAPP(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(product_prod(finite_Cartesian_vec(real,X0),finite_Cartesian_vec(real,X0)),sTfun(set(sum_sum(X0,X0)),$o)),denotational_Vagree(X0),X7),X7),X11))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_agree__refl)).
% 3.31/0.91 thf(f3408,plain,(
% 3.31/0.91 spl132_143),
% 3.31/0.91 inference(avatar_split_clause,[],[f1695,f3406])).
% 3.31/0.91 thf(f3406,plain,(
% 3.31/0.91 spl132_143 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X2 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK55(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK55(X0,X1),X3),X2))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_143])])).
% 3.31/0.91 thf(f1695,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK55(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK55(X0,X1),X3),X2)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1397])).
% 3.31/0.91 thf(f1397,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK55(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK55(X0,X1),X3),X2))))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f1194,f1396])).
% 3.31/0.91 thf(f1396,plain,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (? [X4 : X1] : (vAPP(X1,X0,X3,X4) != vAPP(X1,X0,X2,X4)) => (vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK55(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK55(X0,X1),X3),X2))))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1194,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | ? [X4 : X1] : (vAPP(X1,X0,X3,X4) != vAPP(X1,X0,X2,X4)))),
% 3.31/0.91 inference(ennf_transformation,[],[f937])).
% 3.31/0.91 thf(f937,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (! [X4 : X1] : (vAPP(X1,X0,X3,X4) = vAPP(X1,X0,X2,X4)) => (X2 = X3))),
% 3.31/0.91 inference(rectify,[],[f49])).
% 3.31/0.91 thf(f49,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType,X54 : X0 > X2,X55 : X0 > X2] : (! [X23 : X0] : (vAPP(X0,X2,X54,X23) = vAPP(X0,X2,X55,X23)) => (X54 = X55))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_ext)).
% 3.31/0.91 thf(f3404,plain,(
% 3.31/0.91 spl132_142),
% 3.31/0.91 inference(avatar_split_clause,[],[f1746,f3402])).
% 3.31/0.91 thf(f3402,plain,(
% 3.31/0.91 spl132_142 <=> ! [X1 : $tType,X0 : $tType,X5 : trm(X1,X0),X4 : trm(X1,X0),X3 : X0 > trm(X1,X0),X2 : X1] : (vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5) != vAPP(sTfun(X0,trm(X1,X0)),trm(X1,X0),vAPP(X1,sTfun(sTfun(X0,trm(X1,X0)),trm(X1,X0)),function(X1,X0),X2),X3))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_142])])).
% 3.31/0.91 thf(f1746,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0 > trm(X1,X0),X4 : trm(X1,X0),X5 : trm(X1,X0)] : ((vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5) != vAPP(sTfun(X0,trm(X1,X0)),trm(X1,X0),vAPP(X1,sTfun(sTfun(X0,trm(X1,X0)),trm(X1,X0)),function(X1,X0),X2),X3))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f948])).
% 3.31/0.91 thf(f948,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0 > trm(X1,X0),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X4),X5) != vAPP(sTfun(X0,trm(X1,X0)),trm(X1,X0),vAPP(X1,sTfun(sTfun(X0,trm(X1,X0)),trm(X1,X0)),function(X1,X0),X2),X3))),
% 3.31/0.91 inference(rectify,[],[f77])).
% 3.31/0.91 thf(f77,axiom,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X41 : X0,X42 : X1 > trm(X0,X1),X45 : trm(X0,X1),X46 : trm(X0,X1)] : (vAPP(sTfun(X1,trm(X0,X1)),trm(X0,X1),vAPP(X0,sTfun(sTfun(X1,trm(X0,X1)),trm(X0,X1)),function(X0,X1),X41),X42) != vAPP(trm(X0,X1),trm(X0,X1),vAPP(trm(X0,X1),sTfun(trm(X0,X1),trm(X0,X1)),plus(X0,X1),X45),X46))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_trm_Odistinct_I23_J)).
% 3.31/0.91 thf(f3400,plain,(
% 3.31/0.91 spl132_141),
% 3.31/0.91 inference(avatar_split_clause,[],[f1745,f3398])).
% 3.31/0.91 thf(f3398,plain,(
% 3.31/0.91 spl132_141 <=> ! [X1 : $tType,X0 : $tType,X5 : trm(X1,X0),X4 : trm(X1,X0),X3 : X0 > trm(X1,X0),X2 : X1] : (vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5) != vAPP(sTfun(X0,trm(X1,X0)),trm(X1,X0),vAPP(X1,sTfun(sTfun(X0,trm(X1,X0)),trm(X1,X0)),function(X1,X0),X2),X3))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_141])])).
% 3.31/0.91 thf(f1745,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0 > trm(X1,X0),X4 : trm(X1,X0),X5 : trm(X1,X0)] : ((vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5) != vAPP(sTfun(X0,trm(X1,X0)),trm(X1,X0),vAPP(X1,sTfun(sTfun(X0,trm(X1,X0)),trm(X1,X0)),function(X1,X0),X2),X3))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f947])).
% 3.31/0.91 thf(f947,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0 > trm(X1,X0),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5) != vAPP(sTfun(X0,trm(X1,X0)),trm(X1,X0),vAPP(X1,sTfun(sTfun(X0,trm(X1,X0)),trm(X1,X0)),function(X1,X0),X2),X3))),
% 3.31/0.91 inference(rectify,[],[f78])).
% 3.31/0.91 thf(f78,axiom,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X41 : X0,X42 : X1 > trm(X0,X1),X49 : trm(X0,X1),X50 : trm(X0,X1)] : (vAPP(sTfun(X1,trm(X0,X1)),trm(X0,X1),vAPP(X0,sTfun(sTfun(X1,trm(X0,X1)),trm(X0,X1)),function(X0,X1),X41),X42) != vAPP(trm(X0,X1),trm(X0,X1),vAPP(trm(X0,X1),sTfun(trm(X0,X1),trm(X0,X1)),times(X0,X1),X49),X50))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_trm_Odistinct_I25_J)).
% 3.31/0.91 thf(f3379,plain,(
% 3.31/0.91 spl132_140 | ~spl132_26 | ~spl132_36),
% 3.31/0.91 inference(avatar_split_clause,[],[f2260,f2234,f2162,f3376])).
% 3.31/0.91 thf(f3376,plain,(
% 3.31/0.91 spl132_140 <=> ($true = type(real))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_140])])).
% 3.31/0.91 thf(f2162,plain,(
% 3.31/0.91 spl132_26 <=> (linorder(real) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_26])])).
% 3.31/0.91 thf(f2260,plain,(
% 3.31/0.91 ($true = type(real)) | (~spl132_26 | ~spl132_36)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2255])).
% 3.31/0.91 thf(f2255,plain,(
% 3.31/0.91 ($true != $true) | ($true = type(real)) | (~spl132_26 | ~spl132_36)),
% 3.31/0.91 inference(superposition,[],[f2235,f2164])).
% 3.31/0.91 thf(f2164,plain,(
% 3.31/0.91 (linorder(real) = $true) | ~spl132_26),
% 3.31/0.91 inference(avatar_component_clause,[],[f2162])).
% 3.31/0.91 thf(f3368,plain,(
% 3.31/0.91 spl132_139),
% 3.31/0.91 inference(avatar_split_clause,[],[f1744,f3366])).
% 3.31/0.91 thf(f3366,plain,(
% 3.31/0.91 spl132_139 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : (vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_139])])).
% 3.31/0.91 thf(f1744,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : ((vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f946])).
% 3.31/0.91 thf(f946,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : (vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))),
% 3.31/0.91 inference(rectify,[],[f85])).
% 3.31/0.91 thf(f85,axiom,(
% 3.31/0.91 ! [X0 : $tType,X6 : $tType,X2 : $tType,X83 : X0 > X2 > X6,X32 : X0,X33 : X2] : (vAPP(product_prod(X0,X2),X6,vAPP(sTfun(X0,sTfun(X2,X6)),sTfun(product_prod(X0,X2),X6),product_rec_prod(X0,X2,X6),X83),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X32),X33)) = vAPP(X2,X6,vAPP(X0,sTfun(X2,X6),X83,X32),X33))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_old_Oprod_Orec)).
% 3.31/0.91 thf(f3364,plain,(
% 3.31/0.91 spl132_138),
% 3.31/0.91 inference(avatar_split_clause,[],[f1709,f3362])).
% 3.31/0.91 thf(f3362,plain,(
% 3.31/0.91 spl132_138 <=> ! [X0 : $tType,X3 : X0,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_138])])).
% 3.31/0.91 thf(f1709,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : set(X0),X3 : X0,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1209])).
% 3.31/0.91 thf(f1209,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 inference(flattening,[],[f1208])).
% 3.31/0.91 thf(f1208,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : ((($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 inference(ennf_transformation,[],[f735])).
% 3.31/0.91 thf(f735,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2))))),
% 3.31/0.91 inference(fool_elimination,[],[f734])).
% 3.31/0.91 thf(f734,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)))),
% 3.31/0.91 inference(rectify,[],[f122])).
% 3.31/0.91 thf(f122,axiom,(
% 3.31/0.91 ! [X0 : $tType,X11 : set(X0),X12 : set(X0),X79 : X0] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X11),X12) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X79),X11) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X79),X12)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_subsetD)).
% 3.31/0.91 thf(f3360,plain,(
% 3.31/0.91 spl132_137),
% 3.31/0.91 inference(avatar_split_clause,[],[f1678,f3358])).
% 3.31/0.91 thf(f3358,plain,(
% 3.31/0.91 spl132_137 <=> ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : ($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_137])])).
% 3.31/0.91 thf(f1678,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f691])).
% 3.31/0.91 thf(f691,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0)] : ($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))),
% 3.31/0.91 inference(fool_elimination,[],[f690])).
% 3.31/0.91 thf(f690,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0)] : vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))),
% 3.31/0.91 inference(rectify,[],[f17])).
% 3.31/0.91 thf(f17,axiom,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X14 : frechet_strm(X0,X1)] : vAPP(set(trm(X0,X1)),$o,vAPP(trm(X0,X1),sTfun(set(trm(X0,X1)),$o),member(trm(X0,X1)),vAPP(frechet_strm(X0,X1),trm(X0,X1),frechet_raw_term(X0,X1),X14)),vAPP(sTfun(trm(X0,X1),$o),set(trm(X0,X1)),collect(trm(X0,X1)),dfree(X0,X1)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_raw__term)).
% 3.31/0.91 thf(f3356,plain,(
% 3.31/0.91 spl132_136),
% 3.31/0.91 inference(avatar_split_clause,[],[f1674,f3354])).
% 3.31/0.91 thf(f1674,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1387])).
% 3.31/0.91 thf(f1387,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0)] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))) & (vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)) = X2))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f1183,f1386])).
% 3.31/0.91 thf(f1386,plain,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : (? [X3 : trm(X1,X0)] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X3),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))) & (vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X3) = X2)) => (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))) & (vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)) = X2)))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1183,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0)] : ? [X3 : trm(X1,X0)] : (($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X3),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))) & (vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X3) = X2))),
% 3.31/0.91 inference(ennf_transformation,[],[f929])).
% 3.31/0.91 thf(f929,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0)] : ~! [X3 : trm(X1,X0)] : ((vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X3) = X2) => ($true != vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X3),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.91 inference(flattening,[],[f687])).
% 3.31/0.91 thf(f687,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0)] : ~! [X3 : trm(X1,X0)] : ((vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X3) = X2) => ~($true = vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X3),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0)))))),
% 3.31/0.91 inference(fool_elimination,[],[f686])).
% 3.31/0.91 thf(f686,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0)] : ~! [X3 : trm(X1,X0)] : ((vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),X3) = X2) => ~vAPP(set(trm(X1,X0)),$o,vAPP(trm(X1,X0),sTfun(set(trm(X1,X0)),$o),member(trm(X1,X0)),X3),vAPP(sTfun(trm(X1,X0),$o),set(trm(X1,X0)),collect(trm(X1,X0)),dfree(X1,X0))))),
% 3.31/0.91 inference(rectify,[],[f37])).
% 3.31/0.91 thf(f37,axiom,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X14 : frechet_strm(X0,X1)] : ~! [X34 : trm(X0,X1)] : ((vAPP(trm(X0,X1),frechet_strm(X0,X1),frechet_simple_term(X0,X1),X34) = X14) => ~vAPP(set(trm(X0,X1)),$o,vAPP(trm(X0,X1),sTfun(set(trm(X0,X1)),$o),member(trm(X0,X1)),X34),vAPP(sTfun(trm(X0,X1),$o),set(trm(X0,X1)),collect(trm(X0,X1)),dfree(X0,X1))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_simple__term__cases)).
% 3.31/0.91 thf(f3352,plain,(
% 3.31/0.91 spl132_135),
% 3.31/0.91 inference(avatar_split_clause,[],[f1743,f3350])).
% 3.31/0.91 thf(f3350,plain,(
% 3.31/0.91 spl132_135 <=> ! [X1 : $tType,X0 : $tType,X5 : trm(X1,X0),X4 : trm(X1,X0),X3 : trm(X1,X0),X2 : trm(X1,X0)] : (vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5) != vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X2),X3))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_135])])).
% 3.31/0.91 thf(f1743,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0),X4 : trm(X1,X0),X5 : trm(X1,X0)] : ((vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5) != vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X2),X3))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f945])).
% 3.31/0.91 thf(f945,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0),X3 : trm(X1,X0),X4 : trm(X1,X0),X5 : trm(X1,X0)] : (vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),times(X1,X0),X4),X5) != vAPP(trm(X1,X0),trm(X1,X0),vAPP(trm(X1,X0),sTfun(trm(X1,X0),trm(X1,X0)),plus(X1,X0),X2),X3))),
% 3.31/0.91 inference(rectify,[],[f79])).
% 3.31/0.91 thf(f79,axiom,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X45 : trm(X0,X1),X46 : trm(X0,X1),X49 : trm(X0,X1),X50 : trm(X0,X1)] : (vAPP(trm(X0,X1),trm(X0,X1),vAPP(trm(X0,X1),sTfun(trm(X0,X1),trm(X0,X1)),plus(X0,X1),X45),X46) != vAPP(trm(X0,X1),trm(X0,X1),vAPP(trm(X0,X1),sTfun(trm(X0,X1),trm(X0,X1)),times(X0,X1),X49),X50))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_trm_Odistinct_I31_J)).
% 3.31/0.91 thf(f3315,plain,(
% 3.31/0.91 spl132_134),
% 3.31/0.91 inference(avatar_split_clause,[],[f1742,f3313])).
% 3.31/0.91 thf(f3313,plain,(
% 3.31/0.91 spl132_134 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : X2 > X1,X4 : X0 > X1,X5 : X2] : (vAPP(sum_sum(X2,X0),X1,vAPP(sTfun(X0,X1),sTfun(sum_sum(X2,X0),X1),vAPP(sTfun(X2,X1),sTfun(sTfun(X0,X1),sTfun(sum_sum(X2,X0),X1)),sum_rec_sum(X2,X1,X0),X3),X4),vAPP(X2,sum_sum(X2,X0),sum_Inl(X2,X0),X5)) = vAPP(X2,X1,X3,X5))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_134])])).
% 3.31/0.91 thf(f1742,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2 > X1,X4 : X0 > X1,X5 : X2] : ((vAPP(sum_sum(X2,X0),X1,vAPP(sTfun(X0,X1),sTfun(sum_sum(X2,X0),X1),vAPP(sTfun(X2,X1),sTfun(sTfun(X0,X1),sTfun(sum_sum(X2,X0),X1)),sum_rec_sum(X2,X1,X0),X3),X4),vAPP(X2,sum_sum(X2,X0),sum_Inl(X2,X0),X5)) = vAPP(X2,X1,X3,X5))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f944])).
% 3.31/0.91 thf(f944,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X1,X4 : X0 > X1,X5 : X2] : (vAPP(sum_sum(X2,X0),X1,vAPP(sTfun(X0,X1),sTfun(sum_sum(X2,X0),X1),vAPP(sTfun(X2,X1),sTfun(sTfun(X0,X1),sTfun(sum_sum(X2,X0),X1)),sum_rec_sum(X2,X1,X0),X3),X4),vAPP(X2,sum_sum(X2,X0),sum_Inl(X2,X0),X5)) = vAPP(X2,X1,X3,X5))),
% 3.31/0.91 inference(rectify,[],[f130])).
% 3.31/0.91 thf(f130,axiom,(
% 3.31/0.91 ! [X2 : $tType,X6 : $tType,X0 : $tType,X83 : X0 > X6,X103 : X2 > X6,X32 : X0] : (vAPP(sum_sum(X0,X2),X6,vAPP(sTfun(X2,X6),sTfun(sum_sum(X0,X2),X6),vAPP(sTfun(X0,X6),sTfun(sTfun(X2,X6),sTfun(sum_sum(X0,X2),X6)),sum_rec_sum(X0,X6,X2),X83),X103),vAPP(X0,sum_sum(X0,X2),sum_Inl(X0,X2),X32)) = vAPP(X0,X6,X83,X32))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_old_Osum_Osimps_I7_J)).
% 3.31/0.91 thf(f3311,plain,(
% 3.31/0.91 spl132_133),
% 3.31/0.91 inference(avatar_split_clause,[],[f1677,f3309])).
% 3.31/0.91 thf(f3309,plain,(
% 3.31/0.91 spl132_133 <=> ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0)] : ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVT(X1,X0),X2)),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X2)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_133])])).
% 3.31/0.91 thf(f1677,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : trm(X1,X0)] : (($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVT(X1,X0),X2)),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X2)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f689])).
% 3.31/0.91 thf(f689,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0)] : ($true = vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVT(X1,X0),X2)),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X2)))),
% 3.31/0.91 inference(fool_elimination,[],[f688])).
% 3.31/0.91 thf(f688,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : trm(X1,X0)] : vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVT(X1,X0),X2)),vAPP(trm(X1,X0),set(sum_sum(X0,X0)),static_FVDiff(X1,X0),X2))),
% 3.31/0.91 inference(rectify,[],[f168])).
% 3.31/0.91 thf(f168,axiom,(
% 3.31/0.91 ! [X0 : $tType,X2 : $tType,X54 : trm(X2,X0)] : vAPP(set(sum_sum(X0,X0)),$o,vAPP(set(sum_sum(X0,X0)),sTfun(set(sum_sum(X0,X0)),$o),ord_less_eq(set(sum_sum(X0,X0))),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVT(X2,X0),X54)),vAPP(trm(X2,X0),set(sum_sum(X0,X0)),static_FVDiff(X2,X0),X54))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_FVDiff__sub)).
% 3.31/0.91 thf(f3307,plain,(
% 3.31/0.91 spl132_132),
% 3.31/0.91 inference(avatar_split_clause,[],[f1668,f3305])).
% 3.31/0.91 thf(f3305,plain,(
% 3.31/0.91 spl132_132 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK44(X0),X2),X1)),X2)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_132])])).
% 3.31/0.91 thf(f1668,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK44(X0),X2),X1)),X2))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1383])).
% 3.31/0.91 thf(f1383,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK44(X0),X2),X1)),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK44(X0),X2),X1)),X1))))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f1176,f1382])).
% 3.31/0.91 thf(f1382,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (? [X3 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))) => (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK44(X0),X2),X1)),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK44(X0),X2),X1)),X1))))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1176,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ? [X3 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))))),
% 3.31/0.91 inference(ennf_transformation,[],[f677])).
% 3.31/0.91 thf(f677,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (! [X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2))) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 inference(fool_elimination,[],[f676])).
% 3.31/0.91 thf(f676,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (! [X3 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))),
% 3.31/0.91 inference(rectify,[],[f103])).
% 3.31/0.91 thf(f103,axiom,(
% 3.31/0.91 ! [X0 : $tType,X11 : set(X0),X12 : set(X0)] : (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),X11) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),X12)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X11),X12))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_subsetI)).
% 3.31/0.91 thf(f3303,plain,(
% 3.31/0.91 spl132_131),
% 3.31/0.91 inference(avatar_split_clause,[],[f1667,f3301])).
% 3.31/0.91 thf(f3301,plain,(
% 3.31/0.91 spl132_131 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK44(X0),X2),X1)),X1)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_131])])).
% 3.31/0.91 thf(f1667,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK44(X0),X2),X1)),X1))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1383])).
% 3.31/0.91 thf(f3299,plain,(
% 3.31/0.91 spl132_130),
% 3.31/0.91 inference(avatar_split_clause,[],[f1592,f3297])).
% 3.31/0.91 thf(f3297,plain,(
% 3.31/0.91 spl132_130 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X4 : X1,X3 : X1 > X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | (ord(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_130])])).
% 3.31/0.91 thf(f1592,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0,X4 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | (ord(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1086])).
% 3.31/0.91 thf(f1086,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > X0,X4 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3))) | (ord(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f549])).
% 3.31/0.91 thf(f549,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((ord(X0) = $true) => ! [X2 : X1 > X0,X3 : X1 > X0,X4 : X1] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4)))))),
% 3.31/0.91 inference(fool_elimination,[],[f548])).
% 3.31/0.91 thf(f548,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (ord(X0) => ! [X2 : X1 > X0,X3 : X1 > X0,X4 : X1] : (vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))))),
% 3.31/0.91 inference(rectify,[],[f136])).
% 3.31/0.91 thf(f136,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType] : (ord(X2) => ! [X54 : X0 > X2,X55 : X0 > X2,X14 : X0] : (vAPP(sTfun(X0,X2),$o,vAPP(sTfun(X0,X2),sTfun(sTfun(X0,X2),$o),ord_less_eq(sTfun(X0,X2)),X54),X55) => vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(X0,X2,X54,X14)),vAPP(X0,X2,X55,X14))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_le__funE)).
% 3.31/0.91 thf(f3155,plain,(
% 3.31/0.91 spl132_129),
% 3.31/0.91 inference(avatar_split_clause,[],[f1664,f3153])).
% 3.31/0.91 thf(f3153,plain,(
% 3.31/0.91 spl132_129 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK42(X0),X2),X1))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_129])])).
% 3.31/0.91 thf(f1664,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK42(X0),X2),X1)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1379])).
% 3.31/0.91 thf(f1379,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK42(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK42(X0),X2),X1)))))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f1174,f1378])).
% 3.31/0.91 thf(f1378,plain,(
% 3.31/0.91 ! [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),sK42(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK42(X0),X2),X1)))))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1174,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))))),
% 3.31/0.91 inference(ennf_transformation,[],[f673])).
% 3.31/0.91 thf(f673,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) => ($true = vAPP(X0,$o,X2,X3))) => ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)))),
% 3.31/0.91 inference(fool_elimination,[],[f672])).
% 3.31/0.91 thf(f672,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (vAPP(X0,$o,X1,X3) => vAPP(X0,$o,X2,X3)) => vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2))),
% 3.31/0.91 inference(rectify,[],[f132])).
% 3.31/0.91 thf(f132,axiom,(
% 3.31/0.91 ! [X0 : $tType,X24 : X0 > $o,X53 : X0 > $o] : (! [X23 : X0] : (vAPP(X0,$o,X24,X23) => vAPP(X0,$o,X53,X23)) => vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X24),X53))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_predicate1I)).
% 3.31/0.91 thf(f3151,plain,(
% 3.31/0.91 spl132_128),
% 3.31/0.91 inference(avatar_split_clause,[],[f1663,f3149])).
% 3.31/0.91 thf(f3149,plain,(
% 3.31/0.91 spl132_128 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK42(X0),X2),X1))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_128])])).
% 3.31/0.91 thf(f1663,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK42(X0),X2),X1)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1379])).
% 3.31/0.91 thf(f3147,plain,(
% 3.31/0.91 spl132_127),
% 3.31/0.91 inference(avatar_split_clause,[],[f1641,f3145])).
% 3.31/0.91 thf(f3145,plain,(
% 3.31/0.91 spl132_127 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : frechet_good_interp(X2,X1,X0)] : ((vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),sK32(X0,X1,X2),X3)) = X3) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_127])])).
% 3.31/0.91 thf(f1641,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : frechet_good_interp(X2,X1,X0)] : ((vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),sK32(X0,X1,X2),X3)) = X3) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1365])).
% 3.31/0.91 thf(f3143,plain,(
% 3.31/0.91 spl132_126),
% 3.31/0.91 inference(avatar_split_clause,[],[f1638,f3141])).
% 3.31/0.91 thf(f3141,plain,(
% 3.31/0.91 spl132_126 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : frechet_good_interp(X2,X1,X0)] : ((vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)) = X3) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_126])])).
% 3.31/0.91 thf(f1638,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : frechet_good_interp(X2,X1,X0)] : ((vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)) = X3) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1130])).
% 3.31/0.91 thf(f1130,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0)] : (vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)) = X3) | (finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true))),
% 3.31/0.91 inference(flattening,[],[f1129])).
% 3.31/0.91 thf(f1129,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : frechet_good_interp(X2,X1,X0)] : (vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)) = X3) | ((finite_finite(X0) != $true) | (finite_finite(X1) != $true) | (finite_finite(X2) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f629])).
% 3.31/0.91 thf(f629,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (((finite_finite(X0) = $true) & (finite_finite(X1) = $true) & (finite_finite(X2) = $true)) => ! [X3 : frechet_good_interp(X2,X1,X0)] : (vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)) = X3))),
% 3.31/0.91 inference(fool_elimination,[],[f628])).
% 3.31/0.91 thf(f628,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite(X0) & finite_finite(X1) & finite_finite(X2)) => ! [X3 : frechet_good_interp(X2,X1,X0)] : (vAPP(denota1663640101rp_ext(X2,X1,X0,product_unit),frechet_good_interp(X2,X1,X0),freche227871258interp(X2,X1,X0),vAPP(frechet_good_interp(X2,X1,X0),denota1663640101rp_ext(X2,X1,X0,product_unit),freche229654227interp(X2,X1,X0),X3)) = X3))),
% 3.31/0.91 inference(rectify,[],[f84])).
% 3.31/0.91 thf(f84,axiom,(
% 3.31/0.91 ! [X1 : $tType,X2 : $tType,X0 : $tType] : ((finite_finite(X1) & finite_finite(X2) & finite_finite(X0)) => ! [X14 : frechet_good_interp(X0,X2,X1)] : (vAPP(denota1663640101rp_ext(X0,X2,X1,product_unit),frechet_good_interp(X0,X2,X1),freche227871258interp(X0,X2,X1),vAPP(frechet_good_interp(X0,X2,X1),denota1663640101rp_ext(X0,X2,X1,product_unit),freche229654227interp(X0,X2,X1),X14)) = X14))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_raw__interp__inverse)).
% 3.31/0.91 thf(f3139,plain,(
% 3.31/0.91 spl132_125),
% 3.31/0.91 inference(avatar_split_clause,[],[f1492,f3137])).
% 3.31/0.91 thf(f3137,plain,(
% 3.31/0.91 spl132_125 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_125])])).
% 3.31/0.91 thf(f1492,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f979])).
% 3.31/0.91 thf(f979,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (order(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f978])).
% 3.31/0.91 thf(f978,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (order(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f395])).
% 3.31/0.91 thf(f395,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)))))),
% 3.31/0.91 inference(fool_elimination,[],[f394])).
% 3.31/0.91 thf(f394,plain,(
% 3.31/0.91 ! [X0 : $tType] : (order(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))))),
% 3.31/0.91 inference(rectify,[],[f158])).
% 3.31/0.91 thf(f158,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (order(X0) => ! [X33 : X0,X32 : X0,X79 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X33),X32) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X79),X33) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X79),X32))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_dual__order_Otrans)).
% 3.31/0.91 thf(f3135,plain,(
% 3.31/0.91 spl132_124),
% 3.31/0.91 inference(avatar_split_clause,[],[f1483,f3133])).
% 3.31/0.91 thf(f3133,plain,(
% 3.31/0.91 spl132_124 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (preorder(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_124])])).
% 3.31/0.91 thf(f1483,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (preorder(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f966])).
% 3.31/0.91 thf(f966,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (preorder(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f965])).
% 3.31/0.91 thf(f965,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (preorder(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f377])).
% 3.31/0.91 thf(f377,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))))),
% 3.31/0.91 inference(fool_elimination,[],[f376])).
% 3.31/0.91 thf(f376,plain,(
% 3.31/0.91 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))))),
% 3.31/0.91 inference(rectify,[],[f155])).
% 3.31/0.91 thf(f155,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (preorder(X0) => ! [X14 : X0,X15 : X0,X106 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X14),X15) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X15),X106) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X14),X106))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_order__trans)).
% 3.31/0.91 thf(f3126,plain,(
% 3.31/0.91 spl132_123),
% 3.31/0.91 inference(avatar_split_clause,[],[f1690,f3124])).
% 3.31/0.91 thf(f3124,plain,(
% 3.31/0.91 spl132_123 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0)] : ((X2 = X3) | (vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)) | (vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_123])])).
% 3.31/0.91 thf(f1690,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : ((X2 = X3) | (vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)) | (vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1186])).
% 3.31/0.91 thf(f1186,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : ((X2 = X3) | (vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)) | (vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3)))),
% 3.31/0.91 inference(flattening,[],[f1185])).
% 3.31/0.91 thf(f1185,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : (((X2 = X3) | (vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3))) | (vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3)))),
% 3.31/0.91 inference(ennf_transformation,[],[f934])).
% 3.31/0.91 thf(f934,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : ((vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2) = vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X3)) => ((vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2) = vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X3)) => (X2 = X3)))),
% 3.31/0.91 inference(rectify,[],[f73])).
% 3.31/0.91 thf(f73,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType,X59 : product_prod(X0,X2),X75 : product_prod(X0,X2)] : ((vAPP(product_prod(X0,X2),X0,product_fst(X0,X2),X59) = vAPP(product_prod(X0,X2),X0,product_fst(X0,X2),X75)) => ((vAPP(product_prod(X0,X2),X2,product_snd(X0,X2),X59) = vAPP(product_prod(X0,X2),X2,product_snd(X0,X2),X75)) => (X59 = X75)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_prod__eqI)).
% 3.31/0.91 thf(f3118,plain,(
% 3.31/0.91 spl132_122),
% 3.31/0.91 inference(avatar_split_clause,[],[f1610,f3116])).
% 3.31/0.91 thf(f3116,plain,(
% 3.31/0.91 spl132_122 <=> ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),bNF_eq_onp(X0),X1)),vEQ(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_122])])).
% 3.31/0.91 thf(f1610,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),bNF_eq_onp(X0),X1)),vEQ(X0)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f585])).
% 3.31/0.91 thf(f585,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),bNF_eq_onp(X0),X1)),vEQ(X0)))),
% 3.31/0.91 inference(fool_elimination,[],[f584])).
% 3.31/0.91 thf(f584,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),bNF_eq_onp(X0),X1)),(^[X2 : X0, X3 : X0] : ((X2 = X3))))),
% 3.31/0.91 inference(rectify,[],[f253])).
% 3.31/0.91 thf(f253,axiom,(
% 3.31/0.91 ! [X0 : $tType,X24 : X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),bNF_eq_onp(X0),X24)),(^[X70 : X0, X71 : X0] : ((X70 = X71))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_eq__onp__le__eq)).
% 3.31/0.91 thf(f3097,plain,(
% 3.31/0.91 spl132_121),
% 3.31/0.91 inference(avatar_split_clause,[],[f1697,f3095])).
% 3.31/0.91 thf(f3095,plain,(
% 3.31/0.91 spl132_121 <=> ! [X1 : $tType,X0 : $tType,X3 : frechet_strm(X1,X0),X2 : frechet_strm(X1,X0) > $o] : (($true = vAPP(frechet_strm(X1,X0),$o,X2,X3)) | ($true != vAPP(frechet_strm(X1,X0),$o,X2,vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(sTfun(frechet_strm(X1,X0),$o),trm(X1,X0),sK56(X0,X1),X2)))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_121])])).
% 3.31/0.91 thf(f1697,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0) > $o,X3 : frechet_strm(X1,X0)] : (($true = vAPP(frechet_strm(X1,X0),$o,X2,X3)) | ($true != vAPP(frechet_strm(X1,X0),$o,X2,vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(sTfun(frechet_strm(X1,X0),$o),trm(X1,X0),sK56(X0,X1),X2))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1399])).
% 3.31/0.91 thf(f3093,plain,(
% 3.31/0.91 spl132_120),
% 3.31/0.91 inference(avatar_split_clause,[],[f1669,f3091])).
% 3.31/0.91 thf(f3091,plain,(
% 3.31/0.91 spl132_120 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_120])])).
% 3.31/0.91 thf(f1669,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1178])).
% 3.31/0.91 thf(f1178,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 inference(flattening,[],[f1177])).
% 3.31/0.91 thf(f1177,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 3.31/0.91 inference(ennf_transformation,[],[f679])).
% 3.31/0.91 thf(f679,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) => (X1 = X2)))),
% 3.31/0.91 inference(fool_elimination,[],[f678])).
% 3.31/0.91 thf(f678,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1) => (X1 = X2)))),
% 3.31/0.91 inference(rectify,[],[f110])).
% 3.31/0.91 thf(f110,axiom,(
% 3.31/0.91 ! [X0 : $tType,X11 : set(X0),X12 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X11),X12) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X12),X11) => (X11 = X12)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_subset__antisym)).
% 3.31/0.91 thf(f3087,plain,(
% 3.31/0.91 spl132_119),
% 3.31/0.91 inference(avatar_split_clause,[],[f1476,f3085])).
% 3.31/0.91 thf(f3085,plain,(
% 3.31/0.91 spl132_119 <=> ! [X0 : $tType,X1 : product_prod(X0,X0)] : ((vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),vAPP(product_prod(X0,X0),X0,sK4(X0),X1)),vAPP(product_prod(X0,X0),X0,sK5(X0),X1)) = X1) | (euclid1155270486miring(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_119])])).
% 3.31/0.91 thf(f1476,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : product_prod(X0,X0)] : ((vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),vAPP(product_prod(X0,X0),X0,sK4(X0),X1)),vAPP(product_prod(X0,X0),X0,sK5(X0),X1)) = X1) | (euclid1155270486miring(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1327])).
% 3.31/0.91 thf(f1327,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : product_prod(X0,X0)] : (vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),vAPP(product_prod(X0,X0),X0,sK4(X0),X1)),vAPP(product_prod(X0,X0),X0,sK5(X0),X1)) = X1) | (euclid1155270486miring(X0) != $true))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f958,f1326])).
% 3.31/0.91 thf(f1326,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : product_prod(X0,X0)] : (? [X2 : X0,X3 : X0] : (vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3) = X1) => (vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),vAPP(product_prod(X0,X0),X0,sK4(X0),X1)),vAPP(product_prod(X0,X0),X0,sK5(X0),X1)) = X1))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f958,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : product_prod(X0,X0)] : ? [X2 : X0,X3 : X0] : (vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3) = X1) | (euclid1155270486miring(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f363])).
% 3.31/0.91 thf(f363,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((euclid1155270486miring(X0) = $true) => ! [X1 : product_prod(X0,X0)] : ~! [X2 : X0,X3 : X0] : (vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3) != X1))),
% 3.31/0.91 inference(fool_elimination,[],[f362])).
% 3.31/0.91 thf(f362,plain,(
% 3.31/0.91 ! [X0 : $tType] : (euclid1155270486miring(X0) => ! [X1 : product_prod(X0,X0)] : ~! [X2 : X0,X3 : X0] : (vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3) != X1))),
% 3.31/0.91 inference(rectify,[],[f111])).
% 3.31/0.91 thf(f111,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (euclid1155270486miring(X0) => ! [X14 : product_prod(X0,X0)] : ~! [X57 : X0,X58 : X0] : (vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X57),X58) != X14))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_gcd_Ocases)).
% 3.31/0.91 thf(f3078,plain,(
% 3.31/0.91 spl132_118),
% 3.31/0.91 inference(avatar_split_clause,[],[f1543,f3076])).
% 3.31/0.91 thf(f3076,plain,(
% 3.31/0.91 spl132_118 <=> ! [X0 : $tType,X1 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_118])])).
% 3.31/0.91 thf(f1543,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f463])).
% 3.31/0.91 thf(f463,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)),
% 3.31/0.91 inference(fool_elimination,[],[f462])).
% 3.31/0.91 thf(f462,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X2 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)))) = X1)),
% 3.31/0.91 inference(rectify,[],[f47])).
% 3.31/0.91 thf(f47,axiom,(
% 3.31/0.91 ! [X0 : $tType,X11 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X20 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X20),X11)))) = X11)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq)).
% 3.31/0.91 thf(f3051,plain,(
% 3.31/0.91 spl132_117),
% 3.31/0.91 inference(avatar_split_clause,[],[f1676,f3049])).
% 3.31/0.91 thf(f3049,plain,(
% 3.31/0.91 spl132_117 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK49(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK50(X0,X1),X2)) = X2)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_117])])).
% 3.31/0.91 thf(f1676,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK49(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK50(X0,X1),X2)) = X2)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1391])).
% 3.31/0.91 thf(f1391,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK49(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK50(X0,X1),X2)) = X2)),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50])],[f931,f1390])).
% 3.31/0.91 thf(f1390,plain,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : (? [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2) => (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK49(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK50(X0,X1),X2)) = X2))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f931,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : ? [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2)),
% 3.31/0.91 inference(rectify,[],[f56])).
% 3.31/0.91 thf(f56,axiom,(
% 3.31/0.91 ! [X0 : $tType,X2 : $tType,X59 : product_prod(X0,X2)] : ? [X23 : X0,X34 : X2] : (vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X23),X34) = X59)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_surj__pair)).
% 3.31/0.91 thf(f3047,plain,(
% 3.31/0.91 spl132_116),
% 3.31/0.91 inference(avatar_split_clause,[],[f1675,f3045])).
% 3.31/0.91 thf(f1675,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK47(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK48(X0,X1),X2)) = X2)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1389])).
% 3.31/0.91 thf(f1389,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK47(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK48(X0,X1),X2)) = X2)),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48])],[f1184,f1388])).
% 3.31/0.91 thf(f1388,plain,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : (? [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2) => (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK47(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK48(X0,X1),X2)) = X2))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1184,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : ? [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2)),
% 3.31/0.91 inference(ennf_transformation,[],[f930])).
% 3.31/0.91 thf(f930,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : ~! [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) != X2)),
% 3.31/0.91 inference(rectify,[],[f53])).
% 3.31/0.91 thf(f53,axiom,(
% 3.31/0.91 ! [X0 : $tType,X2 : $tType,X15 : product_prod(X0,X2)] : ~! [X57 : X0,X58 : X2] : (vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X57),X58) != X15)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_old_Oprod_Oexhaust)).
% 3.31/0.91 thf(f3043,plain,(
% 3.31/0.91 spl132_115),
% 3.31/0.91 inference(avatar_split_clause,[],[f1613,f3041])).
% 3.31/0.91 thf(f3041,plain,(
% 3.31/0.91 spl132_115 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : (vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)) = X2)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_115])])).
% 3.31/0.91 thf(f1613,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)) = X2)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f923])).
% 3.31/0.91 thf(f923,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0)] : (vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,product_snd(X1,X0),X2)) = X2)),
% 3.31/0.91 inference(rectify,[],[f80])).
% 3.31/0.91 thf(f80,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType,X78 : product_prod(X0,X2)] : (vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),vAPP(product_prod(X0,X2),X0,product_fst(X0,X2),X78)),vAPP(product_prod(X0,X2),X2,product_snd(X0,X2),X78)) = X78)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_surjective__pairing)).
% 3.31/0.91 thf(f3015,plain,(
% 3.31/0.91 spl132_114),
% 3.31/0.91 inference(avatar_split_clause,[],[f1705,f3013])).
% 3.31/0.91 thf(f3013,plain,(
% 3.31/0.91 spl132_114 <=> ! [X0 : $tType,X3 : X0 > $o,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X3,X2)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3)) | ($true != vAPP(X0,$o,X1,X2)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_114])])).
% 3.31/0.91 thf(f1705,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X3,X2)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3)) | ($true != vAPP(X0,$o,X1,X2))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1202])).
% 3.31/0.91 thf(f1202,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (($true = vAPP(X0,$o,X3,X2)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3)) | ($true != vAPP(X0,$o,X1,X2)))),
% 3.31/0.91 inference(flattening,[],[f1201])).
% 3.31/0.91 thf(f1201,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : ((($true = vAPP(X0,$o,X3,X2)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3))) | ($true != vAPP(X0,$o,X1,X2)))),
% 3.31/0.91 inference(ennf_transformation,[],[f727])).
% 3.31/0.91 thf(f727,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) => (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3)) => ($true = vAPP(X0,$o,X3,X2))))),
% 3.31/0.91 inference(fool_elimination,[],[f726])).
% 3.31/0.91 thf(f726,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (vAPP(X0,$o,X1,X2) => (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3) => vAPP(X0,$o,X3,X2)))),
% 3.31/0.91 inference(rectify,[],[f133])).
% 3.31/0.91 thf(f133,axiom,(
% 3.31/0.91 ! [X0 : $tType,X24 : X0 > $o,X14 : X0,X53 : X0 > $o] : (vAPP(X0,$o,X24,X14) => (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X24),X53) => vAPP(X0,$o,X53,X14)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_rev__predicate1D)).
% 3.31/0.91 thf(f3011,plain,(
% 3.31/0.91 spl132_113),
% 3.31/0.91 inference(avatar_split_clause,[],[f1572,f3009])).
% 3.31/0.91 thf(f3009,plain,(
% 3.31/0.91 spl132_113 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X2 : set(X1)] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),vAPP(X0,sTfun(X1,X0),kCOMB,X3))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_113])])).
% 3.31/0.91 thf(f1572,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : set(X1),X3 : X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),vAPP(X0,sTfun(X1,X0),kCOMB,X3))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1059])).
% 3.31/0.91 thf(f1059,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (! [X2 : set(X1),X3 : X0] : ($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),vAPP(X0,sTfun(X1,X0),kCOMB,X3))) | (topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true))),
% 3.31/0.91 inference(flattening,[],[f1058])).
% 3.31/0.91 thf(f1058,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (! [X2 : set(X1),X3 : X0] : ($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),vAPP(X0,sTfun(X1,X0),kCOMB,X3))) | ((topolo503727757_space(X0) != $true) | (topolo503727757_space(X1) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f513])).
% 3.31/0.91 thf(f513,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((topolo503727757_space(X0) = $true) & (topolo503727757_space(X1) = $true)) => ! [X2 : set(X1),X3 : X0] : ($true = vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),vAPP(X0,sTfun(X1,X0),kCOMB,X3))))),
% 3.31/0.91 inference(fool_elimination,[],[f512])).
% 3.31/0.91 thf(f512,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((topolo503727757_space(X0) & topolo503727757_space(X1)) => ! [X2 : set(X1),X3 : X0] : vAPP(sTfun(X1,X0),$o,vAPP(set(X1),sTfun(sTfun(X1,X0),$o),topolo2071040574ous_on(X1,X0),X2),(^[X4 : X1] : (X3))))),
% 3.31/0.91 inference(rectify,[],[f233])).
% 3.31/0.91 thf(f233,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType] : ((topolo503727757_space(X2) & topolo503727757_space(X0)) => ! [X111 : set(X0),X79 : X2] : vAPP(sTfun(X0,X2),$o,vAPP(set(X0),sTfun(sTfun(X0,X2),$o),topolo2071040574ous_on(X0,X2),X111),(^[X20 : X0] : (X79))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_continuous__on__const)).
% 3.31/0.91 thf(f3003,plain,(
% 3.31/0.91 spl132_112),
% 3.31/0.91 inference(avatar_split_clause,[],[f1508,f3001])).
% 3.31/0.91 thf(f3001,plain,(
% 3.31/0.91 spl132_112 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_112])])).
% 3.31/0.91 thf(f1508,plain,(
% 3.31/0.91 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1337])).
% 3.31/0.91 thf(f1337,plain,(
% 3.31/0.91 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2] : ((($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) & ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0)))),
% 3.31/0.91 inference(rectify,[],[f1336])).
% 3.31/0.91 thf(f1336,plain,(
% 3.31/0.91 ! [X3 : X0,X2 : X0,X0 : $tType,X1 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)))),
% 3.31/0.91 inference(nnf_transformation,[],[f1321])).
% 3.31/0.91 thf(f2999,plain,(
% 3.31/0.91 spl132_111),
% 3.31/0.91 inference(avatar_split_clause,[],[f1507,f2997])).
% 3.31/0.91 thf(f2997,plain,(
% 3.31/0.91 spl132_111 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_111])])).
% 3.31/0.91 thf(f1507,plain,(
% 3.31/0.91 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1337])).
% 3.31/0.91 thf(f2995,plain,(
% 3.31/0.91 spl132_110),
% 3.31/0.91 inference(avatar_split_clause,[],[f1506,f2993])).
% 3.31/0.91 thf(f2993,plain,(
% 3.31/0.91 spl132_110 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_110])])).
% 3.31/0.91 thf(f1506,plain,(
% 3.31/0.91 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1335])).
% 3.31/0.91 thf(f1335,plain,(
% 3.31/0.91 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2] : ((($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) & ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0)))),
% 3.31/0.91 inference(rectify,[],[f1334])).
% 3.31/0.91 thf(f1334,plain,(
% 3.31/0.91 ! [X3 : X0,X1 : X0,X0 : $tType,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)))),
% 3.31/0.91 inference(nnf_transformation,[],[f1322])).
% 3.31/0.91 thf(f2991,plain,(
% 3.31/0.91 spl132_109),
% 3.31/0.91 inference(avatar_split_clause,[],[f1505,f2989])).
% 3.31/0.91 thf(f2989,plain,(
% 3.31/0.91 spl132_109 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_109])])).
% 3.31/0.91 thf(f1505,plain,(
% 3.31/0.91 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1335])).
% 3.31/0.91 thf(f2987,plain,(
% 3.31/0.91 spl132_108),
% 3.31/0.91 inference(avatar_split_clause,[],[f1504,f2985])).
% 3.31/0.91 thf(f2985,plain,(
% 3.31/0.91 spl132_108 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_108])])).
% 3.31/0.91 thf(f1504,plain,(
% 3.31/0.91 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1333])).
% 3.31/0.91 thf(f1333,plain,(
% 3.31/0.91 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2] : ((($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) & ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0)))),
% 3.31/0.91 inference(rectify,[],[f1332])).
% 3.31/0.91 thf(f1332,plain,(
% 3.31/0.91 ! [X2 : X0,X3 : X0,X0 : $tType,X1 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)))),
% 3.31/0.91 inference(nnf_transformation,[],[f1323])).
% 3.31/0.91 thf(f2983,plain,(
% 3.31/0.91 spl132_107),
% 3.31/0.91 inference(avatar_split_clause,[],[f1503,f2981])).
% 3.31/0.91 thf(f2981,plain,(
% 3.31/0.91 spl132_107 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_107])])).
% 3.31/0.91 thf(f1503,plain,(
% 3.31/0.91 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1333])).
% 3.31/0.91 thf(f2979,plain,(
% 3.31/0.91 spl132_106),
% 3.31/0.91 inference(avatar_split_clause,[],[f1502,f2977])).
% 3.31/0.91 thf(f2977,plain,(
% 3.31/0.91 spl132_106 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_106])])).
% 3.31/0.91 thf(f1502,plain,(
% 3.31/0.91 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1331])).
% 3.31/0.91 thf(f1331,plain,(
% 3.31/0.91 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2] : ((($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) & ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0)))),
% 3.31/0.91 inference(rectify,[],[f1330])).
% 3.31/0.91 thf(f1330,plain,(
% 3.31/0.91 ! [X1 : X0,X2 : X0,X0 : $tType,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)))),
% 3.31/0.91 inference(nnf_transformation,[],[f1324])).
% 3.31/0.91 thf(f2975,plain,(
% 3.31/0.91 spl132_105),
% 3.31/0.91 inference(avatar_split_clause,[],[f1501,f2973])).
% 3.31/0.91 thf(f2973,plain,(
% 3.31/0.91 spl132_105 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_105])])).
% 3.31/0.91 thf(f1501,plain,(
% 3.31/0.91 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1331])).
% 3.31/0.91 thf(f2964,plain,(
% 3.31/0.91 spl132_104),
% 3.31/0.91 inference(avatar_split_clause,[],[f1489,f2962])).
% 3.31/0.91 thf(f2962,plain,(
% 3.31/0.91 spl132_104 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_104])])).
% 3.31/0.91 thf(f1489,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f973])).
% 3.31/0.91 thf(f973,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (order(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f972])).
% 3.31/0.91 thf(f972,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (order(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f389])).
% 3.31/0.91 thf(f389,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) => (X1 = X2))))),
% 3.31/0.91 inference(fool_elimination,[],[f388])).
% 3.31/0.91 thf(f388,plain,(
% 3.31/0.91 ! [X0 : $tType] : (order(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1) => (X1 = X2))))),
% 3.31/0.91 inference(rectify,[],[f154])).
% 3.31/0.91 thf(f154,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (order(X0) => ! [X32 : X0,X33 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X32),X33) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X33),X32) => (X32 = X33))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_order__class_Oorder_Oantisym)).
% 3.31/0.91 thf(f2946,plain,(
% 3.31/0.91 spl132_103),
% 3.31/0.91 inference(avatar_split_clause,[],[f1552,f2944])).
% 3.31/0.91 thf(f2944,plain,(
% 3.31/0.91 spl132_103 <=> ! [X1 : $tType,X0 : $tType] : ((top_top(product_prod(X0,X1)) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),top_top(X0)),top_top(X1))) | (top(X0) != $true) | (top(X1) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_103])])).
% 3.31/0.91 thf(f1552,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : ((top_top(product_prod(X0,X1)) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),top_top(X0)),top_top(X1))) | (top(X0) != $true) | (top(X1) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1027])).
% 3.31/0.91 thf(f1027,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top_top(product_prod(X0,X1)) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),top_top(X0)),top_top(X1))) | (top(X0) != $true) | (top(X1) != $true))),
% 3.31/0.91 inference(flattening,[],[f1026])).
% 3.31/0.91 thf(f1026,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top_top(product_prod(X0,X1)) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),top_top(X0)),top_top(X1))) | ((top(X0) != $true) | (top(X1) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f481])).
% 3.31/0.91 thf(f481,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((top(X0) = $true) & (top(X1) = $true)) => (top_top(product_prod(X0,X1)) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),top_top(X0)),top_top(X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f480])).
% 3.31/0.91 thf(f480,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top(X0) & top(X1)) => (top_top(product_prod(X0,X1)) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),top_top(X0)),top_top(X1))))),
% 3.31/0.91 inference(rectify,[],[f193])).
% 3.31/0.91 thf(f193,axiom,(
% 3.31/0.91 ! [X0 : $tType,X2 : $tType] : ((top(X0) & top(X2)) => (top_top(product_prod(X0,X2)) = vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),top_top(X0)),top_top(X2))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_top__prod__def)).
% 3.31/0.91 thf(f2932,plain,(
% 3.31/0.91 spl132_102),
% 3.31/0.91 inference(avatar_split_clause,[],[f1499,f2930])).
% 3.31/0.91 thf(f2930,plain,(
% 3.31/0.91 spl132_102 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (linorder(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_102])])).
% 3.31/0.91 thf(f1499,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (linorder(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f989])).
% 3.31/0.91 thf(f989,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (linorder(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f407])).
% 3.31/0.91 thf(f407,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))))),
% 3.31/0.91 inference(fool_elimination,[],[f406])).
% 3.31/0.91 thf(f406,plain,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 3.31/0.91 inference(rectify,[],[f145])).
% 3.31/0.91 thf(f145,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => ! [X14 : X0,X15 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X15),X14) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X14),X15)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_linear)).
% 3.31/0.91 thf(f2924,plain,(
% 3.31/0.91 spl132_101),
% 3.31/0.91 inference(avatar_split_clause,[],[f1584,f2922])).
% 3.31/0.91 thf(f2922,plain,(
% 3.31/0.91 spl132_101 <=> ! [X0 : $tType,X1 : set(X0)] : ((top_top(set(X0)) = X1) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK28(X0),X1)),X1)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_101])])).
% 3.31/0.91 thf(f1584,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : set(X0)] : ((top_top(set(X0)) = X1) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK28(X0),X1)),X1))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1357])).
% 3.31/0.91 thf(f1357,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : ((top_top(set(X0)) = X1) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK28(X0),X1)),X1)))),
% 3.31/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f1078,f1356])).
% 3.31/0.91 thf(f1356,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : (? [X2 : X0] : ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK28(X0),X1)),X1)))),
% 3.31/0.91 introduced(choice_axiom,[])).
% 3.31/0.91 thf(f1078,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : ((top_top(set(X0)) = X1) | ? [X2 : X0] : ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)))),
% 3.31/0.91 inference(ennf_transformation,[],[f533])).
% 3.31/0.91 thf(f533,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => (top_top(set(X0)) = X1))),
% 3.31/0.91 inference(fool_elimination,[],[f532])).
% 3.31/0.91 thf(f532,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1) => (top_top(set(X0)) = X1))),
% 3.31/0.91 inference(rectify,[],[f189])).
% 3.31/0.91 thf(f189,axiom,(
% 3.31/0.91 ! [X0 : $tType,X11 : set(X0)] : (! [X23 : X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),X11) => (top_top(set(X0)) = X11))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_UNIV__eq__I)).
% 3.31/0.91 thf(f2918,plain,(
% 3.31/0.91 spl132_100),
% 3.31/0.91 inference(avatar_split_clause,[],[f1681,f2916])).
% 3.31/0.91 thf(f1681,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0] : ((vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X2),X3)) = X2)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f933])).
% 3.31/0.91 thf(f933,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0] : (vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X2),X3)) = X2)),
% 3.31/0.91 inference(rectify,[],[f67])).
% 3.31/0.91 thf(f67,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType,X37 : X0,X38 : X2] : (vAPP(product_prod(X0,X2),X0,product_fst(X0,X2),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X37),X38)) = X37)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_fst__conv)).
% 3.31/0.91 thf(f2914,plain,(
% 3.31/0.91 spl132_99),
% 3.31/0.91 inference(avatar_split_clause,[],[f1680,f2912])).
% 3.31/0.91 thf(f1680,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : ((vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3)) = X3)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f932])).
% 3.31/0.91 thf(f932,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : (vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3)) = X3)),
% 3.31/0.91 inference(rectify,[],[f69])).
% 3.31/0.91 thf(f69,axiom,(
% 3.31/0.91 ! [X69 : $tType,X0 : $tType,X37 : X69,X38 : X0] : (vAPP(product_prod(X69,X0),X0,product_snd(X69,X0),vAPP(X0,product_prod(X69,X0),vAPP(X69,sTfun(X0,product_prod(X69,X0)),product_Pair(X69,X0),X37),X38)) = X38)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_snd__conv)).
% 3.31/0.91 thf(f2898,plain,(
% 3.31/0.91 spl132_98),
% 3.31/0.91 inference(avatar_split_clause,[],[f1673,f2896])).
% 3.31/0.91 thf(f1673,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : ((vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(frechet_strm(X1,X0),trm(X1,X0),sK46(X0,X1),X2)) = X2)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1387])).
% 3.31/0.91 thf(f2894,plain,(
% 3.31/0.91 spl132_97),
% 3.31/0.91 inference(avatar_split_clause,[],[f1611,f2892])).
% 3.31/0.91 thf(f2892,plain,(
% 3.31/0.91 spl132_97 <=> ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : (vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X2)) = X2)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_97])])).
% 3.31/0.91 thf(f1611,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : frechet_strm(X1,X0)] : ((vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X2)) = X2)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f921])).
% 3.31/0.91 thf(f921,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : frechet_strm(X1,X0)] : (vAPP(trm(X1,X0),frechet_strm(X1,X0),frechet_simple_term(X1,X0),vAPP(frechet_strm(X1,X0),trm(X1,X0),frechet_raw_term(X1,X0),X2)) = X2)),
% 3.31/0.91 inference(rectify,[],[f38])).
% 3.31/0.91 thf(f38,axiom,(
% 3.31/0.91 ! [X1 : $tType,X0 : $tType,X14 : frechet_strm(X0,X1)] : (vAPP(trm(X0,X1),frechet_strm(X0,X1),frechet_simple_term(X0,X1),vAPP(frechet_strm(X0,X1),trm(X0,X1),frechet_raw_term(X0,X1),X14)) = X14)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_raw__term__inverse)).
% 3.31/0.91 thf(f2890,plain,(
% 3.31/0.91 spl132_96),
% 3.31/0.91 inference(avatar_split_clause,[],[f1496,f2888])).
% 3.31/0.91 thf(f2888,plain,(
% 3.31/0.91 spl132_96 <=> ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(sTfun(X0,X0),$o,vAPP(set(X0),sTfun(sTfun(X0,X0),$o),topolo2071040574ous_on(X0,X0),X1),iCOMB)) | (topolo503727757_space(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_96])])).
% 3.31/0.91 thf(f1496,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(sTfun(X0,X0),$o,vAPP(set(X0),sTfun(sTfun(X0,X0),$o),topolo2071040574ous_on(X0,X0),X1),iCOMB)) | (topolo503727757_space(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f986])).
% 3.31/0.91 thf(f986,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : set(X0)] : ($true = vAPP(sTfun(X0,X0),$o,vAPP(set(X0),sTfun(sTfun(X0,X0),$o),topolo2071040574ous_on(X0,X0),X1),iCOMB)) | (topolo503727757_space(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f403])).
% 3.31/0.91 thf(f403,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((topolo503727757_space(X0) = $true) => ! [X1 : set(X0)] : ($true = vAPP(sTfun(X0,X0),$o,vAPP(set(X0),sTfun(sTfun(X0,X0),$o),topolo2071040574ous_on(X0,X0),X1),iCOMB)))),
% 3.31/0.91 inference(fool_elimination,[],[f402])).
% 3.31/0.91 thf(f402,plain,(
% 3.31/0.91 ! [X0 : $tType] : (topolo503727757_space(X0) => ! [X1 : set(X0)] : vAPP(sTfun(X0,X0),$o,vAPP(set(X0),sTfun(sTfun(X0,X0),$o),topolo2071040574ous_on(X0,X0),X1),(^[X2 : X0] : (X2))))),
% 3.31/0.91 inference(rectify,[],[f234])).
% 3.31/0.91 thf(f234,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (topolo503727757_space(X0) => ! [X111 : set(X0)] : vAPP(sTfun(X0,X0),$o,vAPP(set(X0),sTfun(sTfun(X0,X0),$o),topolo2071040574ous_on(X0,X0),X111),(^[X20 : X0] : (X20))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_continuous__on__id)).
% 3.31/0.91 thf(f2859,plain,(
% 3.31/0.91 spl132_95),
% 3.31/0.91 inference(avatar_split_clause,[],[f1551,f2857])).
% 3.31/0.91 thf(f2857,plain,(
% 3.31/0.91 spl132_95 <=> ! [X1 : $tType,X0 : $tType] : ((top_top(X1) = vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),top_top(product_prod(X1,X0)))) | (top(X0) != $true) | (top(X1) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_95])])).
% 3.31/0.91 thf(f1551,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : ((top_top(X1) = vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),top_top(product_prod(X1,X0)))) | (top(X0) != $true) | (top(X1) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1025])).
% 3.31/0.91 thf(f1025,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top_top(X1) = vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),top_top(product_prod(X1,X0)))) | (top(X0) != $true) | (top(X1) != $true))),
% 3.31/0.91 inference(flattening,[],[f1024])).
% 3.31/0.91 thf(f1024,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top_top(X1) = vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),top_top(product_prod(X1,X0)))) | ((top(X0) != $true) | (top(X1) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f479])).
% 3.31/0.91 thf(f479,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((top(X0) = $true) & (top(X1) = $true)) => (top_top(X1) = vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),top_top(product_prod(X1,X0)))))),
% 3.31/0.91 inference(fool_elimination,[],[f478])).
% 3.31/0.91 thf(f478,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top(X0) & top(X1)) => (top_top(X1) = vAPP(product_prod(X1,X0),X1,product_fst(X1,X0),top_top(product_prod(X1,X0)))))),
% 3.31/0.91 inference(rectify,[],[f177])).
% 3.31/0.91 thf(f177,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType] : ((top(X2) & top(X0)) => (vAPP(product_prod(X0,X2),X0,product_fst(X0,X2),top_top(product_prod(X0,X2))) = top_top(X0)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_fst__top)).
% 3.31/0.91 thf(f2855,plain,(
% 3.31/0.91 spl132_94 | ~spl132_7 | ~spl132_40),
% 3.31/0.91 inference(avatar_split_clause,[],[f2313,f2250,f2067,f2852])).
% 3.31/0.91 thf(f2852,plain,(
% 3.31/0.91 spl132_94 <=> ($true = type(a))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_94])])).
% 3.31/0.91 thf(f2250,plain,(
% 3.31/0.91 spl132_40 <=> ! [X0 : $tType] : ((type(X0) = $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_40])])).
% 3.31/0.91 thf(f2313,plain,(
% 3.31/0.91 ($true = type(a)) | (~spl132_7 | ~spl132_40)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2300])).
% 3.31/0.91 thf(f2300,plain,(
% 3.31/0.91 ($true != $true) | ($true = type(a)) | (~spl132_7 | ~spl132_40)),
% 3.31/0.91 inference(superposition,[],[f2251,f2069])).
% 3.31/0.91 thf(f2251,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((finite_finite(X0) != $true) | (type(X0) = $true)) ) | ~spl132_40),
% 3.31/0.91 inference(avatar_component_clause,[],[f2250])).
% 3.31/0.91 thf(f2850,plain,(
% 3.31/0.91 spl132_93),
% 3.31/0.91 inference(avatar_split_clause,[],[f1550,f2848])).
% 3.31/0.91 thf(f2848,plain,(
% 3.31/0.91 spl132_93 <=> ! [X1 : $tType,X0 : $tType] : ((top_top(X1) = vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),top_top(product_prod(X0,X1)))) | (top(X0) != $true) | (top(X1) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_93])])).
% 3.31/0.91 thf(f1550,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : ((top_top(X1) = vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),top_top(product_prod(X0,X1)))) | (top(X0) != $true) | (top(X1) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1023])).
% 3.31/0.91 thf(f1023,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top_top(X1) = vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),top_top(product_prod(X0,X1)))) | (top(X0) != $true) | (top(X1) != $true))),
% 3.31/0.91 inference(flattening,[],[f1022])).
% 3.31/0.91 thf(f1022,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top_top(X1) = vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),top_top(product_prod(X0,X1)))) | ((top(X0) != $true) | (top(X1) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f477])).
% 3.31/0.91 thf(f477,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((top(X0) = $true) & (top(X1) = $true)) => (top_top(X1) = vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),top_top(product_prod(X0,X1)))))),
% 3.31/0.91 inference(fool_elimination,[],[f476])).
% 3.31/0.91 thf(f476,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top(X0) & top(X1)) => (top_top(X1) = vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),top_top(product_prod(X0,X1)))))),
% 3.31/0.91 inference(rectify,[],[f178])).
% 3.31/0.91 thf(f178,axiom,(
% 3.31/0.91 ! [X2 : $tType,X0 : $tType] : ((top(X2) & top(X0)) => (top_top(X0) = vAPP(product_prod(X2,X0),X0,product_snd(X2,X0),top_top(product_prod(X2,X0)))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_snd__top)).
% 3.31/0.91 thf(f2846,plain,(
% 3.31/0.91 spl132_92),
% 3.31/0.91 inference(avatar_split_clause,[],[f1479,f2844])).
% 3.31/0.91 thf(f2844,plain,(
% 3.31/0.91 spl132_92 <=> ! [X0 : $tType,X1 : X0] : ((top_top(X0) = X1) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),top_top(X0)),X1)) | (order_top(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_92])])).
% 3.31/0.91 thf(f1479,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : X0] : ((top_top(X0) = X1) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),top_top(X0)),X1)) | (order_top(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f961])).
% 3.31/0.91 thf(f961,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0] : ((top_top(X0) = X1) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),top_top(X0)),X1))) | (order_top(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f369])).
% 3.31/0.91 thf(f369,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((order_top(X0) = $true) => ! [X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),top_top(X0)),X1)) => (top_top(X0) = X1)))),
% 3.31/0.91 inference(fool_elimination,[],[f368])).
% 3.31/0.91 thf(f368,plain,(
% 3.31/0.91 ! [X0 : $tType] : (order_top(X0) => ! [X1 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),top_top(X0)),X1) => (top_top(X0) = X1)))),
% 3.31/0.91 inference(rectify,[],[f180])).
% 3.31/0.91 thf(f180,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (order_top(X0) => ! [X32 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),top_top(X0)),X32) => (top_top(X0) = X32)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_top_Oextremum__uniqueI)).
% 3.31/0.91 thf(f2836,plain,(
% 3.31/0.91 spl132_91),
% 3.31/0.91 inference(avatar_split_clause,[],[f1619,f2834])).
% 3.31/0.91 thf(f2834,plain,(
% 3.31/0.91 spl132_91 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_91])])).
% 3.31/0.91 thf(f1619,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f593])).
% 3.31/0.91 thf(f593,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)),
% 3.31/0.91 inference(fool_elimination,[],[f592])).
% 3.31/0.91 thf(f592,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)),
% 3.31/0.91 inference(rectify,[],[f316])).
% 3.31/0.91 thf(f316,axiom,(
% 3.31/0.91 ! [X0 : $tType,X14 : X0,X15 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X14),X15) = X14)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T)).
% 3.31/0.91 thf(f2832,plain,(
% 3.31/0.91 spl132_90),
% 3.31/0.91 inference(avatar_split_clause,[],[f1618,f2830])).
% 3.31/0.91 thf(f2830,plain,(
% 3.31/0.91 spl132_90 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_90])])).
% 3.31/0.91 thf(f1618,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f591])).
% 3.31/0.91 thf(f591,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)),
% 3.31/0.91 inference(fool_elimination,[],[f590])).
% 3.31/0.91 thf(f590,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)),
% 3.31/0.91 inference(rectify,[],[f315])).
% 3.31/0.91 thf(f315,axiom,(
% 3.31/0.91 ! [X0 : $tType,X14 : X0,X15 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X14),X15) = X15)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T)).
% 3.31/0.91 thf(f2828,plain,(
% 3.31/0.91 spl132_89),
% 3.31/0.91 inference(avatar_split_clause,[],[f1471,f2826])).
% 3.31/0.91 thf(f2826,plain,(
% 3.31/0.91 spl132_89 <=> ! [X0 : $tType] : (top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP($o,sTfun(X0,$o),kCOMB,$true)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_89])])).
% 3.31/0.91 thf(f1471,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP($o,sTfun(X0,$o),kCOMB,$true)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f353])).
% 3.31/0.91 thf(f353,plain,(
% 3.31/0.91 ! [X0 : $tType] : (top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP($o,sTfun(X0,$o),kCOMB,$true)))),
% 3.31/0.91 inference(fool_elimination,[],[f352])).
% 3.31/0.91 thf(f352,plain,(
% 3.31/0.91 ! [X0 : $tType] : (top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X1 : X0] : ($true))))),
% 3.31/0.91 inference(rectify,[],[f187])).
% 3.31/0.91 thf(f187,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X20 : X0] : ($true))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_UNIV__def)).
% 3.31/0.91 thf(f2816,plain,(
% 3.31/0.91 spl132_88),
% 3.31/0.91 inference(avatar_split_clause,[],[f1587,f2814])).
% 3.31/0.91 thf(f2814,plain,(
% 3.31/0.91 spl132_88 <=> ! [X1 : $tType,X0 : $tType] : ((top_top(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,top_top(X0))) | (top(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_88])])).
% 3.31/0.91 thf(f1587,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : ((top_top(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,top_top(X0))) | (top(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1081])).
% 3.31/0.91 thf(f1081,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top_top(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,top_top(X0))) | (top(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f539])).
% 3.31/0.91 thf(f539,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top(X0) = $true) => (top_top(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,top_top(X0))))),
% 3.31/0.91 inference(fool_elimination,[],[f538])).
% 3.31/0.91 thf(f538,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (top(X0) => (top_top(sTfun(X1,X0)) = (^[X2 : X1] : (top_top(X0)))))),
% 3.31/0.91 inference(rectify,[],[f174])).
% 3.31/0.91 thf(f174,axiom,(
% 3.31/0.91 ! [X1 : $tType,X63 : $tType] : (top(X1) => (top_top(sTfun(X63,X1)) = (^[X20 : X63] : (top_top(X1)))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_top__apply)).
% 3.31/0.91 thf(f2812,plain,(
% 3.31/0.91 spl132_87 | ~spl132_4 | ~spl132_40),
% 3.31/0.91 inference(avatar_split_clause,[],[f2312,f2250,f2052,f2809])).
% 3.31/0.91 thf(f2809,plain,(
% 3.31/0.91 spl132_87 <=> ($true = type(b))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_87])])).
% 3.31/0.91 thf(f2312,plain,(
% 3.31/0.91 ($true = type(b)) | (~spl132_4 | ~spl132_40)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2301])).
% 3.31/0.91 thf(f2301,plain,(
% 3.31/0.91 ($true != $true) | ($true = type(b)) | (~spl132_4 | ~spl132_40)),
% 3.31/0.91 inference(superposition,[],[f2251,f2054])).
% 3.31/0.91 thf(f2807,plain,(
% 3.31/0.91 spl132_86),
% 3.31/0.91 inference(avatar_split_clause,[],[f1607,f2805])).
% 3.31/0.91 thf(f2805,plain,(
% 3.31/0.91 spl132_86 <=> ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),top_top(set(X0))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_86])])).
% 3.31/0.91 thf(f1607,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),top_top(set(X0))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f579])).
% 3.31/0.91 thf(f579,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),top_top(set(X0))))),
% 3.31/0.91 inference(fool_elimination,[],[f578])).
% 3.31/0.91 thf(f578,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),top_top(set(X0)))),
% 3.31/0.91 inference(rectify,[],[f185])).
% 3.31/0.91 thf(f185,axiom,(
% 3.31/0.91 ! [X0 : $tType,X11 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X11),top_top(set(X0)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_subset__UNIV)).
% 3.31/0.91 thf(f2795,plain,(
% 3.31/0.91 spl132_85),
% 3.31/0.91 inference(avatar_split_clause,[],[f1480,f2793])).
% 3.31/0.91 thf(f2793,plain,(
% 3.31/0.91 spl132_85 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),top_top(X0))) | (order_top(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_85])])).
% 3.31/0.91 thf(f1480,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),top_top(X0))) | (order_top(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f962])).
% 3.31/0.91 thf(f962,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),top_top(X0))) | (order_top(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f371])).
% 3.31/0.91 thf(f371,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((order_top(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),top_top(X0))))),
% 3.31/0.91 inference(fool_elimination,[],[f370])).
% 3.31/0.91 thf(f370,plain,(
% 3.31/0.91 ! [X0 : $tType] : (order_top(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),top_top(X0)))),
% 3.31/0.91 inference(rectify,[],[f182])).
% 3.31/0.91 thf(f182,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (order_top(X0) => ! [X32 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X32),top_top(X0)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_top__greatest)).
% 3.31/0.91 thf(f2771,plain,(
% 3.31/0.91 spl132_84),
% 3.31/0.91 inference(avatar_split_clause,[],[f1717,f2769])).
% 3.31/0.91 thf(f2769,plain,(
% 3.31/0.91 spl132_84 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : X0] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),top_top(sTfun(X0,sTfun(X1,$o))),X2),X3))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_84])])).
% 3.31/0.91 thf(f1717,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),top_top(sTfun(X0,sTfun(X1,$o))),X2),X3))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f749])).
% 3.31/0.91 thf(f749,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),top_top(sTfun(X0,sTfun(X1,$o))),X2),X3))),
% 3.31/0.91 inference(fool_elimination,[],[f748])).
% 3.31/0.91 thf(f748,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),top_top(sTfun(X0,sTfun(X1,$o))),X2),X3)),
% 3.31/0.91 inference(rectify,[],[f232])).
% 3.31/0.91 thf(f232,axiom,(
% 3.31/0.91 ! [X0 : $tType,X2 : $tType,X14 : X0,X15 : X2] : vAPP(X2,$o,vAPP(X0,sTfun(X2,$o),top_top(sTfun(X0,sTfun(X2,$o))),X14),X15)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_top2I)).
% 3.31/0.91 thf(f2767,plain,(
% 3.31/0.91 spl132_83 | ~spl132_8 | ~spl132_40),
% 3.31/0.91 inference(avatar_split_clause,[],[f2311,f2250,f2072,f2764])).
% 3.31/0.91 thf(f2764,plain,(
% 3.31/0.91 spl132_83 <=> ($true = type(c))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_83])])).
% 3.31/0.91 thf(f2311,plain,(
% 3.31/0.91 ($true = type(c)) | (~spl132_8 | ~spl132_40)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2302])).
% 3.31/0.91 thf(f2302,plain,(
% 3.31/0.91 ($true != $true) | ($true = type(c)) | (~spl132_8 | ~spl132_40)),
% 3.31/0.91 inference(superposition,[],[f2251,f2074])).
% 3.31/0.91 thf(f2762,plain,(
% 3.31/0.91 spl132_82),
% 3.31/0.91 inference(avatar_split_clause,[],[f1606,f2760])).
% 3.31/0.91 thf(f2760,plain,(
% 3.31/0.91 spl132_82 <=> ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_82])])).
% 3.31/0.91 thf(f1606,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f577])).
% 3.31/0.91 thf(f577,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1))),
% 3.31/0.91 inference(fool_elimination,[],[f576])).
% 3.31/0.91 thf(f576,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1)),
% 3.31/0.91 inference(rectify,[],[f116])).
% 3.31/0.91 thf(f116,axiom,(
% 3.31/0.91 ! [X0 : $tType,X11 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X11),X11)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_subset__refl)).
% 3.31/0.91 thf(f2758,plain,(
% 3.31/0.91 spl132_81),
% 3.31/0.91 inference(avatar_split_clause,[],[f1605,f2756])).
% 3.31/0.91 thf(f2756,plain,(
% 3.31/0.91 spl132_81 <=> ! [X0 : $tType,X1 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),top_top(set(X0))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_81])])).
% 3.31/0.91 thf(f1605,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),top_top(set(X0))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f575])).
% 3.31/0.91 thf(f575,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),top_top(set(X0))))),
% 3.31/0.91 inference(fool_elimination,[],[f574])).
% 3.31/0.91 thf(f574,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),top_top(set(X0)))),
% 3.31/0.91 inference(rectify,[],[f175])).
% 3.31/0.91 thf(f175,axiom,(
% 3.31/0.91 ! [X0 : $tType,X14 : X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),top_top(set(X0)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_UNIV__I)).
% 3.31/0.91 thf(f2754,plain,(
% 3.31/0.91 spl132_80),
% 3.31/0.91 inference(avatar_split_clause,[],[f1487,f2752])).
% 3.31/0.91 thf(f2752,plain,(
% 3.31/0.91 spl132_80 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_80])])).
% 3.31/0.91 thf(f1487,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f970])).
% 3.31/0.91 thf(f970,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f385])).
% 3.31/0.91 thf(f385,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)))),
% 3.31/0.91 inference(fool_elimination,[],[f384])).
% 3.31/0.91 thf(f384,plain,(
% 3.31/0.91 ! [X0 : $tType] : (order(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1))),
% 3.31/0.91 inference(rectify,[],[f156])).
% 3.31/0.91 thf(f156,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (order(X0) => ! [X32 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X32),X32))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_dual__order_Orefl)).
% 3.31/0.91 thf(f2750,plain,(
% 3.31/0.91 spl132_79),
% 3.31/0.91 inference(avatar_split_clause,[],[f1481,f2748])).
% 3.31/0.91 thf(f2748,plain,(
% 3.31/0.91 spl132_79 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_79])])).
% 3.31/0.91 thf(f1481,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f963])).
% 3.31/0.91 thf(f963,plain,(
% 3.31/0.91 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f373])).
% 3.31/0.91 thf(f373,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)))),
% 3.31/0.91 inference(fool_elimination,[],[f372])).
% 3.31/0.91 thf(f372,plain,(
% 3.31/0.91 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1))),
% 3.31/0.91 inference(rectify,[],[f129])).
% 3.31/0.91 thf(f129,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (preorder(X0) => ! [X14 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X14),X14))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_order__refl)).
% 3.31/0.91 thf(f2746,plain,(
% 3.31/0.91 spl132_78),
% 3.31/0.91 inference(avatar_split_clause,[],[f1469,f2744])).
% 3.31/0.91 thf(f2744,plain,(
% 3.31/0.91 spl132_78 <=> ! [X0 : $tType] : (top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),top_top(sTfun(X0,$o))))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_78])])).
% 3.31/0.91 thf(f1469,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),top_top(sTfun(X0,$o))))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f202])).
% 3.31/0.91 thf(f202,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),top_top(sTfun(X0,$o))))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_top__set__def)).
% 3.31/0.91 thf(f2740,plain,(
% 3.31/0.91 ~spl132_77),
% 3.31/0.91 inference(avatar_split_clause,[],[f1457,f2737])).
% 3.31/0.91 thf(f1457,plain,(
% 3.31/0.91 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2)) != $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f916])).
% 3.31/0.91 thf(f916,plain,(
% 3.31/0.91 (vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2)) != $true)),
% 3.31/0.91 inference(flattening,[],[f329])).
% 3.31/0.91 thf(f329,plain,(
% 3.31/0.91 ~(vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2)) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f328])).
% 3.31/0.91 thf(f328,plain,(
% 3.31/0.91 ~vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2))),
% 3.31/0.91 inference(rectify,[],[f325])).
% 3.31/0.91 thf(f325,negated_conjecture,(
% 3.31/0.91 ~vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2))),
% 3.31/0.91 inference(negated_conjecture,[],[f324])).
% 3.31/0.91 thf(f324,conjecture,(
% 3.31/0.91 vAPP(set(sum_sum(c,c)),$o,vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o),vAPP(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(product_prod(finite_Cartesian_vec(real,c),finite_Cartesian_vec(real,c)),sTfun(set(sum_sum(c,c)),$o)),denotational_Vagree(c),nu),nu2),vAPP(trm(a,c),set(sum_sum(c,c)),static_FVDiff(a,c),t2))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 3.31/0.91 thf(f2699,plain,(
% 3.31/0.91 spl132_76 | ~spl132_3 | ~spl132_40),
% 3.31/0.91 inference(avatar_split_clause,[],[f2310,f2250,f2047,f2696])).
% 3.31/0.91 thf(f2696,plain,(
% 3.31/0.91 spl132_76 <=> ($true = type(sc))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_76])])).
% 3.31/0.91 thf(f2310,plain,(
% 3.31/0.91 ($true = type(sc)) | (~spl132_3 | ~spl132_40)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2303])).
% 3.31/0.91 thf(f2303,plain,(
% 3.31/0.91 ($true != $true) | ($true = type(sc)) | (~spl132_3 | ~spl132_40)),
% 3.31/0.91 inference(superposition,[],[f2251,f2049])).
% 3.31/0.91 thf(f2570,plain,(
% 3.31/0.91 spl132_75 | ~spl132_5 | ~spl132_40),
% 3.31/0.91 inference(avatar_split_clause,[],[f2309,f2250,f2057,f2567])).
% 3.31/0.91 thf(f2567,plain,(
% 3.31/0.91 spl132_75 <=> ($true = type(sf))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_75])])).
% 3.31/0.91 thf(f2309,plain,(
% 3.31/0.91 ($true = type(sf)) | (~spl132_5 | ~spl132_40)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2304])).
% 3.31/0.91 thf(f2304,plain,(
% 3.31/0.91 ($true != $true) | ($true = type(sf)) | (~spl132_5 | ~spl132_40)),
% 3.31/0.91 inference(superposition,[],[f2251,f2059])).
% 3.31/0.91 thf(f2523,plain,(
% 3.31/0.91 spl132_74),
% 3.31/0.91 inference(avatar_split_clause,[],[f1583,f2521])).
% 3.31/0.91 thf(f2521,plain,(
% 3.31/0.91 spl132_74 <=> ! [X1 : $tType,X0 : $tType] : (($true = finite_finite(sTfun(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_74])])).
% 3.31/0.91 thf(f1583,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = finite_finite(sTfun(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1077])).
% 3.31/0.91 thf(f1077,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = finite_finite(sTfun(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1076])).
% 3.31/0.91 thf(f1076,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = finite_finite(sTfun(X0,X1))) | ((finite_finite(X1) != $true) | (finite_finite(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f531])).
% 3.31/0.91 thf(f531,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((finite_finite(X1) = $true) & (finite_finite(X0) = $true)) => ($true = finite_finite(sTfun(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f530])).
% 3.31/0.91 thf(f530,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X1) & finite_finite(X0)) => finite_finite(sTfun(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f269])).
% 3.31/0.91 thf(f269,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((finite_finite(X138) & finite_finite(X137)) => finite_finite(sTfun(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite)).
% 3.31/0.91 thf(f2519,plain,(
% 3.31/0.91 spl132_73),
% 3.31/0.91 inference(avatar_split_clause,[],[f1582,f2517])).
% 3.31/0.91 thf(f2517,plain,(
% 3.31/0.91 spl132_73 <=> ! [X1 : $tType,X0 : $tType] : (($true = finite_finite(product_prod(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_73])])).
% 3.31/0.91 thf(f1582,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = finite_finite(product_prod(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1075])).
% 3.31/0.91 thf(f1075,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = finite_finite(product_prod(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1074])).
% 3.31/0.91 thf(f1074,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = finite_finite(product_prod(X0,X1))) | ((finite_finite(X1) != $true) | (finite_finite(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f529])).
% 3.31/0.91 thf(f529,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((finite_finite(X1) = $true) & (finite_finite(X0) = $true)) => ($true = finite_finite(product_prod(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f528])).
% 3.31/0.91 thf(f528,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X1) & finite_finite(X0)) => finite_finite(product_prod(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f296])).
% 3.31/0.91 thf(f296,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((finite_finite(X138) & finite_finite(X137)) => finite_finite(product_prod(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Finite__Set_Ofinite_26)).
% 3.31/0.91 thf(f2515,plain,(
% 3.31/0.91 spl132_72 | ~spl132_2 | ~spl132_39),
% 3.31/0.91 inference(avatar_split_clause,[],[f2294,f2246,f2042,f2512])).
% 3.31/0.91 thf(f2512,plain,(
% 3.31/0.91 spl132_72 <=> ($true = ord(sz))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_72])])).
% 3.31/0.91 thf(f2042,plain,(
% 3.31/0.91 spl132_2 <=> (linorder(sz) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_2])])).
% 3.31/0.91 thf(f2246,plain,(
% 3.31/0.91 spl132_39 <=> ! [X0 : $tType] : ((ord(X0) = $true) | (linorder(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_39])])).
% 3.31/0.91 thf(f2294,plain,(
% 3.31/0.91 ($true = ord(sz)) | (~spl132_2 | ~spl132_39)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2291])).
% 3.31/0.91 thf(f2291,plain,(
% 3.31/0.91 ($true != $true) | ($true = ord(sz)) | (~spl132_2 | ~spl132_39)),
% 3.31/0.91 inference(superposition,[],[f2247,f2044])).
% 3.31/0.91 thf(f2044,plain,(
% 3.31/0.91 (linorder(sz) = $true) | ~spl132_2),
% 3.31/0.91 inference(avatar_component_clause,[],[f2042])).
% 3.31/0.91 thf(f2247,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((linorder(X0) != $true) | (ord(X0) = $true)) ) | ~spl132_39),
% 3.31/0.91 inference(avatar_component_clause,[],[f2246])).
% 3.31/0.91 thf(f2510,plain,(
% 3.31/0.91 spl132_71),
% 3.31/0.91 inference(avatar_split_clause,[],[f1581,f2508])).
% 3.31/0.91 thf(f2508,plain,(
% 3.31/0.91 spl132_71 <=> ! [X1 : $tType,X0 : $tType] : (($true = finite_finite(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_71])])).
% 3.31/0.91 thf(f1581,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = finite_finite(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1073])).
% 3.31/0.91 thf(f1073,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = finite_finite(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1072])).
% 3.31/0.91 thf(f1072,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = finite_finite(finite_Cartesian_vec(X0,X1))) | ((finite_finite(X1) != $true) | (finite_finite(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f527])).
% 3.31/0.91 thf(f527,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((finite_finite(X1) = $true) & (finite_finite(X0) = $true)) => ($true = finite_finite(finite_Cartesian_vec(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f526])).
% 3.31/0.91 thf(f526,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X1) & finite_finite(X0)) => finite_finite(finite_Cartesian_vec(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f310])).
% 3.31/0.91 thf(f310,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((finite_finite(X138) & finite_finite(X137)) => finite_finite(finite_Cartesian_vec(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_40)).
% 3.31/0.91 thf(f2506,plain,(
% 3.31/0.91 spl132_70),
% 3.31/0.91 inference(avatar_split_clause,[],[f1580,f2504])).
% 3.31/0.91 thf(f2504,plain,(
% 3.31/0.91 spl132_70 <=> ! [X1 : $tType,X0 : $tType] : (($true = finite_finite(sum_sum(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_70])])).
% 3.31/0.91 thf(f1580,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = finite_finite(sum_sum(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1071])).
% 3.31/0.91 thf(f1071,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = finite_finite(sum_sum(X0,X1))) | (finite_finite(X1) != $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1070])).
% 3.31/0.91 thf(f1070,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = finite_finite(sum_sum(X0,X1))) | ((finite_finite(X1) != $true) | (finite_finite(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f525])).
% 3.31/0.91 thf(f525,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((finite_finite(X1) = $true) & (finite_finite(X0) = $true)) => ($true = finite_finite(sum_sum(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f524])).
% 3.31/0.91 thf(f524,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X1) & finite_finite(X0)) => finite_finite(sum_sum(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f292])).
% 3.31/0.91 thf(f292,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((finite_finite(X138) & finite_finite(X137)) => finite_finite(sum_sum(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Finite__Set_Ofinite_22)).
% 3.31/0.91 thf(f2502,plain,(
% 3.31/0.91 spl132_69),
% 3.31/0.91 inference(avatar_split_clause,[],[f1579,f2500])).
% 3.31/0.91 thf(f2500,plain,(
% 3.31/0.91 spl132_69 <=> ! [X1 : $tType,X0 : $tType] : (($true = linorder(finite_Cartesian_vec(X0,X1))) | ($true != cARD_1(X1)) | (linorder(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_69])])).
% 3.31/0.91 thf(f1579,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = linorder(finite_Cartesian_vec(X0,X1))) | ($true != cARD_1(X1)) | (linorder(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1069])).
% 3.31/0.91 thf(f1069,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = linorder(finite_Cartesian_vec(X0,X1))) | ($true != cARD_1(X1)) | (linorder(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1068])).
% 3.31/0.91 thf(f1068,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = linorder(finite_Cartesian_vec(X0,X1))) | (($true != cARD_1(X1)) | (linorder(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f523])).
% 3.31/0.91 thf(f523,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((($true = cARD_1(X1)) & (linorder(X0) = $true)) => ($true = linorder(finite_Cartesian_vec(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f522])).
% 3.31/0.91 thf(f522,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((cARD_1(X1) & linorder(X0)) => linorder(finite_Cartesian_vec(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f309])).
% 3.31/0.91 thf(f309,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((cARD_1(X138) & linorder(X137)) => linorder(finite_Cartesian_vec(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_39)).
% 3.31/0.91 thf(f2498,plain,(
% 3.31/0.91 spl132_68),
% 3.31/0.91 inference(avatar_split_clause,[],[f1578,f2496])).
% 3.31/0.91 thf(f2496,plain,(
% 3.31/0.91 spl132_68 <=> ! [X1 : $tType,X0 : $tType] : (($true = topolo503727757_space(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (topolo503727757_space(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_68])])).
% 3.31/0.91 thf(f1578,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = topolo503727757_space(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (topolo503727757_space(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1067])).
% 3.31/0.91 thf(f1067,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = topolo503727757_space(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (topolo503727757_space(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1066])).
% 3.31/0.91 thf(f1066,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = topolo503727757_space(finite_Cartesian_vec(X0,X1))) | ((finite_finite(X1) != $true) | (topolo503727757_space(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f521])).
% 3.31/0.91 thf(f521,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((finite_finite(X1) = $true) & (topolo503727757_space(X0) = $true)) => ($true = topolo503727757_space(finite_Cartesian_vec(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f520])).
% 3.31/0.91 thf(f520,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X1) & topolo503727757_space(X0)) => topolo503727757_space(finite_Cartesian_vec(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f307])).
% 3.31/0.91 thf(f307,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((finite_finite(X138) & topolo503727757_space(X137)) => topolo503727757_space(finite_Cartesian_vec(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_37)).
% 3.31/0.91 thf(f2494,plain,(
% 3.31/0.91 spl132_67),
% 3.31/0.91 inference(avatar_split_clause,[],[f1577,f2492])).
% 3.31/0.91 thf(f2492,plain,(
% 3.31/0.91 spl132_67 <=> ! [X1 : $tType,X0 : $tType] : (($true = topolo503727757_space(product_prod(X0,X1))) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_67])])).
% 3.31/0.91 thf(f1577,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = topolo503727757_space(product_prod(X0,X1))) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1065])).
% 3.31/0.91 thf(f1065,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = topolo503727757_space(product_prod(X0,X1))) | (topolo503727757_space(X1) != $true) | (topolo503727757_space(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1064])).
% 3.31/0.91 thf(f1064,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = topolo503727757_space(product_prod(X0,X1))) | ((topolo503727757_space(X1) != $true) | (topolo503727757_space(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f519])).
% 3.31/0.91 thf(f519,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((topolo503727757_space(X1) = $true) & (topolo503727757_space(X0) = $true)) => ($true = topolo503727757_space(product_prod(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f518])).
% 3.31/0.91 thf(f518,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((topolo503727757_space(X1) & topolo503727757_space(X0)) => topolo503727757_space(product_prod(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f293])).
% 3.31/0.91 thf(f293,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((topolo503727757_space(X138) & topolo503727757_space(X137)) => topolo503727757_space(product_prod(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Topological__Spaces_Otopological__space_23)).
% 3.31/0.91 thf(f2490,plain,(
% 3.31/0.91 spl132_66),
% 3.31/0.91 inference(avatar_split_clause,[],[f1571,f2488])).
% 3.31/0.91 thf(f2488,plain,(
% 3.31/0.91 spl132_66 <=> ! [X1 : $tType,X0 : $tType] : (($true = ord(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (ord(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_66])])).
% 3.31/0.91 thf(f1571,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (ord(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1057])).
% 3.31/0.91 thf(f1057,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = ord(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (ord(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1056])).
% 3.31/0.91 thf(f1056,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = ord(finite_Cartesian_vec(X0,X1))) | ((finite_finite(X1) != $true) | (ord(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f511])).
% 3.31/0.91 thf(f511,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((finite_finite(X1) = $true) & (ord(X0) = $true)) => ($true = ord(finite_Cartesian_vec(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f510])).
% 3.31/0.91 thf(f510,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X1) & ord(X0)) => ord(finite_Cartesian_vec(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f312])).
% 3.31/0.91 thf(f312,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((finite_finite(X138) & ord(X137)) => ord(finite_Cartesian_vec(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_42)).
% 3.31/0.91 thf(f2486,plain,(
% 3.31/0.91 spl132_65),
% 3.31/0.91 inference(avatar_split_clause,[],[f1570,f2484])).
% 3.31/0.91 thf(f2484,plain,(
% 3.31/0.91 spl132_65 <=> ! [X1 : $tType,X0 : $tType] : (($true = ord(product_prod(X0,X1))) | ($true != ord(X1)) | (ord(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_65])])).
% 3.31/0.91 thf(f1570,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(product_prod(X0,X1))) | ($true != ord(X1)) | (ord(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1055])).
% 3.31/0.91 thf(f1055,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = ord(product_prod(X0,X1))) | ($true != ord(X1)) | (ord(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1054])).
% 3.31/0.91 thf(f1054,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = ord(product_prod(X0,X1))) | (($true != ord(X1)) | (ord(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f509])).
% 3.31/0.91 thf(f509,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((($true = ord(X1)) & (ord(X0) = $true)) => ($true = ord(product_prod(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f508])).
% 3.31/0.91 thf(f508,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((ord(X1) & ord(X0)) => ord(product_prod(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f299])).
% 3.31/0.91 thf(f299,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((ord(X138) & ord(X137)) => ord(product_prod(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oord_29)).
% 3.31/0.91 thf(f2482,plain,(
% 3.31/0.91 spl132_64),
% 3.31/0.91 inference(avatar_split_clause,[],[f1560,f2480])).
% 3.31/0.91 thf(f2480,plain,(
% 3.31/0.91 spl132_64 <=> ! [X1 : $tType,X0 : $tType] : (($true = order(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (order(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_64])])).
% 3.31/0.91 thf(f1560,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = order(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (order(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1039])).
% 3.31/0.91 thf(f1039,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = order(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (order(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1038])).
% 3.31/0.91 thf(f1038,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = order(finite_Cartesian_vec(X0,X1))) | ((finite_finite(X1) != $true) | (order(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f493])).
% 3.31/0.91 thf(f493,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((finite_finite(X1) = $true) & (order(X0) = $true)) => ($true = order(finite_Cartesian_vec(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f492])).
% 3.31/0.91 thf(f492,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X1) & order(X0)) => order(finite_Cartesian_vec(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f311])).
% 3.31/0.91 thf(f311,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((finite_finite(X138) & order(X137)) => order(finite_Cartesian_vec(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_41)).
% 3.31/0.91 thf(f2478,plain,(
% 3.31/0.91 spl132_63),
% 3.31/0.91 inference(avatar_split_clause,[],[f1559,f2476])).
% 3.31/0.91 thf(f2476,plain,(
% 3.31/0.91 spl132_63 <=> ! [X1 : $tType,X0 : $tType] : (($true = preorder(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (order(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_63])])).
% 3.31/0.91 thf(f1559,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (order(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1037])).
% 3.31/0.91 thf(f1037,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = preorder(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | (order(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1036])).
% 3.31/0.91 thf(f1036,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = preorder(finite_Cartesian_vec(X0,X1))) | ((finite_finite(X1) != $true) | (order(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f491])).
% 3.31/0.91 thf(f491,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((finite_finite(X1) = $true) & (order(X0) = $true)) => ($true = preorder(finite_Cartesian_vec(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f490])).
% 3.31/0.91 thf(f490,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X1) & order(X0)) => preorder(finite_Cartesian_vec(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f308])).
% 3.31/0.91 thf(f308,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((finite_finite(X138) & order(X137)) => preorder(finite_Cartesian_vec(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_38)).
% 3.31/0.91 thf(f2474,plain,(
% 3.31/0.91 spl132_62),
% 3.31/0.91 inference(avatar_split_clause,[],[f1558,f2472])).
% 3.31/0.91 thf(f2472,plain,(
% 3.31/0.91 spl132_62 <=> ! [X1 : $tType,X0 : $tType] : (($true = order(product_prod(X0,X1))) | (order(X1) != $true) | (order(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_62])])).
% 3.31/0.91 thf(f1558,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = order(product_prod(X0,X1))) | (order(X1) != $true) | (order(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1035])).
% 3.31/0.91 thf(f1035,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = order(product_prod(X0,X1))) | (order(X1) != $true) | (order(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1034])).
% 3.31/0.91 thf(f1034,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = order(product_prod(X0,X1))) | ((order(X1) != $true) | (order(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f489])).
% 3.31/0.91 thf(f489,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((order(X1) = $true) & (order(X0) = $true)) => ($true = order(product_prod(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f488])).
% 3.31/0.91 thf(f488,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((order(X1) & order(X0)) => order(product_prod(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f297])).
% 3.31/0.91 thf(f297,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((order(X138) & order(X137)) => order(product_prod(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oorder_27)).
% 3.31/0.91 thf(f2470,plain,(
% 3.31/0.91 spl132_61),
% 3.31/0.91 inference(avatar_split_clause,[],[f1553,f2468])).
% 3.31/0.91 thf(f2468,plain,(
% 3.31/0.91 spl132_61 <=> ! [X1 : $tType,X0 : $tType] : (($true = top(product_prod(X0,X1))) | (top(X1) != $true) | (top(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_61])])).
% 3.31/0.91 thf(f1553,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = top(product_prod(X0,X1))) | (top(X1) != $true) | (top(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1029])).
% 3.31/0.91 thf(f1029,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = top(product_prod(X0,X1))) | (top(X1) != $true) | (top(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1028])).
% 3.31/0.91 thf(f1028,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = top(product_prod(X0,X1))) | ((top(X1) != $true) | (top(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f483])).
% 3.31/0.91 thf(f483,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((top(X1) = $true) & (top(X0) = $true)) => ($true = top(product_prod(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f482])).
% 3.31/0.91 thf(f482,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top(X1) & top(X0)) => top(product_prod(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f298])).
% 3.31/0.91 thf(f298,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((top(X138) & top(X137)) => top(product_prod(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Otop_28)).
% 3.31/0.91 thf(f2466,plain,(
% 3.31/0.91 spl132_60),
% 3.31/0.91 inference(avatar_split_clause,[],[f1549,f2464])).
% 3.31/0.91 thf(f2464,plain,(
% 3.31/0.91 spl132_60 <=> ! [X1 : $tType,X0 : $tType] : (($true = preorder(product_prod(X0,X1))) | ($true != preorder(X1)) | (preorder(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_60])])).
% 3.31/0.91 thf(f1549,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(product_prod(X0,X1))) | ($true != preorder(X1)) | (preorder(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1021])).
% 3.31/0.91 thf(f1021,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = preorder(product_prod(X0,X1))) | ($true != preorder(X1)) | (preorder(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1020])).
% 3.31/0.91 thf(f1020,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = preorder(product_prod(X0,X1))) | (($true != preorder(X1)) | (preorder(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f475])).
% 3.31/0.91 thf(f475,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((($true = preorder(X1)) & (preorder(X0) = $true)) => ($true = preorder(product_prod(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f474])).
% 3.31/0.91 thf(f474,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((preorder(X1) & preorder(X0)) => preorder(product_prod(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f295])).
% 3.31/0.91 thf(f295,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((preorder(X138) & preorder(X137)) => preorder(product_prod(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Opreorder_25)).
% 3.31/0.91 thf(f2462,plain,(
% 3.31/0.91 spl132_59),
% 3.31/0.91 inference(avatar_split_clause,[],[f1548,f2460])).
% 3.31/0.91 thf(f2460,plain,(
% 3.31/0.91 spl132_59 <=> ! [X1 : $tType,X0 : $tType] : (($true = real_V55928688vector(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | ($true != real_V55928688vector(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_59])])).
% 3.31/0.91 thf(f1548,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = real_V55928688vector(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | ($true != real_V55928688vector(X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1019])).
% 3.31/0.91 thf(f1019,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = real_V55928688vector(finite_Cartesian_vec(X0,X1))) | (finite_finite(X1) != $true) | ($true != real_V55928688vector(X0)))),
% 3.31/0.91 inference(flattening,[],[f1018])).
% 3.31/0.91 thf(f1018,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = real_V55928688vector(finite_Cartesian_vec(X0,X1))) | ((finite_finite(X1) != $true) | ($true != real_V55928688vector(X0))))),
% 3.31/0.91 inference(ennf_transformation,[],[f473])).
% 3.31/0.91 thf(f473,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (((finite_finite(X1) = $true) & ($true = real_V55928688vector(X0))) => ($true = real_V55928688vector(finite_Cartesian_vec(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f472])).
% 3.31/0.91 thf(f472,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X1) & real_V55928688vector(X0)) => real_V55928688vector(finite_Cartesian_vec(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f263])).
% 3.31/0.91 thf(f263,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((finite_finite(X138) & real_V55928688vector(X137)) => real_V55928688vector(finite_Cartesian_vec(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_1)).
% 3.31/0.91 thf(f2458,plain,(
% 3.31/0.91 spl132_58),
% 3.31/0.91 inference(avatar_split_clause,[],[f1547,f2456])).
% 3.31/0.91 thf(f2456,plain,(
% 3.31/0.91 spl132_58 <=> ! [X1 : $tType,X0 : $tType] : (($true = topolo503727757_space(bounde2145540817linfun(X0,X1))) | ($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_58])])).
% 3.31/0.91 thf(f1547,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = topolo503727757_space(bounde2145540817linfun(X0,X1))) | ($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1017])).
% 3.31/0.91 thf(f1017,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = topolo503727757_space(bounde2145540817linfun(X0,X1))) | ($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0)))),
% 3.31/0.91 inference(flattening,[],[f1016])).
% 3.31/0.91 thf(f1016,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = topolo503727757_space(bounde2145540817linfun(X0,X1))) | (($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0))))),
% 3.31/0.91 inference(ennf_transformation,[],[f471])).
% 3.31/0.91 thf(f471,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((($true = real_V55928688vector(X1)) & ($true = real_V55928688vector(X0))) => ($true = topolo503727757_space(bounde2145540817linfun(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f470])).
% 3.31/0.91 thf(f470,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((real_V55928688vector(X1) & real_V55928688vector(X0)) => topolo503727757_space(bounde2145540817linfun(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f313])).
% 3.31/0.91 thf(f313,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((real_V55928688vector(X138) & real_V55928688vector(X137)) => topolo503727757_space(bounde2145540817linfun(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Bounded__Linear__Function_Oblinfun___Topological__Spaces_Otopological__space_43)).
% 3.31/0.91 thf(f2454,plain,(
% 3.31/0.91 spl132_57),
% 3.31/0.91 inference(avatar_split_clause,[],[f1546,f2452])).
% 3.31/0.91 thf(f2452,plain,(
% 3.31/0.91 spl132_57 <=> ! [X1 : $tType,X0 : $tType] : (($true = real_V55928688vector(product_prod(X0,X1))) | ($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_57])])).
% 3.31/0.91 thf(f1546,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = real_V55928688vector(product_prod(X0,X1))) | ($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1015])).
% 3.31/0.91 thf(f1015,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = real_V55928688vector(product_prod(X0,X1))) | ($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0)))),
% 3.31/0.91 inference(flattening,[],[f1014])).
% 3.31/0.91 thf(f1014,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = real_V55928688vector(product_prod(X0,X1))) | (($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0))))),
% 3.31/0.91 inference(ennf_transformation,[],[f469])).
% 3.31/0.91 thf(f469,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((($true = real_V55928688vector(X1)) & ($true = real_V55928688vector(X0))) => ($true = real_V55928688vector(product_prod(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f468])).
% 3.31/0.91 thf(f468,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((real_V55928688vector(X1) & real_V55928688vector(X0)) => real_V55928688vector(product_prod(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f264])).
% 3.31/0.91 thf(f264,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((real_V55928688vector(X138) & real_V55928688vector(X137)) => real_V55928688vector(product_prod(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_2)).
% 3.31/0.91 thf(f2450,plain,(
% 3.31/0.91 spl132_56),
% 3.31/0.91 inference(avatar_split_clause,[],[f1545,f2448])).
% 3.31/0.91 thf(f2448,plain,(
% 3.31/0.91 spl132_56 <=> ! [X1 : $tType,X0 : $tType] : (($true = order_top(product_prod(X0,X1))) | ($true != order_top(X1)) | (order_top(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_56])])).
% 3.31/0.91 thf(f1545,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = order_top(product_prod(X0,X1))) | ($true != order_top(X1)) | (order_top(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1013])).
% 3.31/0.91 thf(f1013,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = order_top(product_prod(X0,X1))) | ($true != order_top(X1)) | (order_top(X0) != $true))),
% 3.31/0.91 inference(flattening,[],[f1012])).
% 3.31/0.91 thf(f1012,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = order_top(product_prod(X0,X1))) | (($true != order_top(X1)) | (order_top(X0) != $true)))),
% 3.31/0.91 inference(ennf_transformation,[],[f467])).
% 3.31/0.91 thf(f467,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((($true = order_top(X1)) & (order_top(X0) = $true)) => ($true = order_top(product_prod(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f466])).
% 3.31/0.91 thf(f466,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((order_top(X1) & order_top(X0)) => order_top(product_prod(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f294])).
% 3.31/0.91 thf(f294,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((order_top(X138) & order_top(X137)) => order_top(product_prod(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oorder__top_24)).
% 3.31/0.91 thf(f2446,plain,(
% 3.31/0.91 spl132_55),
% 3.31/0.91 inference(avatar_split_clause,[],[f1544,f2444])).
% 3.31/0.91 thf(f2444,plain,(
% 3.31/0.91 spl132_55 <=> ! [X1 : $tType,X0 : $tType] : (($true = real_V55928688vector(bounde2145540817linfun(X0,X1))) | ($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_55])])).
% 3.31/0.91 thf(f1544,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = real_V55928688vector(bounde2145540817linfun(X0,X1))) | ($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1011])).
% 3.31/0.91 thf(f1011,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = real_V55928688vector(bounde2145540817linfun(X0,X1))) | ($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0)))),
% 3.31/0.91 inference(flattening,[],[f1010])).
% 3.31/0.91 thf(f1010,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = real_V55928688vector(bounde2145540817linfun(X0,X1))) | (($true != real_V55928688vector(X1)) | ($true != real_V55928688vector(X0))))),
% 3.31/0.91 inference(ennf_transformation,[],[f465])).
% 3.31/0.91 thf(f465,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((($true = real_V55928688vector(X1)) & ($true = real_V55928688vector(X0))) => ($true = real_V55928688vector(bounde2145540817linfun(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f464])).
% 3.31/0.91 thf(f464,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((real_V55928688vector(X1) & real_V55928688vector(X0)) => real_V55928688vector(bounde2145540817linfun(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f262])).
% 3.31/0.91 thf(f262,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : ((real_V55928688vector(X138) & real_V55928688vector(X137)) => real_V55928688vector(bounde2145540817linfun(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Bounded__Linear__Function_Oblinfun___Real__Vector__Spaces_Oreal__normed__vector)).
% 3.31/0.91 thf(f2442,plain,(
% 3.31/0.91 spl132_54),
% 3.31/0.91 inference(avatar_split_clause,[],[f1465,f2439])).
% 3.31/0.91 thf(f2439,plain,(
% 3.31/0.91 spl132_54 <=> (p(sc,sf,sz) = predicational(sc,sf,sz))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_54])])).
% 3.31/0.91 thf(f1465,plain,(
% 3.31/0.91 (p(sc,sf,sz) = predicational(sc,sf,sz))),
% 3.31/0.91 inference(cnf_transformation,[],[f14])).
% 3.31/0.91 thf(f14,axiom,(
% 3.31/0.91 (p(sc,sf,sz) = predicational(sc,sf,sz))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_P__def)).
% 3.31/0.91 thf(f2437,plain,(
% 3.31/0.91 spl132_53 | ~spl132_2 | ~spl132_38),
% 3.31/0.91 inference(avatar_split_clause,[],[f2279,f2242,f2042,f2434])).
% 3.31/0.91 thf(f2434,plain,(
% 3.31/0.91 spl132_53 <=> ($true = order(sz))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_53])])).
% 3.31/0.91 thf(f2242,plain,(
% 3.31/0.91 spl132_38 <=> ! [X0 : $tType] : ((order(X0) = $true) | (linorder(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_38])])).
% 3.31/0.91 thf(f2279,plain,(
% 3.31/0.91 ($true = order(sz)) | (~spl132_2 | ~spl132_38)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2276])).
% 3.31/0.91 thf(f2276,plain,(
% 3.31/0.91 ($true != $true) | ($true = order(sz)) | (~spl132_2 | ~spl132_38)),
% 3.31/0.91 inference(superposition,[],[f2243,f2044])).
% 3.31/0.91 thf(f2243,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((linorder(X0) != $true) | (order(X0) = $true)) ) | ~spl132_38),
% 3.31/0.91 inference(avatar_component_clause,[],[f2242])).
% 3.31/0.91 thf(f2432,plain,(
% 3.31/0.91 spl132_52),
% 3.31/0.91 inference(avatar_split_clause,[],[f1815,f2429])).
% 3.31/0.91 thf(f2429,plain,(
% 3.31/0.91 spl132_52 <=> (vAPP(trm(a,c),$o,dfree(a,c),t2) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_52])])).
% 3.31/0.91 thf(f1815,plain,(
% 3.31/0.91 (vAPP(trm(a,c),$o,dfree(a,c),t2) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f905])).
% 3.31/0.91 thf(f905,plain,(
% 3.31/0.91 (vAPP(trm(a,c),$o,dfree(a,c),t2) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f904])).
% 3.31/0.91 thf(f904,plain,(
% 3.31/0.91 vAPP(trm(a,c),$o,dfree(a,c),t2)),
% 3.31/0.91 inference(rectify,[],[f4])).
% 3.31/0.91 thf(f4,axiom,(
% 3.31/0.91 vAPP(trm(a,c),$o,dfree(a,c),t2)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_dfree2)).
% 3.31/0.91 thf(f2427,plain,(
% 3.31/0.91 spl132_51),
% 3.31/0.91 inference(avatar_split_clause,[],[f1814,f2424])).
% 3.31/0.91 thf(f2424,plain,(
% 3.31/0.91 spl132_51 <=> (vAPP(trm(a,c),$o,dfree(a,c),t1) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_51])])).
% 3.31/0.91 thf(f1814,plain,(
% 3.31/0.91 (vAPP(trm(a,c),$o,dfree(a,c),t1) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f903])).
% 3.31/0.91 thf(f903,plain,(
% 3.31/0.91 (vAPP(trm(a,c),$o,dfree(a,c),t1) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f902])).
% 3.31/0.91 thf(f902,plain,(
% 3.31/0.91 vAPP(trm(a,c),$o,dfree(a,c),t1)),
% 3.31/0.91 inference(rectify,[],[f8])).
% 3.31/0.91 thf(f8,axiom,(
% 3.31/0.91 vAPP(trm(a,c),$o,dfree(a,c),t1)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_dfree1)).
% 3.31/0.91 thf(f2370,plain,(
% 3.31/0.91 spl132_50),
% 3.31/0.91 inference(avatar_split_clause,[],[f1604,f2368])).
% 3.31/0.91 thf(f2368,plain,(
% 3.31/0.91 spl132_50 <=> ! [X0 : $tType,X1 : X0] : ($true = vAPP(X0,$o,top_top(sTfun(X0,$o)),X1))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_50])])).
% 3.31/0.91 thf(f1604,plain,(
% 3.31/0.91 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,top_top(sTfun(X0,$o)),X1))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f573])).
% 3.31/0.91 thf(f573,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0] : ($true = vAPP(X0,$o,top_top(sTfun(X0,$o)),X1))),
% 3.31/0.91 inference(fool_elimination,[],[f572])).
% 3.31/0.91 thf(f572,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : X0] : vAPP(X0,$o,top_top(sTfun(X0,$o)),X1)),
% 3.31/0.91 inference(rectify,[],[f231])).
% 3.31/0.91 thf(f231,axiom,(
% 3.31/0.91 ! [X0 : $tType,X14 : X0] : vAPP(X0,$o,top_top(sTfun(X0,$o)),X14)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_top1I)).
% 3.31/0.91 thf(f2366,plain,(
% 3.31/0.91 spl132_49 | ~spl132_2 | ~spl132_37),
% 3.31/0.91 inference(avatar_split_clause,[],[f2269,f2238,f2042,f2363])).
% 3.31/0.91 thf(f2363,plain,(
% 3.31/0.91 spl132_49 <=> ($true = preorder(sz))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_49])])).
% 3.31/0.91 thf(f2238,plain,(
% 3.31/0.91 spl132_37 <=> ! [X0 : $tType] : ((preorder(X0) = $true) | (linorder(X0) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_37])])).
% 3.31/0.91 thf(f2269,plain,(
% 3.31/0.91 ($true = preorder(sz)) | (~spl132_2 | ~spl132_37)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2266])).
% 3.31/0.91 thf(f2266,plain,(
% 3.31/0.91 ($true != $true) | ($true = preorder(sz)) | (~spl132_2 | ~spl132_37)),
% 3.31/0.91 inference(superposition,[],[f2239,f2044])).
% 3.31/0.91 thf(f2239,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((linorder(X0) != $true) | (preorder(X0) = $true)) ) | ~spl132_37),
% 3.31/0.91 inference(avatar_component_clause,[],[f2238])).
% 3.31/0.91 thf(f2361,plain,(
% 3.31/0.91 spl132_48),
% 3.31/0.91 inference(avatar_split_clause,[],[f1595,f2359])).
% 3.31/0.91 thf(f2359,plain,(
% 3.31/0.91 spl132_48 <=> ! [X1 : $tType,X0 : $tType] : (($true = topolo503727757_space(sTfun(X0,X1))) | (topolo503727757_space(X1) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_48])])).
% 3.31/0.91 thf(f1595,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = topolo503727757_space(sTfun(X0,X1))) | (topolo503727757_space(X1) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1089])).
% 3.31/0.91 thf(f1089,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = topolo503727757_space(sTfun(X0,X1))) | (topolo503727757_space(X1) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f555])).
% 3.31/0.91 thf(f555,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((topolo503727757_space(X1) = $true) => ($true = topolo503727757_space(sTfun(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f554])).
% 3.31/0.91 thf(f554,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (topolo503727757_space(X1) => topolo503727757_space(sTfun(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f266])).
% 3.31/0.91 thf(f266,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : (topolo503727757_space(X138) => topolo503727757_space(sTfun(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space)).
% 3.31/0.91 thf(f2357,plain,(
% 3.31/0.91 spl132_47),
% 3.31/0.91 inference(avatar_split_clause,[],[f1594,f2355])).
% 3.31/0.91 thf(f2355,plain,(
% 3.31/0.91 spl132_47 <=> ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X0,X1))) | ($true != ord(X1)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_47])])).
% 3.31/0.91 thf(f1594,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X0,X1))) | ($true != ord(X1))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1088])).
% 3.31/0.91 thf(f1088,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = ord(sTfun(X0,X1))) | ($true != ord(X1)))),
% 3.31/0.91 inference(ennf_transformation,[],[f553])).
% 3.31/0.91 thf(f553,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = ord(X1)) => ($true = ord(sTfun(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f552])).
% 3.31/0.91 thf(f552,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (ord(X1) => ord(sTfun(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f272])).
% 3.31/0.91 thf(f272,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : (ord(X138) => ord(sTfun(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord)).
% 3.31/0.91 thf(f2353,plain,(
% 3.31/0.91 spl132_46),
% 3.31/0.91 inference(avatar_split_clause,[],[f1589,f2351])).
% 3.31/0.91 thf(f2351,plain,(
% 3.31/0.91 spl132_46 <=> ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X0,X1))) | (order(X1) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_46])])).
% 3.31/0.91 thf(f1589,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X0,X1))) | (order(X1) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1083])).
% 3.31/0.91 thf(f1083,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = order(sTfun(X0,X1))) | (order(X1) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f543])).
% 3.31/0.91 thf(f543,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((order(X1) = $true) => ($true = order(sTfun(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f542])).
% 3.31/0.91 thf(f542,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (order(X1) => order(sTfun(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f270])).
% 3.31/0.91 thf(f270,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : (order(X138) => order(sTfun(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder)).
% 3.31/0.91 thf(f2349,plain,(
% 3.31/0.91 spl132_45),
% 3.31/0.91 inference(avatar_split_clause,[],[f1588,f2347])).
% 3.31/0.91 thf(f2347,plain,(
% 3.31/0.91 spl132_45 <=> ! [X1 : $tType,X0 : $tType] : (($true = top(sTfun(X0,X1))) | (top(X1) != $true))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_45])])).
% 3.31/0.91 thf(f1588,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = top(sTfun(X0,X1))) | (top(X1) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1082])).
% 3.31/0.91 thf(f1082,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = top(sTfun(X0,X1))) | (top(X1) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f541])).
% 3.31/0.91 thf(f541,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : ((top(X1) = $true) => ($true = top(sTfun(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f540])).
% 3.31/0.91 thf(f540,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (top(X1) => top(sTfun(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f271])).
% 3.31/0.91 thf(f271,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : (top(X138) => top(sTfun(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop)).
% 3.31/0.91 thf(f2345,plain,(
% 3.31/0.91 spl132_44),
% 3.31/0.91 inference(avatar_split_clause,[],[f1586,f2343])).
% 3.31/0.91 thf(f2343,plain,(
% 3.31/0.91 spl132_44 <=> ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_44])])).
% 3.31/0.91 thf(f1586,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1080])).
% 3.31/0.91 thf(f1080,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1)))),
% 3.31/0.91 inference(ennf_transformation,[],[f537])).
% 3.31/0.91 thf(f537,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = preorder(X1)) => ($true = preorder(sTfun(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f536])).
% 3.31/0.91 thf(f536,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (preorder(X1) => preorder(sTfun(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f268])).
% 3.31/0.91 thf(f268,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : (preorder(X138) => preorder(sTfun(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder)).
% 3.31/0.91 thf(f2341,plain,(
% 3.31/0.91 spl132_43),
% 3.31/0.91 inference(avatar_split_clause,[],[f1585,f2339])).
% 3.31/0.91 thf(f2339,plain,(
% 3.31/0.91 spl132_43 <=> ! [X1 : $tType,X0 : $tType] : (($true = order_top(sTfun(X0,X1))) | ($true != order_top(X1)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_43])])).
% 3.31/0.91 thf(f1585,plain,(
% 3.31/0.91 ( ! [X1 : $tType,X0 : $tType] : (($true = order_top(sTfun(X0,X1))) | ($true != order_top(X1))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1079])).
% 3.31/0.91 thf(f1079,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = order_top(sTfun(X0,X1))) | ($true != order_top(X1)))),
% 3.31/0.91 inference(ennf_transformation,[],[f535])).
% 3.31/0.91 thf(f535,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (($true = order_top(X1)) => ($true = order_top(sTfun(X0,X1))))),
% 3.31/0.91 inference(fool_elimination,[],[f534])).
% 3.31/0.91 thf(f534,plain,(
% 3.31/0.91 ! [X0 : $tType,X1 : $tType] : (order_top(X1) => order_top(sTfun(X0,X1)))),
% 3.31/0.91 inference(rectify,[],[f267])).
% 3.31/0.91 thf(f267,axiom,(
% 3.31/0.91 ! [X137 : $tType,X138 : $tType] : (order_top(X138) => order_top(sTfun(X137,X138)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top)).
% 3.31/0.91 thf(f2319,plain,(
% 3.31/0.91 spl132_42),
% 3.31/0.91 inference(avatar_split_clause,[],[f1529,f2317])).
% 3.31/0.91 thf(f1529,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : (($true = finite_finite(set(X0))) | (finite_finite(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1008])).
% 3.31/0.91 thf(f1008,plain,(
% 3.31/0.91 ! [X0 : $tType] : (($true = finite_finite(set(X0))) | (finite_finite(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f437])).
% 3.31/0.91 thf(f437,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((finite_finite(X0) = $true) => ($true = finite_finite(set(X0))))),
% 3.31/0.91 inference(fool_elimination,[],[f436])).
% 3.31/0.91 thf(f436,plain,(
% 3.31/0.91 ! [X0 : $tType] : (finite_finite(X0) => finite_finite(set(X0)))),
% 3.31/0.91 inference(rectify,[],[f275])).
% 3.31/0.91 thf(f275,axiom,(
% 3.31/0.91 ! [X137 : $tType] : (finite_finite(X137) => finite_finite(set(X137)))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_6)).
% 3.31/0.91 thf(f2287,plain,(
% 3.31/0.91 spl132_41 | ~spl132_2 | ~spl132_36),
% 3.31/0.91 inference(avatar_split_clause,[],[f2259,f2234,f2042,f2284])).
% 3.31/0.91 thf(f2284,plain,(
% 3.31/0.91 spl132_41 <=> ($true = type(sz))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_41])])).
% 3.31/0.91 thf(f2259,plain,(
% 3.31/0.91 ($true = type(sz)) | (~spl132_2 | ~spl132_36)),
% 3.31/0.91 inference(trivial_inequality_removal,[],[f2256])).
% 3.31/0.91 thf(f2256,plain,(
% 3.31/0.91 ($true != $true) | ($true = type(sz)) | (~spl132_2 | ~spl132_36)),
% 3.31/0.91 inference(superposition,[],[f2235,f2044])).
% 3.31/0.91 thf(f2252,plain,(
% 3.31/0.91 spl132_40),
% 3.31/0.91 inference(avatar_split_clause,[],[f1528,f2250])).
% 3.31/0.91 thf(f1528,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((type(X0) = $true) | (finite_finite(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f1007])).
% 3.31/0.91 thf(f1007,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((type(X0) = $true) | (finite_finite(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f435])).
% 3.31/0.91 thf(f435,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((finite_finite(X0) = $true) => (type(X0) = $true))),
% 3.31/0.91 inference(fool_elimination,[],[f434])).
% 3.31/0.91 thf(f434,plain,(
% 3.31/0.91 ! [X0 : $tType] : (finite_finite(X0) => type(X0))),
% 3.31/0.91 inference(rectify,[],[f257])).
% 3.31/0.91 thf(f257,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (finite_finite(X0) => type(X0))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Finite__Set_Ofinite___HOL_Otype)).
% 3.31/0.91 thf(f2248,plain,(
% 3.31/0.91 spl132_39),
% 3.31/0.91 inference(avatar_split_clause,[],[f1520,f2246])).
% 3.31/0.91 thf(f1520,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((ord(X0) = $true) | (linorder(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f998])).
% 3.31/0.91 thf(f998,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((ord(X0) = $true) | (linorder(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f421])).
% 3.31/0.91 thf(f421,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((linorder(X0) = $true) => (ord(X0) = $true))),
% 3.31/0.91 inference(fool_elimination,[],[f420])).
% 3.31/0.91 thf(f420,plain,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => ord(X0))),
% 3.31/0.91 inference(rectify,[],[f259])).
% 3.31/0.91 thf(f259,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => ord(X0))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oord)).
% 3.31/0.91 thf(f2244,plain,(
% 3.31/0.91 spl132_38),
% 3.31/0.91 inference(avatar_split_clause,[],[f1519,f2242])).
% 3.31/0.91 thf(f1519,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((order(X0) = $true) | (linorder(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f997])).
% 3.31/0.91 thf(f997,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((order(X0) = $true) | (linorder(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f419])).
% 3.31/0.91 thf(f419,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((linorder(X0) = $true) => (order(X0) = $true))),
% 3.31/0.91 inference(fool_elimination,[],[f418])).
% 3.31/0.91 thf(f418,plain,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => order(X0))),
% 3.31/0.91 inference(rectify,[],[f260])).
% 3.31/0.91 thf(f260,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => order(X0))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oorder)).
% 3.31/0.91 thf(f2240,plain,(
% 3.31/0.91 spl132_37),
% 3.31/0.91 inference(avatar_split_clause,[],[f1518,f2238])).
% 3.31/0.91 thf(f1518,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((preorder(X0) = $true) | (linorder(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f996])).
% 3.31/0.91 thf(f996,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((preorder(X0) = $true) | (linorder(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f417])).
% 3.31/0.91 thf(f417,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((linorder(X0) = $true) => (preorder(X0) = $true))),
% 3.31/0.91 inference(fool_elimination,[],[f416])).
% 3.31/0.91 thf(f416,plain,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => preorder(X0))),
% 3.31/0.91 inference(rectify,[],[f261])).
% 3.31/0.91 thf(f261,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => preorder(X0))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Opreorder)).
% 3.31/0.91 thf(f2236,plain,(
% 3.31/0.91 spl132_36),
% 3.31/0.91 inference(avatar_split_clause,[],[f1517,f2234])).
% 3.31/0.91 thf(f1517,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : ((type(X0) = $true) | (linorder(X0) != $true)) )),
% 3.31/0.91 inference(cnf_transformation,[],[f995])).
% 3.31/0.91 thf(f995,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((type(X0) = $true) | (linorder(X0) != $true))),
% 3.31/0.91 inference(ennf_transformation,[],[f415])).
% 3.31/0.91 thf(f415,plain,(
% 3.31/0.91 ! [X0 : $tType] : ((linorder(X0) = $true) => (type(X0) = $true))),
% 3.31/0.91 inference(fool_elimination,[],[f414])).
% 3.31/0.91 thf(f414,plain,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => type(X0))),
% 3.31/0.91 inference(rectify,[],[f258])).
% 3.31/0.91 thf(f258,axiom,(
% 3.31/0.91 ! [X0 : $tType] : (linorder(X0) => type(X0))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___HOL_Otype)).
% 3.31/0.91 thf(f2204,plain,(
% 3.31/0.91 spl132_35),
% 3.31/0.91 inference(avatar_split_clause,[],[f327,f2202])).
% 3.31/0.91 thf(f327,plain,(
% 3.31/0.91 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.31/0.91 introduced(fool_axiom,[])).
% 3.31/0.91 thf(f2200,plain,(
% 3.31/0.91 spl132_34),
% 3.31/0.91 inference(avatar_split_clause,[],[f1536,f2198])).
% 3.31/0.91 thf(f2198,plain,(
% 3.31/0.91 spl132_34 <=> ! [X0 : $tType] : ($true = ord(set(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_34])])).
% 3.31/0.91 thf(f1536,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : (($true = ord(set(X0)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f449])).
% 3.31/0.91 thf(f449,plain,(
% 3.31/0.91 ! [X0 : $tType] : ($true = ord(set(X0)))),
% 3.31/0.91 inference(fool_elimination,[],[f448])).
% 3.31/0.91 thf(f448,plain,(
% 3.31/0.91 ! [X0 : $tType] : ord(set(X0))),
% 3.31/0.91 inference(rectify,[],[f278])).
% 3.31/0.91 thf(f278,axiom,(
% 3.31/0.91 ! [X137 : $tType] : ord(set(X137))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_9)).
% 3.31/0.91 thf(f2196,plain,(
% 3.31/0.91 spl132_33),
% 3.31/0.91 inference(avatar_split_clause,[],[f1535,f2194])).
% 3.31/0.91 thf(f2194,plain,(
% 3.31/0.91 spl132_33 <=> ! [X0 : $tType] : ($true = order(set(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_33])])).
% 3.31/0.91 thf(f1535,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : (($true = order(set(X0)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f447])).
% 3.31/0.91 thf(f447,plain,(
% 3.31/0.91 ! [X0 : $tType] : ($true = order(set(X0)))),
% 3.31/0.91 inference(fool_elimination,[],[f446])).
% 3.31/0.91 thf(f446,plain,(
% 3.31/0.91 ! [X0 : $tType] : order(set(X0))),
% 3.31/0.91 inference(rectify,[],[f276])).
% 3.31/0.91 thf(f276,axiom,(
% 3.31/0.91 ! [X137 : $tType] : order(set(X137))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_7)).
% 3.31/0.91 thf(f2192,plain,(
% 3.31/0.91 spl132_32),
% 3.31/0.91 inference(avatar_split_clause,[],[f1534,f2190])).
% 3.31/0.91 thf(f2190,plain,(
% 3.31/0.91 spl132_32 <=> ! [X0 : $tType] : ($true = top(set(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_32])])).
% 3.31/0.91 thf(f1534,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : (($true = top(set(X0)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f445])).
% 3.31/0.91 thf(f445,plain,(
% 3.31/0.91 ! [X0 : $tType] : ($true = top(set(X0)))),
% 3.31/0.91 inference(fool_elimination,[],[f444])).
% 3.31/0.91 thf(f444,plain,(
% 3.31/0.91 ! [X0 : $tType] : top(set(X0))),
% 3.31/0.91 inference(rectify,[],[f277])).
% 3.31/0.91 thf(f277,axiom,(
% 3.31/0.91 ! [X137 : $tType] : top(set(X137))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_8)).
% 3.31/0.91 thf(f2188,plain,(
% 3.31/0.91 spl132_31),
% 3.31/0.91 inference(avatar_split_clause,[],[f1533,f2186])).
% 3.31/0.91 thf(f2186,plain,(
% 3.31/0.91 spl132_31 <=> ! [X0 : $tType] : ($true = preorder(set(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_31])])).
% 3.31/0.91 thf(f1533,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : (($true = preorder(set(X0)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f443])).
% 3.31/0.91 thf(f443,plain,(
% 3.31/0.91 ! [X0 : $tType] : ($true = preorder(set(X0)))),
% 3.31/0.91 inference(fool_elimination,[],[f442])).
% 3.31/0.91 thf(f442,plain,(
% 3.31/0.91 ! [X0 : $tType] : preorder(set(X0))),
% 3.31/0.91 inference(rectify,[],[f274])).
% 3.31/0.91 thf(f274,axiom,(
% 3.31/0.91 ! [X137 : $tType] : preorder(set(X137))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_5)).
% 3.31/0.91 thf(f2184,plain,(
% 3.31/0.91 spl132_30),
% 3.31/0.91 inference(avatar_split_clause,[],[f1532,f2182])).
% 3.31/0.91 thf(f2182,plain,(
% 3.31/0.91 spl132_30 <=> ! [X0 : $tType] : ($true = order_top(set(X0)))),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_30])])).
% 3.31/0.91 thf(f1532,plain,(
% 3.31/0.91 ( ! [X0 : $tType] : (($true = order_top(set(X0)))) )),
% 3.31/0.91 inference(cnf_transformation,[],[f441])).
% 3.31/0.91 thf(f441,plain,(
% 3.31/0.91 ! [X0 : $tType] : ($true = order_top(set(X0)))),
% 3.31/0.91 inference(fool_elimination,[],[f440])).
% 3.31/0.91 thf(f440,plain,(
% 3.31/0.91 ! [X0 : $tType] : order_top(set(X0))),
% 3.31/0.91 inference(rectify,[],[f273])).
% 3.31/0.91 thf(f273,axiom,(
% 3.31/0.91 ! [X137 : $tType] : order_top(set(X137))),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_4)).
% 3.31/0.91 thf(f2180,plain,(
% 3.31/0.91 spl132_29),
% 3.31/0.91 inference(avatar_split_clause,[],[f1813,f2177])).
% 3.31/0.91 thf(f2177,plain,(
% 3.31/0.91 spl132_29 <=> (finite_finite($o) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_29])])).
% 3.31/0.91 thf(f1813,plain,(
% 3.31/0.91 (finite_finite($o) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f901])).
% 3.31/0.91 thf(f901,plain,(
% 3.31/0.91 (finite_finite($o) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f900])).
% 3.31/0.91 thf(f900,plain,(
% 3.31/0.91 finite_finite($o)),
% 3.31/0.91 inference(rectify,[],[f283])).
% 3.31/0.91 thf(f283,axiom,(
% 3.31/0.91 finite_finite($o)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_13)).
% 3.31/0.91 thf(f2175,plain,(
% 3.31/0.91 spl132_28),
% 3.31/0.91 inference(avatar_split_clause,[],[f1812,f2172])).
% 3.31/0.91 thf(f2172,plain,(
% 3.31/0.91 spl132_28 <=> (finite_finite(product_unit) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_28])])).
% 3.31/0.91 thf(f1812,plain,(
% 3.31/0.91 (finite_finite(product_unit) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f899])).
% 3.31/0.91 thf(f899,plain,(
% 3.31/0.91 (finite_finite(product_unit) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f898])).
% 3.31/0.91 thf(f898,plain,(
% 3.31/0.91 finite_finite(product_unit)),
% 3.31/0.91 inference(rectify,[],[f303])).
% 3.31/0.91 thf(f303,axiom,(
% 3.31/0.91 finite_finite(product_unit)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Finite__Set_Ofinite_33)).
% 3.31/0.91 thf(f2170,plain,(
% 3.31/0.91 spl132_27),
% 3.31/0.91 inference(avatar_split_clause,[],[f1811,f2167])).
% 3.31/0.91 thf(f1811,plain,(
% 3.31/0.91 (linorder($o) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f897])).
% 3.31/0.91 thf(f897,plain,(
% 3.31/0.91 (linorder($o) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f896])).
% 3.31/0.91 thf(f896,plain,(
% 3.31/0.91 linorder($o)),
% 3.31/0.91 inference(rectify,[],[f282])).
% 3.31/0.91 thf(f282,axiom,(
% 3.31/0.91 linorder($o)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder)).
% 3.31/0.91 thf(f2165,plain,(
% 3.31/0.91 spl132_26),
% 3.31/0.91 inference(avatar_split_clause,[],[f1810,f2162])).
% 3.31/0.91 thf(f1810,plain,(
% 3.31/0.91 (linorder(real) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f895])).
% 3.31/0.91 thf(f895,plain,(
% 3.31/0.91 (linorder(real) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f894])).
% 3.31/0.91 thf(f894,plain,(
% 3.31/0.91 linorder(real)),
% 3.31/0.91 inference(rectify,[],[f289])).
% 3.31/0.91 thf(f289,axiom,(
% 3.31/0.91 linorder(real)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_19)).
% 3.31/0.91 thf(f2160,plain,(
% 3.31/0.91 spl132_25),
% 3.31/0.91 inference(avatar_split_clause,[],[f1809,f2157])).
% 3.31/0.91 thf(f1809,plain,(
% 3.31/0.91 (linorder(product_unit) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f893])).
% 3.31/0.91 thf(f893,plain,(
% 3.31/0.91 (linorder(product_unit) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f892])).
% 3.31/0.91 thf(f892,plain,(
% 3.31/0.91 linorder(product_unit)),
% 3.31/0.91 inference(rectify,[],[f302])).
% 3.31/0.91 thf(f302,axiom,(
% 3.31/0.91 linorder(product_unit)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Olinorder_32)).
% 3.31/0.91 thf(f2155,plain,(
% 3.31/0.91 spl132_24),
% 3.31/0.91 inference(avatar_split_clause,[],[f1808,f2152])).
% 3.31/0.91 thf(f2152,plain,(
% 3.31/0.91 spl132_24 <=> (topolo503727757_space($o) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_24])])).
% 3.31/0.91 thf(f1808,plain,(
% 3.31/0.91 (topolo503727757_space($o) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f891])).
% 3.31/0.91 thf(f891,plain,(
% 3.31/0.91 (topolo503727757_space($o) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f890])).
% 3.31/0.91 thf(f890,plain,(
% 3.31/0.91 topolo503727757_space($o)),
% 3.31/0.91 inference(rectify,[],[f279])).
% 3.31/0.91 thf(f279,axiom,(
% 3.31/0.91 topolo503727757_space($o)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_10)).
% 3.31/0.91 thf(f2150,plain,(
% 3.31/0.91 spl132_23),
% 3.31/0.91 inference(avatar_split_clause,[],[f1807,f2147])).
% 3.31/0.91 thf(f2147,plain,(
% 3.31/0.91 spl132_23 <=> (topolo503727757_space(real) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_23])])).
% 3.31/0.91 thf(f1807,plain,(
% 3.31/0.91 (topolo503727757_space(real) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f889])).
% 3.31/0.91 thf(f889,plain,(
% 3.31/0.91 (topolo503727757_space(real) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f888])).
% 3.31/0.91 thf(f888,plain,(
% 3.31/0.91 topolo503727757_space(real)),
% 3.31/0.91 inference(rectify,[],[f287])).
% 3.31/0.91 thf(f287,axiom,(
% 3.31/0.91 topolo503727757_space(real)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Otopological__space_17)).
% 3.31/0.91 thf(f2145,plain,(
% 3.31/0.91 spl132_22),
% 3.31/0.91 inference(avatar_split_clause,[],[f1806,f2142])).
% 3.31/0.91 thf(f2142,plain,(
% 3.31/0.91 spl132_22 <=> (ord($o) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_22])])).
% 3.31/0.91 thf(f1806,plain,(
% 3.31/0.91 (ord($o) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f887])).
% 3.31/0.91 thf(f887,plain,(
% 3.31/0.91 (ord($o) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f886])).
% 3.31/0.91 thf(f886,plain,(
% 3.31/0.91 ord($o)),
% 3.31/0.91 inference(rectify,[],[f286])).
% 3.31/0.91 thf(f286,axiom,(
% 3.31/0.91 ord($o)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_16)).
% 3.31/0.91 thf(f2140,plain,(
% 3.31/0.91 spl132_21),
% 3.31/0.91 inference(avatar_split_clause,[],[f1805,f2137])).
% 3.31/0.91 thf(f2137,plain,(
% 3.31/0.91 spl132_21 <=> (ord(real) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_21])])).
% 3.31/0.91 thf(f1805,plain,(
% 3.31/0.91 (ord(real) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f885])).
% 3.31/0.91 thf(f885,plain,(
% 3.31/0.91 (ord(real) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f884])).
% 3.31/0.91 thf(f884,plain,(
% 3.31/0.91 ord(real)),
% 3.31/0.91 inference(rectify,[],[f291])).
% 3.31/0.91 thf(f291,axiom,(
% 3.31/0.91 ord(real)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_21)).
% 3.31/0.91 thf(f2135,plain,(
% 3.31/0.91 spl132_20),
% 3.31/0.91 inference(avatar_split_clause,[],[f1804,f2132])).
% 3.31/0.91 thf(f2132,plain,(
% 3.31/0.91 spl132_20 <=> (ord(product_unit) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_20])])).
% 3.31/0.91 thf(f1804,plain,(
% 3.31/0.91 (ord(product_unit) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f883])).
% 3.31/0.91 thf(f883,plain,(
% 3.31/0.91 (ord(product_unit) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f882])).
% 3.31/0.91 thf(f882,plain,(
% 3.31/0.91 ord(product_unit)),
% 3.31/0.91 inference(rectify,[],[f306])).
% 3.31/0.91 thf(f306,axiom,(
% 3.31/0.91 ord(product_unit)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oord_36)).
% 3.31/0.91 thf(f2130,plain,(
% 3.31/0.91 spl132_19),
% 3.31/0.91 inference(avatar_split_clause,[],[f1803,f2127])).
% 3.31/0.91 thf(f2127,plain,(
% 3.31/0.91 spl132_19 <=> (order($o) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_19])])).
% 3.31/0.91 thf(f1803,plain,(
% 3.31/0.91 (order($o) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f881])).
% 3.31/0.91 thf(f881,plain,(
% 3.31/0.91 (order($o) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f880])).
% 3.31/0.91 thf(f880,plain,(
% 3.31/0.91 order($o)),
% 3.31/0.91 inference(rectify,[],[f284])).
% 3.31/0.91 thf(f284,axiom,(
% 3.31/0.91 order($o)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_14)).
% 3.31/0.91 thf(f2125,plain,(
% 3.31/0.91 spl132_18),
% 3.31/0.91 inference(avatar_split_clause,[],[f1802,f2122])).
% 3.31/0.91 thf(f2122,plain,(
% 3.31/0.91 spl132_18 <=> (order(real) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_18])])).
% 3.31/0.91 thf(f1802,plain,(
% 3.31/0.91 (order(real) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f879])).
% 3.31/0.91 thf(f879,plain,(
% 3.31/0.91 (order(real) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f878])).
% 3.31/0.91 thf(f878,plain,(
% 3.31/0.91 order(real)),
% 3.31/0.91 inference(rectify,[],[f290])).
% 3.31/0.91 thf(f290,axiom,(
% 3.31/0.91 order(real)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_20)).
% 3.31/0.91 thf(f2120,plain,(
% 3.31/0.91 spl132_17),
% 3.31/0.91 inference(avatar_split_clause,[],[f1801,f2117])).
% 3.31/0.91 thf(f2117,plain,(
% 3.31/0.91 spl132_17 <=> (order(product_unit) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_17])])).
% 3.31/0.91 thf(f1801,plain,(
% 3.31/0.91 (order(product_unit) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f877])).
% 3.31/0.91 thf(f877,plain,(
% 3.31/0.91 (order(product_unit) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f876])).
% 3.31/0.91 thf(f876,plain,(
% 3.31/0.91 order(product_unit)),
% 3.31/0.91 inference(rectify,[],[f304])).
% 3.31/0.91 thf(f304,axiom,(
% 3.31/0.91 order(product_unit)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_34)).
% 3.31/0.91 thf(f2115,plain,(
% 3.31/0.91 spl132_16),
% 3.31/0.91 inference(avatar_split_clause,[],[f1800,f2112])).
% 3.31/0.91 thf(f2112,plain,(
% 3.31/0.91 spl132_16 <=> (top($o) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_16])])).
% 3.31/0.91 thf(f1800,plain,(
% 3.31/0.91 (top($o) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f875])).
% 3.31/0.91 thf(f875,plain,(
% 3.31/0.91 (top($o) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f874])).
% 3.31/0.91 thf(f874,plain,(
% 3.31/0.91 top($o)),
% 3.31/0.91 inference(rectify,[],[f285])).
% 3.31/0.91 thf(f285,axiom,(
% 3.31/0.91 top($o)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_15)).
% 3.31/0.91 thf(f2110,plain,(
% 3.31/0.91 spl132_15),
% 3.31/0.91 inference(avatar_split_clause,[],[f1799,f2107])).
% 3.31/0.91 thf(f2107,plain,(
% 3.31/0.91 spl132_15 <=> (top(product_unit) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_15])])).
% 3.31/0.91 thf(f1799,plain,(
% 3.31/0.91 (top(product_unit) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f873])).
% 3.31/0.91 thf(f873,plain,(
% 3.31/0.91 (top(product_unit) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f872])).
% 3.31/0.91 thf(f872,plain,(
% 3.31/0.91 top(product_unit)),
% 3.31/0.91 inference(rectify,[],[f305])).
% 3.31/0.91 thf(f305,axiom,(
% 3.31/0.91 top(product_unit)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Otop_35)).
% 3.31/0.91 thf(f2105,plain,(
% 3.31/0.91 spl132_14),
% 3.31/0.91 inference(avatar_split_clause,[],[f1798,f2102])).
% 3.31/0.91 thf(f2102,plain,(
% 3.31/0.91 spl132_14 <=> (preorder($o) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_14])])).
% 3.31/0.91 thf(f1798,plain,(
% 3.31/0.91 (preorder($o) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f871])).
% 3.31/0.91 thf(f871,plain,(
% 3.31/0.91 (preorder($o) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f870])).
% 3.31/0.91 thf(f870,plain,(
% 3.31/0.91 preorder($o)),
% 3.31/0.91 inference(rectify,[],[f281])).
% 3.31/0.91 thf(f281,axiom,(
% 3.31/0.91 preorder($o)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12)).
% 3.31/0.91 thf(f2100,plain,(
% 3.31/0.91 spl132_13),
% 3.31/0.91 inference(avatar_split_clause,[],[f1797,f2097])).
% 3.31/0.91 thf(f2097,plain,(
% 3.31/0.91 spl132_13 <=> (preorder(real) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_13])])).
% 3.31/0.91 thf(f1797,plain,(
% 3.31/0.91 (preorder(real) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f869])).
% 3.31/0.91 thf(f869,plain,(
% 3.31/0.91 (preorder(real) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f868])).
% 3.31/0.91 thf(f868,plain,(
% 3.31/0.91 preorder(real)),
% 3.31/0.91 inference(rectify,[],[f288])).
% 3.31/0.91 thf(f288,axiom,(
% 3.31/0.91 preorder(real)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_18)).
% 3.31/0.91 thf(f2095,plain,(
% 3.31/0.91 spl132_12),
% 3.31/0.91 inference(avatar_split_clause,[],[f1796,f2092])).
% 3.31/0.91 thf(f2092,plain,(
% 3.31/0.91 spl132_12 <=> (preorder(product_unit) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_12])])).
% 3.31/0.91 thf(f1796,plain,(
% 3.31/0.91 (preorder(product_unit) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f867])).
% 3.31/0.91 thf(f867,plain,(
% 3.31/0.91 (preorder(product_unit) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f866])).
% 3.31/0.91 thf(f866,plain,(
% 3.31/0.91 preorder(product_unit)),
% 3.31/0.91 inference(rectify,[],[f301])).
% 3.31/0.91 thf(f301,axiom,(
% 3.31/0.91 preorder(product_unit)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Opreorder_31)).
% 3.31/0.91 thf(f2090,plain,(
% 3.31/0.91 spl132_11),
% 3.31/0.91 inference(avatar_split_clause,[],[f1795,f2087])).
% 3.31/0.91 thf(f2087,plain,(
% 3.31/0.91 spl132_11 <=> (order_top($o) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_11])])).
% 3.31/0.91 thf(f1795,plain,(
% 3.31/0.91 (order_top($o) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f865])).
% 3.31/0.91 thf(f865,plain,(
% 3.31/0.91 (order_top($o) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f864])).
% 3.31/0.91 thf(f864,plain,(
% 3.31/0.91 order_top($o)),
% 3.31/0.91 inference(rectify,[],[f280])).
% 3.31/0.91 thf(f280,axiom,(
% 3.31/0.91 order_top($o)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_11)).
% 3.31/0.91 thf(f2085,plain,(
% 3.31/0.91 spl132_10),
% 3.31/0.91 inference(avatar_split_clause,[],[f1794,f2082])).
% 3.31/0.91 thf(f2082,plain,(
% 3.31/0.91 spl132_10 <=> (real_V55928688vector(real) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_10])])).
% 3.31/0.91 thf(f1794,plain,(
% 3.31/0.91 (real_V55928688vector(real) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f863])).
% 3.31/0.91 thf(f863,plain,(
% 3.31/0.91 (real_V55928688vector(real) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f862])).
% 3.31/0.91 thf(f862,plain,(
% 3.31/0.91 real_V55928688vector(real)),
% 3.31/0.91 inference(rectify,[],[f265])).
% 3.31/0.91 thf(f265,axiom,(
% 3.31/0.91 real_V55928688vector(real)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector_3)).
% 3.31/0.91 thf(f2080,plain,(
% 3.31/0.91 spl132_9),
% 3.31/0.91 inference(avatar_split_clause,[],[f1793,f2077])).
% 3.31/0.91 thf(f2077,plain,(
% 3.31/0.91 spl132_9 <=> (order_top(product_unit) = $true)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_9])])).
% 3.31/0.91 thf(f1793,plain,(
% 3.31/0.91 (order_top(product_unit) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f861])).
% 3.31/0.91 thf(f861,plain,(
% 3.31/0.91 (order_top(product_unit) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f860])).
% 3.31/0.91 thf(f860,plain,(
% 3.31/0.91 order_top(product_unit)),
% 3.31/0.91 inference(rectify,[],[f300])).
% 3.31/0.91 thf(f300,axiom,(
% 3.31/0.91 order_top(product_unit)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__top_30)).
% 3.31/0.91 thf(f2075,plain,(
% 3.31/0.91 spl132_8),
% 3.31/0.91 inference(avatar_split_clause,[],[f1464,f2072])).
% 3.31/0.91 thf(f1464,plain,(
% 3.31/0.91 (finite_finite(c) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f343])).
% 3.31/0.91 thf(f343,plain,(
% 3.31/0.91 (finite_finite(c) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f342])).
% 3.31/0.91 thf(f342,plain,(
% 3.31/0.91 finite_finite(c)),
% 3.31/0.91 inference(rectify,[],[f317])).
% 3.31/0.91 thf(f317,axiom,(
% 3.31/0.91 finite_finite(c)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0)).
% 3.31/0.91 thf(f2070,plain,(
% 3.31/0.91 spl132_7),
% 3.31/0.91 inference(avatar_split_clause,[],[f1463,f2067])).
% 3.31/0.91 thf(f1463,plain,(
% 3.31/0.91 (finite_finite(a) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f341])).
% 3.31/0.91 thf(f341,plain,(
% 3.31/0.91 (finite_finite(a) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f340])).
% 3.31/0.91 thf(f340,plain,(
% 3.31/0.91 finite_finite(a)),
% 3.31/0.91 inference(rectify,[],[f318])).
% 3.31/0.91 thf(f318,axiom,(
% 3.31/0.91 finite_finite(a)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_1)).
% 3.31/0.91 thf(f2065,plain,(
% 3.31/0.91 spl132_6),
% 3.31/0.91 inference(avatar_split_clause,[],[f1462,f2062])).
% 3.31/0.91 thf(f1462,plain,(
% 3.31/0.91 (finite_finite(sz) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f339])).
% 3.31/0.91 thf(f339,plain,(
% 3.31/0.91 (finite_finite(sz) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f338])).
% 3.31/0.91 thf(f338,plain,(
% 3.31/0.91 finite_finite(sz)),
% 3.31/0.91 inference(rectify,[],[f319])).
% 3.31/0.91 thf(f319,axiom,(
% 3.31/0.91 finite_finite(sz)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_2)).
% 3.31/0.91 thf(f2060,plain,(
% 3.31/0.91 spl132_5),
% 3.31/0.91 inference(avatar_split_clause,[],[f1461,f2057])).
% 3.31/0.91 thf(f1461,plain,(
% 3.31/0.91 (finite_finite(sf) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f337])).
% 3.31/0.91 thf(f337,plain,(
% 3.31/0.91 (finite_finite(sf) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f336])).
% 3.31/0.91 thf(f336,plain,(
% 3.31/0.91 finite_finite(sf)),
% 3.31/0.91 inference(rectify,[],[f321])).
% 3.31/0.91 thf(f321,axiom,(
% 3.31/0.91 finite_finite(sf)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_4)).
% 3.31/0.91 thf(f2055,plain,(
% 3.31/0.91 spl132_4),
% 3.31/0.91 inference(avatar_split_clause,[],[f1460,f2052])).
% 3.31/0.91 thf(f1460,plain,(
% 3.31/0.91 (finite_finite(b) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f335])).
% 3.31/0.91 thf(f335,plain,(
% 3.31/0.91 (finite_finite(b) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f334])).
% 3.31/0.91 thf(f334,plain,(
% 3.31/0.91 finite_finite(b)),
% 3.31/0.91 inference(rectify,[],[f323])).
% 3.31/0.91 thf(f323,axiom,(
% 3.31/0.91 finite_finite(b)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_6)).
% 3.31/0.91 thf(f2050,plain,(
% 3.31/0.91 spl132_3),
% 3.31/0.91 inference(avatar_split_clause,[],[f1459,f2047])).
% 3.31/0.91 thf(f1459,plain,(
% 3.31/0.91 (finite_finite(sc) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f333])).
% 3.31/0.91 thf(f333,plain,(
% 3.31/0.91 (finite_finite(sc) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f332])).
% 3.31/0.91 thf(f332,plain,(
% 3.31/0.91 finite_finite(sc)),
% 3.31/0.91 inference(rectify,[],[f322])).
% 3.31/0.91 thf(f322,axiom,(
% 3.31/0.91 finite_finite(sc)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_5)).
% 3.31/0.91 thf(f2045,plain,(
% 3.31/0.91 spl132_2),
% 3.31/0.91 inference(avatar_split_clause,[],[f1458,f2042])).
% 3.31/0.91 thf(f1458,plain,(
% 3.31/0.91 (linorder(sz) = $true)),
% 3.31/0.91 inference(cnf_transformation,[],[f331])).
% 3.31/0.91 thf(f331,plain,(
% 3.31/0.91 (linorder(sz) = $true)),
% 3.31/0.91 inference(fool_elimination,[],[f330])).
% 3.31/0.91 thf(f330,plain,(
% 3.31/0.91 linorder(sz)),
% 3.31/0.91 inference(rectify,[],[f320])).
% 3.31/0.91 thf(f320,axiom,(
% 3.31/0.91 linorder(sz)),
% 3.31/0.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_3)).
% 3.31/0.91 thf(f2040,plain,(
% 3.31/0.91 ~spl132_1),
% 3.31/0.91 inference(avatar_split_clause,[],[f326,f2037])).
% 3.31/0.91 thf(f2037,plain,(
% 3.31/0.91 spl132_1 <=> ($true = $false)),
% 3.31/0.91 introduced(avatar_definition,[new_symbols(naming,[spl132_1])])).
% 3.31/0.91 thf(f326,plain,(
% 3.31/0.91 ($true != $false)),
% 3.31/0.91 introduced(fool_axiom,[])).
% 3.31/0.91 % SZS output end Proof for theBenchmark
% 3.31/0.91 % (14238)------------------------------
% 3.31/0.91 % (14238)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.31/0.91 % (14238)Termination reason: Refutation
% 3.31/0.91
% 3.31/0.91 % (14238)Memory used [KB]: 8029
% 3.31/0.91 % (14238)Time elapsed: 0.490 s
% 3.31/0.91 % (14238)Instructions burned: 1510 (million)
% 3.31/0.91 % (14221)Success in time 0.53 s
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