TSTP Solution File: ITP103^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP103^2 : 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 : n008.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 22:51:42 EDT 2024
% Result : Theorem 11.34s 1.99s
% Output : Refutation 11.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP103^2 : TPTP v8.2.0. Released v7.5.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 15:40:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (26920)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39 % (26935)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)
% 0.21/0.39 % (26933)WARNING: value z3 for option sas not known
% 0.21/0.40 % (26931)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40 % (26932)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40 % (26934)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (26933)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.40 % (26936)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.40 % (26937)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.42 % (26937)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.43 % Exception at run slice level% Exception at run slice level
% 0.21/0.43
% 0.21/0.43 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44 % (26964)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.44 % (26965)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)
% 0.21/0.44 % (26966)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)
% 0.21/0.47 % (26964)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.47 % (26965)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.48 % Exception at run slice level
% 0.21/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.49 % (26994)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)
% 10.70/1.94 % (26935)First to succeed.
% 11.34/1.99 % (26935)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26920"
% 11.34/1.99 % (26935)Refutation found. Thanks to Tanya!
% 11.34/1.99 % SZS status Theorem for theBenchmark
% 11.34/1.99 % SZS output start Proof for theBenchmark
% 11.34/1.99 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 11.34/1.99 thf(type_def_6, type, list: $tType > $tType).
% 11.34/1.99 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 11.34/1.99 thf(type_def_8, type, nat: $tType).
% 11.34/1.99 thf(type_def_9, type, a: $tType).
% 11.34/1.99 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 11.34/1.99 thf(func_def_1, type, list: $tType > $tType).
% 11.34/1.99 thf(func_def_2, type, nat: $tType).
% 11.34/1.99 thf(func_def_3, type, a: $tType).
% 11.34/1.99 thf(func_def_4, type, type: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_5, type, size: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_6, type, zero: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_7, type, field: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_8, type, order: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_9, type, mult_zero: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_11, type, ordered_ring: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_12, type, wellorder: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_13, type, division_ring: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_14, type, semiring_bits: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_15, type, semidom_divide: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_16, type, semigroup_mult: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_17, type, linordered_idom: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_18, type, linordered_ring: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_19, type, ordered_semiring: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_20, type, linordered_field: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_21, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_22, type, ordered_semiring_0: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_23, type, ordere1490568538miring: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_24, type, linord581940658strict: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_25, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_26, type, linord20386208strict: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_27, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_28, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_29, type, linord893533164strict: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_30, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_31, type, euclid191655569cancel: !>[X0: $tType]:($o)).
% 11.34/1.99 thf(func_def_32, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 11.34/1.99 thf(func_def_33, type, zero_zero: !>[X0: $tType]:(X0)).
% 11.34/1.99 thf(func_def_34, type, product: !>[X0: $tType, X1: $tType]:(list(X0) > list(X1) > list(product_prod(X0,X1)))).
% 11.34/1.99 thf(func_def_35, type, suc: nat > nat).
% 11.34/1.99 thf(func_def_36, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 11.34/1.99 thf(func_def_37, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 11.34/1.99 thf(func_def_38, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 11.34/1.99 thf(func_def_39, type, divide_divide: !>[X0: $tType]:(X0 > X0 > X0)).
% 11.34/1.99 thf(func_def_40, type, k: nat).
% 11.34/1.99 thf(func_def_41, type, n: nat).
% 11.34/1.99 thf(func_def_42, type, xs: list(a)).
% 11.34/1.99 thf(func_def_46, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 11.34/1.99 thf(func_def_47, type, vNOT: $o > $o).
% 11.34/1.99 thf(func_def_48, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
% 11.34/1.99 thf(func_def_49, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 11.34/1.99 thf(func_def_50, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 11.34/1.99 thf(func_def_51, type, vOR: $o > $o > $o).
% 11.34/1.99 thf(func_def_52, type, vAND: $o > $o > $o).
% 11.34/1.99 thf(func_def_53, type, vIMP: $o > $o > $o).
% 11.34/1.99 thf(func_def_54, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
% 11.34/1.99 thf(func_def_55, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 11.34/1.99 thf(func_def_56, type, sP0: nat > (nat > $o) > $o).
% 11.34/1.99 thf(func_def_57, type, sP1: (nat > nat > $o) > $o).
% 11.34/1.99 thf(func_def_58, type, sP2: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > $o)).
% 11.34/1.99 thf(func_def_59, type, sK3: nat > nat).
% 11.34/1.99 thf(func_def_60, type, sK4: nat > nat).
% 11.34/1.99 thf(func_def_61, type, sK5: nat > nat).
% 11.34/1.99 thf(func_def_62, type, sK6: (nat > $o) > nat).
% 11.34/1.99 thf(func_def_63, type, sK7: !>[X0: $tType]:((nat > X0) > nat)).
% 11.34/1.99 thf(func_def_64, type, sK8: !>[X0: $tType]:((nat > X0) > nat)).
% 11.34/1.99 thf(func_def_65, type, sK9: !>[X0: $tType]:(X0 > X0)).
% 11.34/1.99 thf(func_def_66, type, sK10: !>[X0: $tType]:(X0 > X0)).
% 11.34/1.99 thf(func_def_67, type, sK11: !>[X0: $tType]:(X0 > X0 > X0)).
% 11.34/1.99 thf(func_def_68, type, sK12: nat > nat).
% 11.34/1.99 thf(func_def_69, type, sK13: (nat > $o) > nat).
% 11.34/1.99 thf(func_def_70, type, sK14: (nat > $o) > nat).
% 11.34/1.99 thf(func_def_71, type, sK15: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 11.34/1.99 thf(func_def_72, type, sK16: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 11.34/1.99 thf(func_def_73, type, sK17: (nat > $o) > nat).
% 11.34/1.99 thf(func_def_74, type, sK18: (nat > $o) > nat).
% 11.34/1.99 thf(func_def_75, type, sK19: (nat > $o) > nat).
% 11.34/1.99 thf(func_def_76, type, sK20: (nat > $o) > nat).
% 11.34/1.99 thf(func_def_77, type, sK21: nat > nat > nat).
% 11.34/1.99 thf(func_def_78, type, sK22: nat > nat > nat).
% 11.34/1.99 thf(func_def_79, type, sK23: !>[X0: $tType]:(nat > list(X0))).
% 11.34/1.99 thf(func_def_80, type, sK24: !>[X0: $tType]:((list(X0) > $o) > list(X0))).
% 11.34/1.99 thf(func_def_81, type, sK25: (nat > nat > $o) > nat).
% 11.34/1.99 thf(func_def_82, type, sK26: (nat > nat > $o) > nat).
% 11.34/1.99 thf(func_def_83, type, sK27: (nat > nat > $o) > nat).
% 11.34/1.99 thf(func_def_84, type, sK28: (nat > nat > $o) > nat).
% 11.34/1.99 thf(func_def_85, type, sK29: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0)).
% 11.34/1.99 thf(func_def_86, type, sK30: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0)).
% 11.34/1.99 thf(func_def_87, type, sK31: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat)).
% 11.34/1.99 thf(func_def_88, type, sK32: nat > (nat > $o) > nat).
% 11.34/1.99 thf(func_def_89, type, sK33: (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_90, type, sK34: (nat > nat > $o) > nat).
% 11.34/1.99 thf(func_def_91, type, sK35: (nat > nat > $o) > nat).
% 11.34/1.99 thf(func_def_92, type, sK36: (nat > nat > $o) > nat).
% 11.34/1.99 thf(func_def_93, type, sK37: (nat > nat > $o) > nat).
% 11.34/1.99 thf(func_def_94, type, sK38: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 11.34/1.99 thf(func_def_95, type, sK39: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 11.34/1.99 thf(func_def_96, type, sK40: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 11.34/1.99 thf(func_def_98, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 11.34/1.99 thf(func_def_99, type, sK42: nat > (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_100, type, sK43: nat > nat > nat).
% 11.34/1.99 thf(func_def_101, type, sK44: nat > nat > nat).
% 11.34/1.99 thf(func_def_102, type, sK45: (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_103, type, sK46: (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_104, type, sK47: (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_105, type, sK48: (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_106, type, sK49: (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_107, type, sK50: (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_108, type, sK51: (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_109, type, sK52: (nat > $o) > nat > nat).
% 11.34/1.99 thf(func_def_110, type, sK53: nat > nat).
% 11.34/1.99 thf(f39542,plain,(
% 11.34/1.99 $false),
% 11.34/1.99 inference(avatar_sat_refutation,[],[f2248,f2253,f2258,f2263,f2268,f2273,f2278,f2283,f2288,f2293,f2298,f2303,f2308,f2313,f2318,f2323,f2328,f2333,f2338,f2343,f2348,f2353,f2358,f2363,f2367,f2371,f2375,f2407,f2412,f2418,f2422,f2432,f2438,f2442,f2446,f2450,f2454,f2458,f2470,f2474,f2478,f2482,f2487,f2491,f2498,f2502,f2506,f2512,f2526,f2530,f2534,f2538,f2542,f2548,f2552,f2556,f2560,f2564,f2568,f2588,f2630,f2634,f2646,f2650,f2662,f2672,f2676,f2680,f2684,f2688,f2692,f2696,f2761,f2765,f2769,f2786,f2790,f2802,f2834,f2840,f2844,f2848,f2852,f2856,f2940,f2944,f2948,f2962,f2966,f2972,f2978,f2982,f2986,f3007,f3011,f3015,f3021,f3025,f3113,f3117,f3127,f3139,f3149,f3153,f3157,f3161,f3165,f3181,f3193,f3197,f3205,f3209,f3213,f3233,f3237,f3248,f3271,f3277,f3289,f3300,f3311,f3319,f3323,f3327,f3331,f3335,f3339,f3343,f3347,f3351,f3355,f3359,f3367,f3426,f3430,f3596,f3600,f3634,f3638,f3642,f3646,f3650,f3655,f3659,f3687,f3696,f3700,f3726,f3730,f3844,f3849,f3853,f3857,f3891,f3895,f3899,f3903,f3907,f3911,f3915,f3919,f3923,f3927,f3931,f3935,f3939,f3943,f3949,f3953,f3957,f3961,f3965,f3969,f3973,f3977,f3994,f4081,f4149,f4163,f4167,f4171,f4204,f4233,f4245,f4249,f4253,f4257,f4261,f4265,f4269,f4273,f4277,f4281,f4285,f4289,f4293,f4297,f4301,f4305,f4309,f4339,f4412,f4448,f4461,f4465,f4473,f4521,f4539,f4543,f4567,f4571,f4575,f4617,f4635,f4652,f4664,f4755,f4759,f4775,f4779,f4795,f4799,f4863,f4867,f4905,f4909,f4913,f4917,f4921,f4927,f4931,f5228,f5232,f5236,f5240,f5244,f5248,f5252,f5256,f5260,f5264,f5268,f5272,f5276,f6241,f6245,f6249,f6261,f6273,f6287,f6359,f6381,f6554,f6558,f6561,f6602,f8413,f8431,f8712,f8716,f8720,f8724,f8728,f8735,f8739,f8743,f8747,f8751,f8755,f8759,f8763,f8767,f8774,f9054,f9056,f9058,f9060,f9066,f9069,f9071,f9073,f9075,f9077,f9079,f9081,f9083,f9085,f9087,f9089,f9091,f9093,f9095,f9097,f9099,f9101,f9103,f9105,f9107,f9109,f9111,f9113,f9115,f9117,f9119,f9121,f9123,f9125,f9127,f9129,f9131,f9133,f9135,f9137,f11337,f12787,f12941,f12945,f12949,f13008,f13012,f13181,f13297,f13301,f13306,f13310,f13314,f13318,f13322,f13326,f13678,f13682,f13686,f13690,f13694,f13698,f13702,f13717,f13725,f14604,f14608,f14612,f14616,f15027,f15031,f15035,f15128,f15132,f15136,f15140,f15144,f15148,f15672,f15696,f16746,f16750,f16754,f16758,f16762,f16789,f16793,f16797,f16801,f16805,f16813,f16827,f16849,f18376,f18380,f18384,f18388,f18392,f18397,f18492,f18496,f18501,f18516,f18925,f18929,f18933,f19797,f19801,f19805,f19811,f19815,f19819,f19823,f19827,f19831,f19835,f20098,f21001,f21005,f21009,f21020,f21024,f21028,f21032,f21036,f21040,f21044,f21048,f21052,f21056,f21064,f21068,f21072,f21664,f22643,f22673,f22677,f22787,f22791,f22795,f22799,f22803,f22807,f22830,f22835,f22839,f22843,f23615,f23619,f23623,f23627,f23631,f23635,f23639,f23643,f23647,f23658,f24315,f24336,f24340,f24344,f24348,f24352,f24356,f24516,f24520,f24524,f24528,f25021,f25045,f25049,f25053,f25057,f25061,f25065,f25069,f25161,f25165,f25888,f25892,f25896,f26015,f26019,f26023,f26031,f26036,f26400,f26517,f26560,f26588,f26592,f26596,f26867,f26877,f26911,f26915,f27177,f27181,f27185,f27189,f27198,f27202,f27206,f27210,f27214,f27218,f28017,f28021,f28025,f28029,f28033,f28037,f28041,f28045,f28054,f28058,f28062,f28066,f30656,f30660,f30719,f30723,f31985,f31989,f31993,f32123,f32127,f32131,f32135,f32140,f32144,f32148,f32152,f32156,f32160,f32164,f32168,f32172,f32176,f35681,f35685,f35689,f35693,f36295,f36358,f36362,f36367,f36378,f36382,f36386,f36390,f37568,f37572,f37576,f37580,f37584,f37588,f37592,f37657,f37661,f37665,f37669,f38557,f38561,f38565,f38569,f38573,f38578,f38582,f39284,f39288,f39292,f39296,f39323,f39327,f39331,f39335,f39339,f39343,f39347,f39351,f39355,f39359,f39364,f39368,f39372,f39376,f39380,f39384,f39388,f39400,f39531,f39534])).
% 11.34/1.99 thf(f39534,plain,(
% 11.34/1.99 ~spl41_44 | ~spl41_202 | ~spl41_522),
% 11.34/1.99 inference(avatar_contradiction_clause,[],[f39533])).
% 11.34/1.99 thf(f39533,plain,(
% 11.34/1.99 $false | (~spl41_44 | ~spl41_202 | ~spl41_522)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f39532])).
% 11.34/1.99 thf(f39532,plain,(
% 11.34/1.99 ($true = $false) | (~spl41_44 | ~spl41_202 | ~spl41_522)),
% 11.34/1.99 inference(forward_demodulation,[],[f39478,f4411])).
% 11.34/1.99 thf(f4411,plain,(
% 11.34/1.99 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | ~spl41_202),
% 11.34/1.99 inference(avatar_component_clause,[],[f4410])).
% 11.34/1.99 thf(f4410,plain,(
% 11.34/1.99 spl41_202 <=> ! [X0 : nat] : ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_202])])).
% 11.34/1.99 thf(f39478,plain,(
% 11.34/1.99 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),n)) | (~spl41_44 | ~spl41_522)),
% 11.34/1.99 inference(superposition,[],[f2490,f39363])).
% 11.34/1.99 thf(f39363,plain,(
% 11.34/1.99 (n = vAPP(nat,nat,suc,n)) | ~spl41_522),
% 11.34/1.99 inference(avatar_component_clause,[],[f39361])).
% 11.34/1.99 thf(f39361,plain,(
% 11.34/1.99 spl41_522 <=> (n = vAPP(nat,nat,suc,n))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_522])])).
% 11.34/1.99 thf(f2490,plain,(
% 11.34/1.99 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X0)))) ) | ~spl41_44),
% 11.34/1.99 inference(avatar_component_clause,[],[f2489])).
% 11.34/1.99 thf(f2489,plain,(
% 11.34/1.99 spl41_44 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_44])])).
% 11.34/1.99 thf(f39531,plain,(
% 11.34/1.99 ~spl41_28 | ~spl41_522),
% 11.34/1.99 inference(avatar_contradiction_clause,[],[f39530])).
% 11.34/1.99 thf(f39530,plain,(
% 11.34/1.99 $false | (~spl41_28 | ~spl41_522)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f39476])).
% 11.34/1.99 thf(f39476,plain,(
% 11.34/1.99 (n != n) | (~spl41_28 | ~spl41_522)),
% 11.34/1.99 inference(superposition,[],[f2406,f39363])).
% 11.34/1.99 thf(f2406,plain,(
% 11.34/1.99 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,X0) != X0)) ) | ~spl41_28),
% 11.34/1.99 inference(avatar_component_clause,[],[f2405])).
% 11.34/1.99 thf(f2405,plain,(
% 11.34/1.99 spl41_28 <=> ! [X0 : nat] : (vAPP(nat,nat,suc,X0) != X0)),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_28])])).
% 11.34/1.99 thf(f39400,plain,(
% 11.34/1.99 ~spl41_529 | ~spl41_530 | spl41_531 | ~spl41_26 | ~spl41_164 | ~spl41_248),
% 11.34/1.99 inference(avatar_split_clause,[],[f9156,f6251,f3929,f2369,f39398,f39394,f39390])).
% 11.34/1.99 thf(f39390,plain,(
% 11.34/1.99 spl41_529 <=> ($true = linord20386208strict($o))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_529])])).
% 11.34/1.99 thf(f39394,plain,(
% 11.34/1.99 spl41_530 <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),$true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_530])])).
% 11.34/1.99 thf(f39398,plain,(
% 11.34/1.99 spl41_531 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),X0)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),times_times($o),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_531])])).
% 11.34/1.99 thf(f2369,plain,(
% 11.34/1.99 spl41_26 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_26])])).
% 11.34/1.99 thf(f3929,plain,(
% 11.34/1.99 spl41_164 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord20386208strict(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_164])])).
% 11.34/1.99 thf(f6251,plain,(
% 11.34/1.99 spl41_248 <=> ($false = zero_zero($o))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_248])])).
% 11.34/1.99 thf(f9156,plain,(
% 11.34/1.99 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),$true)) | ($true != linord20386208strict($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),times_times($o),X0),X1))) ) | (~spl41_26 | ~spl41_164 | ~spl41_248)),
% 11.34/1.99 inference(forward_demodulation,[],[f9155,f6253])).
% 11.34/1.99 thf(f6253,plain,(
% 11.34/1.99 ($false = zero_zero($o)) | ~spl41_248),
% 11.34/1.99 inference(avatar_component_clause,[],[f6251])).
% 11.34/1.99 thf(f9155,plain,(
% 11.34/1.99 ( ! [X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),zero_zero($o)),X1)) | ($true != linord20386208strict($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),times_times($o),X0),X1))) ) | (~spl41_26 | ~spl41_164 | ~spl41_248)),
% 11.34/1.99 inference(forward_demodulation,[],[f9154,f6253])).
% 11.34/1.99 thf(f9154,plain,(
% 11.34/1.99 ( ! [X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),$true)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),zero_zero($o)),X0)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),zero_zero($o)),X1)) | ($true != linord20386208strict($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),times_times($o),X0),X1))) ) | (~spl41_26 | ~spl41_164 | ~spl41_248)),
% 11.34/1.99 inference(forward_demodulation,[],[f4059,f6253])).
% 11.34/1.99 thf(f4059,plain,(
% 11.34/1.99 ( ! [X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),zero_zero($o)),$true)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),zero_zero($o)),X0)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),zero_zero($o)),X1)) | ($true != linord20386208strict($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),times_times($o),X0),X1))) ) | (~spl41_26 | ~spl41_164)),
% 11.34/1.99 inference(superposition,[],[f3930,f2370])).
% 11.34/1.99 thf(f2370,plain,(
% 11.34/1.99 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl41_26),
% 11.34/1.99 inference(avatar_component_clause,[],[f2369])).
% 11.34/1.99 thf(f3930,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) | (linord20386208strict(X0) != $true)) ) | ~spl41_164),
% 11.34/1.99 inference(avatar_component_clause,[],[f3929])).
% 11.34/1.99 thf(f39388,plain,(
% 11.34/1.99 spl41_528 | ~spl41_26 | ~spl41_174),
% 11.34/1.99 inference(avatar_split_clause,[],[f4134,f3971,f2369,f39386])).
% 11.34/1.99 thf(f39386,plain,(
% 11.34/1.99 spl41_528 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_528])])).
% 11.34/1.99 thf(f3971,plain,(
% 11.34/1.99 spl41_174 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_174])])).
% 11.34/1.99 thf(f4134,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_174)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4133])).
% 11.34/1.99 thf(f4133,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_174)),
% 11.34/1.99 inference(superposition,[],[f3972,f2370])).
% 11.34/1.99 thf(f3972,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true)) ) | ~spl41_174),
% 11.34/1.99 inference(avatar_component_clause,[],[f3971])).
% 11.34/1.99 thf(f39384,plain,(
% 11.34/1.99 spl41_527 | ~spl41_26 | ~spl41_173),
% 11.34/1.99 inference(avatar_split_clause,[],[f4125,f3967,f2369,f39382])).
% 11.34/1.99 thf(f39382,plain,(
% 11.34/1.99 spl41_527 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_527])])).
% 11.34/1.99 thf(f3967,plain,(
% 11.34/1.99 spl41_173 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_173])])).
% 11.34/1.99 thf(f4125,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_173)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4124])).
% 11.34/1.99 thf(f4124,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_173)),
% 11.34/1.99 inference(superposition,[],[f3968,f2370])).
% 11.34/1.99 thf(f3968,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1))) | (linordered_field(X0) != $true)) ) | ~spl41_173),
% 11.34/1.99 inference(avatar_component_clause,[],[f3967])).
% 11.34/1.99 thf(f39380,plain,(
% 11.34/1.99 spl41_526 | ~spl41_26 | ~spl41_172),
% 11.34/1.99 inference(avatar_split_clause,[],[f4116,f3963,f2369,f39378])).
% 11.34/1.99 thf(f39378,plain,(
% 11.34/1.99 spl41_526 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_526])])).
% 11.34/1.99 thf(f3963,plain,(
% 11.34/1.99 spl41_172 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_172])])).
% 11.34/1.99 thf(f4116,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_172)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4115])).
% 11.34/1.99 thf(f4115,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_172)),
% 11.34/1.99 inference(superposition,[],[f3964,f2370])).
% 11.34/1.99 thf(f3964,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true)) ) | ~spl41_172),
% 11.34/1.99 inference(avatar_component_clause,[],[f3963])).
% 11.34/1.99 thf(f39376,plain,(
% 11.34/1.99 spl41_525 | ~spl41_26 | ~spl41_171),
% 11.34/1.99 inference(avatar_split_clause,[],[f4108,f3959,f2369,f39374])).
% 11.34/1.99 thf(f39374,plain,(
% 11.34/1.99 spl41_525 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_525])])).
% 11.34/1.99 thf(f3959,plain,(
% 11.34/1.99 spl41_171 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_171])])).
% 11.34/1.99 thf(f4108,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_171)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4107])).
% 11.34/1.99 thf(f4107,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_171)),
% 11.34/1.99 inference(superposition,[],[f3960,f2370])).
% 11.34/1.99 thf(f3960,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) ) | ~spl41_171),
% 11.34/1.99 inference(avatar_component_clause,[],[f3959])).
% 11.34/1.99 thf(f39372,plain,(
% 11.34/1.99 spl41_524 | ~spl41_26 | ~spl41_170),
% 11.34/1.99 inference(avatar_split_clause,[],[f4101,f3955,f2369,f39370])).
% 11.34/1.99 thf(f39370,plain,(
% 11.34/1.99 spl41_524 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_524])])).
% 11.34/1.99 thf(f3955,plain,(
% 11.34/1.99 spl41_170 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_170])])).
% 11.34/1.99 thf(f4101,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_170)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4100])).
% 11.34/1.99 thf(f4100,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_170)),
% 11.34/1.99 inference(superposition,[],[f3956,f2370])).
% 11.34/1.99 thf(f3956,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true)) ) | ~spl41_170),
% 11.34/1.99 inference(avatar_component_clause,[],[f3955])).
% 11.34/1.99 thf(f39368,plain,(
% 11.34/1.99 spl41_523 | ~spl41_26 | ~spl41_169),
% 11.34/1.99 inference(avatar_split_clause,[],[f4096,f3951,f2369,f39366])).
% 11.34/1.99 thf(f39366,plain,(
% 11.34/1.99 spl41_523 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_523])])).
% 11.34/1.99 thf(f3951,plain,(
% 11.34/1.99 spl41_169 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_169])])).
% 11.34/1.99 thf(f4096,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_169)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4095])).
% 11.34/1.99 thf(f4095,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_169)),
% 11.34/1.99 inference(superposition,[],[f3952,f2370])).
% 11.34/1.99 thf(f3952,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (linordered_field(X0) != $true)) ) | ~spl41_169),
% 11.34/1.99 inference(avatar_component_clause,[],[f3951])).
% 11.34/1.99 thf(f39364,plain,(
% 11.34/1.99 spl41_522 | ~spl41_63 | ~spl41_506),
% 11.34/1.99 inference(avatar_split_clause,[],[f39297,f38575,f2643,f39361])).
% 11.34/1.99 thf(f2643,plain,(
% 11.34/1.99 spl41_63 <=> (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),k) = vAPP(nat,nat,suc,n))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_63])])).
% 11.34/1.99 thf(f38575,plain,(
% 11.34/1.99 spl41_506 <=> (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),k) = n)),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_506])])).
% 11.34/1.99 thf(f39297,plain,(
% 11.34/1.99 (n = vAPP(nat,nat,suc,n)) | (~spl41_63 | ~spl41_506)),
% 11.34/1.99 inference(superposition,[],[f38577,f2645])).
% 11.34/1.99 thf(f2645,plain,(
% 11.34/1.99 (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),k) = vAPP(nat,nat,suc,n)) | ~spl41_63),
% 11.34/1.99 inference(avatar_component_clause,[],[f2643])).
% 11.34/1.99 thf(f38577,plain,(
% 11.34/1.99 (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),k) = n) | ~spl41_506),
% 11.34/1.99 inference(avatar_component_clause,[],[f38575])).
% 11.34/1.99 thf(f39359,plain,(
% 11.34/1.99 spl41_521 | ~spl41_26 | ~spl41_168),
% 11.34/1.99 inference(avatar_split_clause,[],[f4092,f3947,f2369,f39357])).
% 11.34/1.99 thf(f39357,plain,(
% 11.34/1.99 spl41_521 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_521])])).
% 11.34/1.99 thf(f3947,plain,(
% 11.34/1.99 spl41_168 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_168])])).
% 11.34/1.99 thf(f4092,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_168)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4091])).
% 11.34/1.99 thf(f4091,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_168)),
% 11.34/1.99 inference(superposition,[],[f3948,f2370])).
% 11.34/1.99 thf(f3948,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true)) ) | ~spl41_168),
% 11.34/1.99 inference(avatar_component_clause,[],[f3947])).
% 11.34/1.99 thf(f39355,plain,(
% 11.34/1.99 spl41_520 | ~spl41_26 | ~spl41_167),
% 11.34/1.99 inference(avatar_split_clause,[],[f4086,f3941,f2369,f39353])).
% 11.34/1.99 thf(f39353,plain,(
% 11.34/1.99 spl41_520 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_520])])).
% 11.34/1.99 thf(f3941,plain,(
% 11.34/1.99 spl41_167 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_167])])).
% 11.34/1.99 thf(f4086,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_167)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4085])).
% 11.34/1.99 thf(f4085,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_167)),
% 11.34/1.99 inference(superposition,[],[f3942,f2370])).
% 11.34/1.99 thf(f3942,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (linordered_field(X0) != $true)) ) | ~spl41_167),
% 11.34/1.99 inference(avatar_component_clause,[],[f3941])).
% 11.34/1.99 thf(f39351,plain,(
% 11.34/1.99 spl41_519 | ~spl41_26 | ~spl41_166),
% 11.34/1.99 inference(avatar_split_clause,[],[f4076,f3937,f2369,f39349])).
% 11.34/1.99 thf(f39349,plain,(
% 11.34/1.99 spl41_519 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_519])])).
% 11.34/1.99 thf(f3937,plain,(
% 11.34/1.99 spl41_166 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_166])])).
% 11.34/1.99 thf(f4076,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_166)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4075])).
% 11.34/1.99 thf(f4075,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_166)),
% 11.34/1.99 inference(superposition,[],[f3938,f2370])).
% 11.34/1.99 thf(f3938,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (linordered_field(X0) != $true)) ) | ~spl41_166),
% 11.34/1.99 inference(avatar_component_clause,[],[f3937])).
% 11.34/1.99 thf(f39347,plain,(
% 11.34/1.99 spl41_518 | ~spl41_26 | ~spl41_165),
% 11.34/1.99 inference(avatar_split_clause,[],[f4071,f3933,f2369,f39345])).
% 11.34/1.99 thf(f39345,plain,(
% 11.34/1.99 spl41_518 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord581940658strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_518])])).
% 11.34/1.99 thf(f3933,plain,(
% 11.34/1.99 spl41_165 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (linord581940658strict(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_165])])).
% 11.34/1.99 thf(f4071,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord581940658strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_165)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4070])).
% 11.34/1.99 thf(f4070,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord581940658strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_165)),
% 11.34/1.99 inference(superposition,[],[f3934,f2370])).
% 11.34/1.99 thf(f3934,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord581940658strict(X0) != $true)) ) | ~spl41_165),
% 11.34/1.99 inference(avatar_component_clause,[],[f3933])).
% 11.34/1.99 thf(f39343,plain,(
% 11.34/1.99 spl41_517 | ~spl41_26 | ~spl41_164),
% 11.34/1.99 inference(avatar_split_clause,[],[f4065,f3929,f2369,f39341])).
% 11.34/1.99 thf(f39341,plain,(
% 11.34/1.99 spl41_517 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_517])])).
% 11.34/1.99 thf(f4065,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))) ) | (~spl41_26 | ~spl41_164)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4064])).
% 11.34/1.99 thf(f4064,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))) ) | (~spl41_26 | ~spl41_164)),
% 11.34/1.99 inference(superposition,[],[f3930,f2370])).
% 11.34/1.99 thf(f39339,plain,(
% 11.34/1.99 spl41_516 | ~spl41_26 | ~spl41_163),
% 11.34/1.99 inference(avatar_split_clause,[],[f4054,f3925,f2369,f39337])).
% 11.34/1.99 thf(f39337,plain,(
% 11.34/1.99 spl41_516 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_516])])).
% 11.34/1.99 thf(f3925,plain,(
% 11.34/1.99 spl41_163 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord20386208strict(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_163])])).
% 11.34/1.99 thf(f4054,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))) ) | (~spl41_26 | ~spl41_163)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4053])).
% 11.34/1.99 thf(f4053,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))) ) | (~spl41_26 | ~spl41_163)),
% 11.34/1.99 inference(superposition,[],[f3926,f2370])).
% 11.34/1.99 thf(f3926,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linord20386208strict(X0) != $true)) ) | ~spl41_163),
% 11.34/1.99 inference(avatar_component_clause,[],[f3925])).
% 11.34/1.99 thf(f39335,plain,(
% 11.34/1.99 spl41_515 | ~spl41_26 | ~spl41_162),
% 11.34/1.99 inference(avatar_split_clause,[],[f4038,f3921,f2369,f39333])).
% 11.34/1.99 thf(f39333,plain,(
% 11.34/1.99 spl41_515 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_515])])).
% 11.34/1.99 thf(f3921,plain,(
% 11.34/1.99 spl41_162 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linord20386208strict(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_162])])).
% 11.34/1.99 thf(f4038,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_162)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4037])).
% 11.34/1.99 thf(f4037,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_162)),
% 11.34/1.99 inference(superposition,[],[f3922,f2370])).
% 11.34/1.99 thf(f3922,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord20386208strict(X0) != $true)) ) | ~spl41_162),
% 11.34/1.99 inference(avatar_component_clause,[],[f3921])).
% 11.34/1.99 thf(f39331,plain,(
% 11.34/1.99 spl41_514 | ~spl41_26 | ~spl41_161),
% 11.34/1.99 inference(avatar_split_clause,[],[f4029,f3917,f2369,f39329])).
% 11.34/1.99 thf(f39329,plain,(
% 11.34/1.99 spl41_514 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_514])])).
% 11.34/1.99 thf(f3917,plain,(
% 11.34/1.99 spl41_161 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linord20386208strict(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_161])])).
% 11.34/1.99 thf(f4029,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_161)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4028])).
% 11.34/1.99 thf(f4028,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_161)),
% 11.34/1.99 inference(superposition,[],[f3918,f2370])).
% 11.34/1.99 thf(f3918,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (linord20386208strict(X0) != $true)) ) | ~spl41_161),
% 11.34/1.99 inference(avatar_component_clause,[],[f3917])).
% 11.34/1.99 thf(f39327,plain,(
% 11.34/1.99 spl41_513 | ~spl41_26 | ~spl41_160),
% 11.34/1.99 inference(avatar_split_clause,[],[f4023,f3913,f2369,f39325])).
% 11.34/1.99 thf(f39325,plain,(
% 11.34/1.99 spl41_513 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_513])])).
% 11.34/1.99 thf(f3913,plain,(
% 11.34/1.99 spl41_160 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (linord20386208strict(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_160])])).
% 11.34/1.99 thf(f4023,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_160)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4022])).
% 11.34/1.99 thf(f4022,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (linord20386208strict(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_160)),
% 11.34/1.99 inference(superposition,[],[f3914,f2370])).
% 11.34/1.99 thf(f3914,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (linord20386208strict(X0) != $true)) ) | ~spl41_160),
% 11.34/1.99 inference(avatar_component_clause,[],[f3913])).
% 11.34/1.99 thf(f39323,plain,(
% 11.34/1.99 spl41_512 | ~spl41_26 | ~spl41_159),
% 11.34/1.99 inference(avatar_split_clause,[],[f4017,f3909,f2369,f39321])).
% 11.34/1.99 thf(f39321,plain,(
% 11.34/1.99 spl41_512 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | (ordered_semiring_0(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_512])])).
% 11.34/1.99 thf(f3909,plain,(
% 11.34/1.99 spl41_159 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (ordered_semiring_0(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_159])])).
% 11.34/1.99 thf(f4017,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | (ordered_semiring_0(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_159)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4016])).
% 11.34/1.99 thf(f4016,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | (ordered_semiring_0(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_159)),
% 11.34/1.99 inference(superposition,[],[f3910,f2370])).
% 11.34/1.99 thf(f3910,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (ordered_semiring_0(X0) != $true)) ) | ~spl41_159),
% 11.34/1.99 inference(avatar_component_clause,[],[f3909])).
% 11.34/1.99 thf(f39296,plain,(
% 11.34/1.99 spl41_511 | ~spl41_26 | ~spl41_158),
% 11.34/1.99 inference(avatar_split_clause,[],[f4008,f3905,f2369,f39294])).
% 11.34/1.99 thf(f39294,plain,(
% 11.34/1.99 spl41_511 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | (ordered_semiring_0(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_511])])).
% 11.34/1.99 thf(f3905,plain,(
% 11.34/1.99 spl41_158 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (ordered_semiring_0(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_158])])).
% 11.34/1.99 thf(f4008,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | (ordered_semiring_0(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_158)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4007])).
% 11.34/1.99 thf(f4007,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | (ordered_semiring_0(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_158)),
% 11.34/1.99 inference(superposition,[],[f3906,f2370])).
% 11.34/1.99 thf(f3906,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (ordered_semiring_0(X0) != $true)) ) | ~spl41_158),
% 11.34/1.99 inference(avatar_component_clause,[],[f3905])).
% 11.34/1.99 thf(f39292,plain,(
% 11.34/1.99 spl41_510 | ~spl41_26 | ~spl41_156),
% 11.34/1.99 inference(avatar_split_clause,[],[f3999,f3897,f2369,f39290])).
% 11.34/1.99 thf(f39290,plain,(
% 11.34/1.99 spl41_510 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (ordered_semiring_0(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_510])])).
% 11.34/1.99 thf(f3897,plain,(
% 11.34/1.99 spl41_156 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (ordered_semiring_0(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_156])])).
% 11.34/1.99 thf(f3999,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (ordered_semiring_0(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_156)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3998])).
% 11.34/1.99 thf(f3998,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (ordered_semiring_0(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_156)),
% 11.34/1.99 inference(superposition,[],[f3898,f2370])).
% 11.34/1.99 thf(f3898,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (ordered_semiring_0(X0) != $true)) ) | ~spl41_156),
% 11.34/1.99 inference(avatar_component_clause,[],[f3897])).
% 11.34/1.99 thf(f39288,plain,(
% 11.34/1.99 spl41_509 | ~spl41_26 | ~spl41_155),
% 11.34/1.99 inference(avatar_split_clause,[],[f3989,f3893,f2369,f39286])).
% 11.34/1.99 thf(f39286,plain,(
% 11.34/1.99 spl41_509 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (ordered_ring(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_509])])).
% 11.34/1.99 thf(f3893,plain,(
% 11.34/1.99 spl41_155 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (ordered_ring(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_155])])).
% 11.34/1.99 thf(f3989,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (ordered_ring(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_155)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3988])).
% 11.34/1.99 thf(f3988,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (ordered_ring(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_155)),
% 11.34/1.99 inference(superposition,[],[f3894,f2370])).
% 11.34/1.99 thf(f3894,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (ordered_ring(X0) != $true)) ) | ~spl41_155),
% 11.34/1.99 inference(avatar_component_clause,[],[f3893])).
% 11.34/1.99 thf(f39284,plain,(
% 11.34/1.99 spl41_508 | ~spl41_26 | ~spl41_154),
% 11.34/1.99 inference(avatar_split_clause,[],[f3982,f3889,f2369,f39282])).
% 11.34/1.99 thf(f39282,plain,(
% 11.34/1.99 spl41_508 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | (ordered_ring(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_508])])).
% 11.34/1.99 thf(f3889,plain,(
% 11.34/1.99 spl41_154 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (ordered_ring(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_154])])).
% 11.34/1.99 thf(f3982,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | (ordered_ring(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_154)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3981])).
% 11.34/1.99 thf(f3981,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | (ordered_ring(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_154)),
% 11.34/1.99 inference(superposition,[],[f3890,f2370])).
% 11.34/1.99 thf(f3890,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (ordered_ring(X0) != $true)) ) | ~spl41_154),
% 11.34/1.99 inference(avatar_component_clause,[],[f3889])).
% 11.34/1.99 thf(f38582,plain,(
% 11.34/1.99 ~spl41_421 | spl41_507 | ~spl41_44 | ~spl41_200),
% 11.34/1.99 inference(avatar_split_clause,[],[f4444,f4307,f2489,f38580,f26025])).
% 11.34/1.99 thf(f26025,plain,(
% 11.34/1.99 spl41_421 <=> ($true = linordered_field(nat))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_421])])).
% 11.34/1.99 thf(f38580,plain,(
% 11.34/1.99 spl41_507 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_507])])).
% 11.34/1.99 thf(f4307,plain,(
% 11.34/1.99 spl41_200 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_200])])).
% 11.34/1.99 thf(f4444,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true != linordered_field(nat))) ) | (~spl41_44 | ~spl41_200)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4438])).
% 11.34/1.99 thf(f4438,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true != linordered_field(nat))) ) | (~spl41_44 | ~spl41_200)),
% 11.34/1.99 inference(superposition,[],[f4308,f2490])).
% 11.34/1.99 thf(f4308,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) ) | ~spl41_200),
% 11.34/1.99 inference(avatar_component_clause,[],[f4307])).
% 11.34/1.99 thf(f38578,plain,(
% 11.34/1.99 spl41_2 | spl41_506 | ~spl41_305 | ~spl41_438),
% 11.34/1.99 inference(avatar_split_clause,[],[f27870,f27191,f14614,f38575,f2250])).
% 11.34/1.99 thf(f2250,plain,(
% 11.34/1.99 spl41_2 <=> (zero_zero(nat) = k)),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_2])])).
% 11.34/1.99 thf(f14614,plain,(
% 11.34/1.99 spl41_305 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_305])])).
% 11.34/1.99 thf(f27191,plain,(
% 11.34/1.99 spl41_438 <=> (vAPP(list(a),nat,size_size(list(a)),xs) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_438])])).
% 11.34/1.99 thf(f27870,plain,(
% 11.34/1.99 (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),k) = n) | (zero_zero(nat) = k) | (~spl41_305 | ~spl41_438)),
% 11.34/1.99 inference(superposition,[],[f14615,f27193])).
% 11.34/1.99 thf(f27193,plain,(
% 11.34/1.99 (vAPP(list(a),nat,size_size(list(a)),xs) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)) | ~spl41_438),
% 11.34/1.99 inference(avatar_component_clause,[],[f27191])).
% 11.34/1.99 thf(f14615,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1) | (zero_zero(nat) = X0)) ) | ~spl41_305),
% 11.34/1.99 inference(avatar_component_clause,[],[f14614])).
% 11.34/1.99 thf(f38573,plain,(
% 11.34/1.99 spl41_505 | ~spl41_26 | ~spl41_153),
% 11.34/1.99 inference(avatar_split_clause,[],[f3885,f3855,f2369,f38571])).
% 11.34/1.99 thf(f38571,plain,(
% 11.34/1.99 spl41_505 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_505])])).
% 11.34/1.99 thf(f3855,plain,(
% 11.34/1.99 spl41_153 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_153])])).
% 11.34/1.99 thf(f3885,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) ) | (~spl41_26 | ~spl41_153)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3884])).
% 11.34/1.99 thf(f3884,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) ) | (~spl41_26 | ~spl41_153)),
% 11.34/1.99 inference(superposition,[],[f3856,f2370])).
% 11.34/1.99 thf(f3856,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) ) | ~spl41_153),
% 11.34/1.99 inference(avatar_component_clause,[],[f3855])).
% 11.34/1.99 thf(f38569,plain,(
% 11.34/1.99 spl41_504 | ~spl41_26 | ~spl41_152),
% 11.34/1.99 inference(avatar_split_clause,[],[f3879,f3851,f2369,f38567])).
% 11.34/1.99 thf(f38567,plain,(
% 11.34/1.99 spl41_504 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_504])])).
% 11.34/1.99 thf(f3851,plain,(
% 11.34/1.99 spl41_152 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_152])])).
% 11.34/1.99 thf(f3879,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) ) | (~spl41_26 | ~spl41_152)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3878])).
% 11.34/1.99 thf(f3878,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) ) | (~spl41_26 | ~spl41_152)),
% 11.34/1.99 inference(superposition,[],[f3852,f2370])).
% 11.34/1.99 thf(f3852,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) ) | ~spl41_152),
% 11.34/1.99 inference(avatar_component_clause,[],[f3851])).
% 11.34/1.99 thf(f38565,plain,(
% 11.34/1.99 spl41_503 | ~spl41_26 | ~spl41_151),
% 11.34/1.99 inference(avatar_split_clause,[],[f3872,f3847,f2369,f38563])).
% 11.34/1.99 thf(f38563,plain,(
% 11.34/1.99 spl41_503 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X2)) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_503])])).
% 11.34/1.99 thf(f3847,plain,(
% 11.34/1.99 spl41_151 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X2)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_151])])).
% 11.34/1.99 thf(f3872,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X2)) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_151)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3871])).
% 11.34/1.99 thf(f3871,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X2)) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_151)),
% 11.34/1.99 inference(superposition,[],[f3848,f2370])).
% 11.34/1.99 thf(f3848,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X2)) | (linordered_field(X0) != $true)) ) | ~spl41_151),
% 11.34/1.99 inference(avatar_component_clause,[],[f3847])).
% 11.34/1.99 thf(f38561,plain,(
% 11.34/1.99 spl41_502 | ~spl41_26 | ~spl41_150),
% 11.34/1.99 inference(avatar_split_clause,[],[f3863,f3842,f2369,f38559])).
% 11.34/1.99 thf(f38559,plain,(
% 11.34/1.99 spl41_502 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X1)) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_502])])).
% 11.34/1.99 thf(f3842,plain,(
% 11.34/1.99 spl41_150 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_150])])).
% 11.34/1.99 thf(f3863,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X1)) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_150)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3862])).
% 11.34/1.99 thf(f3862,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X1)) | (linordered_field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) ) | (~spl41_26 | ~spl41_150)),
% 11.34/1.99 inference(superposition,[],[f3843,f2370])).
% 11.34/1.99 thf(f3843,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X1)) | (linordered_field(X0) != $true)) ) | ~spl41_150),
% 11.34/1.99 inference(avatar_component_clause,[],[f3842])).
% 11.34/1.99 thf(f38557,plain,(
% 11.34/1.99 spl41_501 | ~spl41_32 | ~spl41_134),
% 11.34/1.99 inference(avatar_split_clause,[],[f3569,f3424,f2430,f38555])).
% 11.34/1.99 thf(f38555,plain,(
% 11.34/1.99 spl41_501 <=> ! [X0 : nat,X1 : nat > nat] : ((zero_zero(nat) = vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK39(nat),vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)),X1))) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),$o),sP2(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less(nat),X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_501])])).
% 11.34/1.99 thf(f2430,plain,(
% 11.34/1.99 spl41_32 <=> ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_32])])).
% 11.34/1.99 thf(f3424,plain,(
% 11.34/1.99 spl41_134 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0 > nat] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)) | (zero_zero(nat) = vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_134])])).
% 11.34/1.99 thf(f3569,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat > nat] : ((zero_zero(nat) = vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK39(nat),vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)),X1))) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),$o),sP2(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)))) ) | (~spl41_32 | ~spl41_134)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3500])).
% 11.34/1.99 thf(f3500,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat > nat] : (($true != $true) | (zero_zero(nat) = vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK39(nat),vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)),X1))) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),$o),sP2(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)))) ) | (~spl41_32 | ~spl41_134)),
% 11.34/1.99 inference(superposition,[],[f2431,f3425])).
% 11.34/1.99 thf(f3425,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > nat] : ((zero_zero(nat) = vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1))) | ($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2))) ) | ~spl41_134),
% 11.34/1.99 inference(avatar_component_clause,[],[f3424])).
% 11.34/1.99 thf(f2431,plain,(
% 11.34/1.99 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | ~spl41_32),
% 11.34/1.99 inference(avatar_component_clause,[],[f2430])).
% 11.34/1.99 thf(f37669,plain,(
% 11.34/1.99 spl41_500 | ~spl41_48 | ~spl41_180),
% 11.34/1.99 inference(avatar_split_clause,[],[f4187,f4165,f2510,f37667])).
% 11.34/1.99 thf(f37667,plain,(
% 11.34/1.99 spl41_500 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_500])])).
% 11.34/1.99 thf(f2510,plain,(
% 11.34/1.99 spl41_48 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,suc,X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_48])])).
% 11.34/1.99 thf(f4165,plain,(
% 11.34/1.99 spl41_180 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_180])])).
% 11.34/1.99 thf(f4187,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) ) | (~spl41_48 | ~spl41_180)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4180])).
% 11.34/1.99 thf(f4180,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) ) | (~spl41_48 | ~spl41_180)),
% 11.34/1.99 inference(superposition,[],[f4166,f2511])).
% 11.34/1.99 thf(f2511,plain,(
% 11.34/1.99 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,suc,X0)))) ) | ~spl41_48),
% 11.34/1.99 inference(avatar_component_clause,[],[f2510])).
% 11.34/1.99 thf(f4166,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl41_180),
% 11.34/1.99 inference(avatar_component_clause,[],[f4165])).
% 11.34/1.99 thf(f37665,plain,(
% 11.34/1.99 spl41_499 | ~spl41_48 | ~spl41_179),
% 11.34/1.99 inference(avatar_split_clause,[],[f4179,f4161,f2510,f37663])).
% 11.34/1.99 thf(f37663,plain,(
% 11.34/1.99 spl41_499 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),vAPP(nat,nat,suc,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_499])])).
% 11.34/1.99 thf(f4161,plain,(
% 11.34/1.99 spl41_179 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_179])])).
% 11.34/1.99 thf(f4179,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),vAPP(nat,nat,suc,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) ) | (~spl41_48 | ~spl41_179)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4172])).
% 11.34/1.99 thf(f4172,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),vAPP(nat,nat,suc,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) ) | (~spl41_48 | ~spl41_179)),
% 11.34/1.99 inference(superposition,[],[f4162,f2511])).
% 11.34/1.99 thf(f4162,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl41_179),
% 11.34/1.99 inference(avatar_component_clause,[],[f4161])).
% 11.34/1.99 thf(f37661,plain,(
% 11.34/1.99 spl41_498 | ~spl41_9 | ~spl41_35 | ~spl41_149),
% 11.34/1.99 inference(avatar_split_clause,[],[f3830,f3728,f2444,f2285,f37659])).
% 11.34/1.99 thf(f37659,plain,(
% 11.34/1.99 spl41_498 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_498])])).
% 11.34/1.99 thf(f2285,plain,(
% 11.34/1.99 spl41_9 <=> (wellorder(nat) = $true)),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_9])])).
% 11.34/1.99 thf(f2444,plain,(
% 11.34/1.99 spl41_35 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_35])])).
% 11.34/1.99 thf(f3728,plain,(
% 11.34/1.99 spl41_149 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1,X6 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2)))) | ($true != wellorder(X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_149])])).
% 11.34/1.99 thf(f3830,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_35 | ~spl41_149)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3829])).
% 11.34/1.99 thf(f3829,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_35 | ~spl41_149)),
% 11.34/1.99 inference(forward_demodulation,[],[f3798,f2287])).
% 11.34/1.99 thf(f2287,plain,(
% 11.34/1.99 (wellorder(nat) = $true) | ~spl41_9),
% 11.34/1.99 inference(avatar_component_clause,[],[f2285])).
% 11.34/1.99 thf(f3798,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (wellorder(nat) != $true) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_149)),
% 11.34/1.99 inference(superposition,[],[f3729,f2445])).
% 11.34/1.99 thf(f2445,plain,(
% 11.34/1.99 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0) | (zero_zero(nat) = X0)) ) | ~spl41_35),
% 11.34/1.99 inference(avatar_component_clause,[],[f2444])).
% 11.34/1.99 thf(f3729,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2)))) | ($true = vAPP(X1,$o,X3,X6)) | ($true = vAPP(X1,$o,X3,X4)) | ($true != wellorder(X0))) ) | ~spl41_149),
% 11.34/1.99 inference(avatar_component_clause,[],[f3728])).
% 11.34/1.99 thf(f37657,plain,(
% 11.34/1.99 spl41_497 | ~spl41_9 | ~spl41_34 | ~spl41_149),
% 11.34/1.99 inference(avatar_split_clause,[],[f3828,f3728,f2440,f2285,f37655])).
% 11.34/1.99 thf(f37655,plain,(
% 11.34/1.99 spl41_497 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_497])])).
% 11.34/1.99 thf(f2440,plain,(
% 11.34/1.99 spl41_34 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_34])])).
% 11.34/1.99 thf(f3828,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_34 | ~spl41_149)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3827])).
% 11.34/1.99 thf(f3827,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_34 | ~spl41_149)),
% 11.34/1.99 inference(forward_demodulation,[],[f3797,f2287])).
% 11.34/1.99 thf(f3797,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (wellorder(nat) != $true) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_149)),
% 11.34/1.99 inference(superposition,[],[f3729,f2441])).
% 11.34/1.99 thf(f2441,plain,(
% 11.34/1.99 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0) | (zero_zero(nat) = X0)) ) | ~spl41_34),
% 11.34/1.99 inference(avatar_component_clause,[],[f2440])).
% 11.34/1.99 thf(f37592,plain,(
% 11.34/1.99 spl41_496 | ~spl41_9 | ~spl41_33 | ~spl41_149),
% 11.34/1.99 inference(avatar_split_clause,[],[f3826,f3728,f2436,f2285,f37590])).
% 11.34/1.99 thf(f37590,plain,(
% 11.34/1.99 spl41_496 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_496])])).
% 11.34/1.99 thf(f2436,plain,(
% 11.34/1.99 spl41_33 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_33])])).
% 11.34/1.99 thf(f3826,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_33 | ~spl41_149)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3825])).
% 11.34/1.99 thf(f3825,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_33 | ~spl41_149)),
% 11.34/1.99 inference(forward_demodulation,[],[f3796,f2287])).
% 11.34/1.99 thf(f3796,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK16(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (wellorder(nat) != $true) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_149)),
% 11.34/1.99 inference(superposition,[],[f3729,f2437])).
% 11.34/1.99 thf(f2437,plain,(
% 11.34/1.99 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0) | (zero_zero(nat) = X0)) ) | ~spl41_33),
% 11.34/1.99 inference(avatar_component_clause,[],[f2436])).
% 11.34/1.99 thf(f37588,plain,(
% 11.34/1.99 spl41_495 | ~spl41_26 | ~spl41_149),
% 11.34/1.99 inference(avatar_split_clause,[],[f3814,f3728,f2369,f37586])).
% 11.34/1.99 thf(f37586,plain,(
% 11.34/1.99 spl41_495 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | ($true != wellorder(X0)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X4),X2)))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_495])])).
% 11.34/1.99 thf(f3814,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | ($true != wellorder(X0)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X4),X2))))) ) | (~spl41_26 | ~spl41_149)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3813])).
% 11.34/1.99 thf(f3813,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true != $true) | ($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | ($true != wellorder(X0)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X4),X2))))) ) | (~spl41_26 | ~spl41_149)),
% 11.34/1.99 inference(superposition,[],[f3729,f2370])).
% 11.34/1.99 thf(f37584,plain,(
% 11.34/1.99 spl41_494 | ~spl41_9 | ~spl41_35 | ~spl41_148),
% 11.34/1.99 inference(avatar_split_clause,[],[f3775,f3724,f2444,f2285,f37582])).
% 11.34/1.99 thf(f37582,plain,(
% 11.34/1.99 spl41_494 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_494])])).
% 11.34/1.99 thf(f3724,plain,(
% 11.34/1.99 spl41_148 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1,X6 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2)))) | ($true != wellorder(X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_148])])).
% 11.34/1.99 thf(f3775,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_35 | ~spl41_148)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3774])).
% 11.34/1.99 thf(f3774,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_35 | ~spl41_148)),
% 11.34/1.99 inference(forward_demodulation,[],[f3743,f2287])).
% 11.34/1.99 thf(f3743,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (wellorder(nat) != $true) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_148)),
% 11.34/1.99 inference(superposition,[],[f3725,f2445])).
% 11.34/1.99 thf(f3725,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2)))) | ($true = vAPP(X1,$o,X3,X6)) | ($true = vAPP(X1,$o,X3,X4)) | ($true != wellorder(X0))) ) | ~spl41_148),
% 11.34/1.99 inference(avatar_component_clause,[],[f3724])).
% 11.34/1.99 thf(f37580,plain,(
% 11.34/1.99 spl41_493 | ~spl41_9 | ~spl41_34 | ~spl41_148),
% 11.34/1.99 inference(avatar_split_clause,[],[f3773,f3724,f2440,f2285,f37578])).
% 11.34/1.99 thf(f37578,plain,(
% 11.34/1.99 spl41_493 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_493])])).
% 11.34/1.99 thf(f3773,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_34 | ~spl41_148)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3772])).
% 11.34/1.99 thf(f3772,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_34 | ~spl41_148)),
% 11.34/1.99 inference(forward_demodulation,[],[f3742,f2287])).
% 11.34/1.99 thf(f3742,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (wellorder(nat) != $true) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_148)),
% 11.34/1.99 inference(superposition,[],[f3725,f2441])).
% 11.34/1.99 thf(f37576,plain,(
% 11.34/1.99 spl41_492 | ~spl41_9 | ~spl41_33 | ~spl41_148),
% 11.34/1.99 inference(avatar_split_clause,[],[f3771,f3724,f2436,f2285,f37574])).
% 11.34/1.99 thf(f37574,plain,(
% 11.34/1.99 spl41_492 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_492])])).
% 11.34/1.99 thf(f3771,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_33 | ~spl41_148)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3770])).
% 11.34/1.99 thf(f3770,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_9 | ~spl41_33 | ~spl41_148)),
% 11.34/1.99 inference(forward_demodulation,[],[f3741,f2287])).
% 11.34/1.99 thf(f3741,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,nat),nat),sK15(nat,nat),X1),suc)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (wellorder(nat) != $true) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_148)),
% 11.34/1.99 inference(superposition,[],[f3725,f2437])).
% 11.34/1.99 thf(f37572,plain,(
% 11.34/1.99 spl41_491 | ~spl41_26 | ~spl41_148),
% 11.34/1.99 inference(avatar_split_clause,[],[f3759,f3724,f2369,f37570])).
% 11.34/1.99 thf(f37570,plain,(
% 11.34/1.99 spl41_491 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | ($true != wellorder(X0)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X4),X2)))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_491])])).
% 11.34/1.99 thf(f3759,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | ($true != wellorder(X0)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X4),X2))))) ) | (~spl41_26 | ~spl41_148)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3758])).
% 11.34/1.99 thf(f3758,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true != $true) | ($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | ($true != wellorder(X0)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X4),X2))))) ) | (~spl41_26 | ~spl41_148)),
% 11.34/1.99 inference(superposition,[],[f3725,f2370])).
% 11.34/1.99 thf(f37568,plain,(
% 11.34/1.99 spl41_490),
% 11.34/1.99 inference(avatar_split_clause,[],[f1612,f37566])).
% 11.34/1.99 thf(f37566,plain,(
% 11.34/1.99 spl41_490 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_490])])).
% 11.34/1.99 thf(f1612,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))) )),
% 11.34/1.99 inference(binary_proxy_clausification,[],[f1428])).
% 11.34/1.99 thf(f1428,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))) )),
% 11.34/1.99 inference(cnf_transformation,[],[f834])).
% 11.34/1.99 thf(f834,plain,(
% 11.34/1.99 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))),
% 11.34/1.99 inference(rectify,[],[f95])).
% 11.34/1.99 thf(f95,axiom,(
% 11.34/1.99 ! [X4 : nat,X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X4)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X4)),X2)))),
% 11.34/1.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Suc__mult__less__cancel1)).
% 11.34/1.99 thf(f36390,plain,(
% 11.34/1.99 spl41_489 | ~spl41_26 | ~spl41_147),
% 11.34/1.99 inference(avatar_split_clause,[],[f3718,f3698,f2369,f36388])).
% 11.34/1.99 thf(f36388,plain,(
% 11.34/1.99 spl41_489 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)) | ($true = vAPP(nat,$o,X0,X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X1)) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X0),X1))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_489])])).
% 11.34/1.99 thf(f3698,plain,(
% 11.34/1.99 spl41_147 <=> ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,X0)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | ($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_147])])).
% 11.34/1.99 thf(f3718,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)) | ($true = vAPP(nat,$o,X0,X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X1)) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X0),X1)))) ) | (~spl41_26 | ~spl41_147)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3717])).
% 11.34/1.99 thf(f3717,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)) | ($true = vAPP(nat,$o,X0,X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X1)) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X0),X1)))) ) | (~spl41_26 | ~spl41_147)),
% 11.34/1.99 inference(superposition,[],[f3699,f2370])).
% 11.34/1.99 thf(f3699,plain,(
% 11.34/1.99 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1))) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | ($true = vAPP(nat,$o,X2,X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl41_147),
% 11.34/1.99 inference(avatar_component_clause,[],[f3698])).
% 11.34/1.99 thf(f36386,plain,(
% 11.34/1.99 spl41_488 | ~spl41_26 | ~spl41_146),
% 11.34/1.99 inference(avatar_split_clause,[],[f3706,f3694,f2369,f36384])).
% 11.34/1.99 thf(f36384,plain,(
% 11.34/1.99 spl41_488 <=> ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1)) = X1) | ($true = vAPP(nat,$o,X2,X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_488])])).
% 11.34/1.99 thf(f3694,plain,(
% 11.34/1.99 spl41_146 <=> ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,X0)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1)) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_146])])).
% 11.34/1.99 thf(f3706,plain,(
% 11.34/1.99 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1)) = X1) | ($true = vAPP(nat,$o,X2,X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_146)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3705])).
% 11.34/1.99 thf(f3705,plain,(
% 11.34/1.99 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1)) = X1) | ($true = vAPP(nat,$o,X2,X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_146)),
% 11.34/1.99 inference(superposition,[],[f3695,f2370])).
% 11.34/1.99 thf(f3695,plain,(
% 11.34/1.99 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1)) = X1) | ($true = vAPP(nat,$o,X2,X0))) ) | ~spl41_146),
% 11.34/1.99 inference(avatar_component_clause,[],[f3694])).
% 11.34/1.99 thf(f36382,plain,(
% 11.34/1.99 spl41_487 | ~spl41_35 | ~spl41_137),
% 11.34/1.99 inference(avatar_split_clause,[],[f3613,f3598,f2444,f36380])).
% 11.34/1.99 thf(f36380,plain,(
% 11.34/1.99 spl41_487 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK40(nat),suc),X1)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_487])])).
% 11.34/1.99 thf(f3598,plain,(
% 11.34/1.99 spl41_137 <=> ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X5 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1)))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_137])])).
% 11.34/1.99 thf(f3613,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK40(nat),suc),X1)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK5,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_137)),
% 11.34/1.99 inference(superposition,[],[f3599,f2445])).
% 11.34/1.99 thf(f3599,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o,X5 : X0] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1)))) | ($true = vAPP(X0,$o,X1,X5)) | ($true = vAPP(X0,$o,X1,X3))) ) | ~spl41_137),
% 11.34/1.99 inference(avatar_component_clause,[],[f3598])).
% 11.34/1.99 thf(f36378,plain,(
% 11.34/1.99 spl41_486 | ~spl41_34 | ~spl41_137),
% 11.34/1.99 inference(avatar_split_clause,[],[f3612,f3598,f2440,f36376])).
% 11.34/1.99 thf(f36376,plain,(
% 11.34/1.99 spl41_486 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK40(nat),suc),X1)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_486])])).
% 11.34/1.99 thf(f3612,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK40(nat),suc),X1)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK4,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_137)),
% 11.34/1.99 inference(superposition,[],[f3599,f2441])).
% 11.34/1.99 thf(f36367,plain,(
% 11.34/1.99 spl41_485 | ~spl41_453 | ~spl41_484),
% 11.34/1.99 inference(avatar_split_clause,[],[f36363,f36360,f28047,f36365])).
% 11.34/1.99 thf(f36365,plain,(
% 11.34/1.99 spl41_485 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : ((n = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK40(nat),suc),X1)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_485])])).
% 11.34/1.99 thf(f28047,plain,(
% 11.34/1.99 spl41_453 <=> (zero_zero(nat) = n)),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_453])])).
% 11.34/1.99 thf(f36360,plain,(
% 11.34/1.99 spl41_484 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK40(nat),suc),X1)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_484])])).
% 11.34/1.99 thf(f36363,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : ((n = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK40(nat),suc),X1)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2))) ) | (~spl41_453 | ~spl41_484)),
% 11.34/1.99 inference(forward_demodulation,[],[f36361,f28049])).
% 11.34/1.99 thf(f28049,plain,(
% 11.34/1.99 (zero_zero(nat) = n) | ~spl41_453),
% 11.34/1.99 inference(avatar_component_clause,[],[f28047])).
% 11.34/1.99 thf(f36361,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK40(nat),suc),X1)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | ~spl41_484),
% 11.34/1.99 inference(avatar_component_clause,[],[f36360])).
% 11.34/1.99 thf(f36362,plain,(
% 11.34/1.99 spl41_484 | ~spl41_33 | ~spl41_137),
% 11.34/1.99 inference(avatar_split_clause,[],[f3611,f3598,f2436,f36360])).
% 11.34/1.99 thf(f3611,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK40(nat),suc),X1)))) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,sK3,X0))) | ($true = vAPP(nat,$o,X1,X2)) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_137)),
% 11.34/1.99 inference(superposition,[],[f3599,f2437])).
% 11.34/1.99 thf(f36358,plain,(
% 11.34/1.99 spl41_483 | ~spl41_132),
% 11.34/1.99 inference(avatar_split_clause,[],[f3411,f3357,f36356])).
% 11.34/1.99 thf(f36356,plain,(
% 11.34/1.99 spl41_483 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > nat,X1 : X0] : ((vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2) != X1) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))) | (X1 = X3))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_483])])).
% 11.34/1.99 thf(f3357,plain,(
% 11.34/1.99 spl41_132 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0 > nat] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_132])])).
% 11.34/1.99 thf(f3411,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2) != X1) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))) | (X1 = X3)) ) | ~spl41_132),
% 11.34/1.99 inference(equality_proxy_clausification,[],[f3410])).
% 11.34/1.99 thf(f3410,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2) != X1) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) ) | ~spl41_132),
% 11.34/1.99 inference(equality_proxy_clausification,[],[f3401])).
% 11.34/1.99 thf(f3401,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2))) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) ) | ~spl41_132),
% 11.34/1.99 inference(primitive_instantiation,[],[f3358])).
% 11.34/1.99 thf(f3358,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > nat] : (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1))) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)) | ($true = vAPP(X0,$o,X2,X3))) ) | ~spl41_132),
% 11.34/1.99 inference(avatar_component_clause,[],[f3357])).
% 11.34/1.99 thf(f36295,plain,(
% 11.34/1.99 ~spl41_63 | ~spl41_121 | ~spl41_259 | ~spl41_318 | ~spl41_439),
% 11.34/1.99 inference(avatar_contradiction_clause,[],[f36294])).
% 11.34/1.99 thf(f36294,plain,(
% 11.34/1.99 $false | (~spl41_63 | ~spl41_121 | ~spl41_259 | ~spl41_318 | ~spl41_439)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f36293])).
% 11.34/1.99 thf(f36293,plain,(
% 11.34/1.99 ($true = $false) | (~spl41_63 | ~spl41_121 | ~spl41_259 | ~spl41_318 | ~spl41_439)),
% 11.34/1.99 inference(forward_demodulation,[],[f36292,f17051])).
% 11.34/1.99 thf(f17051,plain,(
% 11.34/1.99 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X0))) ) | (~spl41_259 | ~spl41_318)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f16918])).
% 11.34/1.99 thf(f16918,plain,(
% 11.34/1.99 ( ! [X0 : nat] : (($true = $false) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X0))) ) | (~spl41_259 | ~spl41_318)),
% 11.34/1.99 inference(superposition,[],[f16753,f8430])).
% 11.34/1.99 thf(f8430,plain,(
% 11.34/1.99 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))))) ) | ~spl41_259),
% 11.34/1.99 inference(avatar_component_clause,[],[f8429])).
% 11.34/1.99 thf(f8429,plain,(
% 11.34/1.99 spl41_259 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_259])])).
% 11.34/1.99 thf(f16753,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl41_318),
% 11.34/1.99 inference(avatar_component_clause,[],[f16752])).
% 11.34/1.99 thf(f16752,plain,(
% 11.34/1.99 spl41_318 <=> ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_318])])).
% 11.34/1.99 thf(f36292,plain,(
% 11.34/1.99 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,n)),n)) | (~spl41_63 | ~spl41_121 | ~spl41_439)),
% 11.34/1.99 inference(forward_demodulation,[],[f36290,f2645])).
% 11.34/1.99 thf(f36290,plain,(
% 11.34/1.99 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),k)),n)) | (~spl41_121 | ~spl41_439)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f36229])).
% 11.34/1.99 thf(f36229,plain,(
% 11.34/1.99 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),k)),n)) | (~spl41_121 | ~spl41_439)),
% 11.34/1.99 inference(superposition,[],[f3310,f27197])).
% 11.34/1.99 thf(f27197,plain,(
% 11.34/1.99 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(a),nat,size_size(list(a)),xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k))) | ~spl41_439),
% 11.34/1.99 inference(avatar_component_clause,[],[f27195])).
% 11.34/1.99 thf(f27195,plain,(
% 11.34/1.99 spl41_439 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(a),nat,size_size(list(a)),xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_439])])).
% 11.34/1.99 thf(f3310,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X2)),X1))) ) | ~spl41_121),
% 11.34/1.99 inference(avatar_component_clause,[],[f3309])).
% 11.34/1.99 thf(f3309,plain,(
% 11.34/1.99 spl41_121 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_121])])).
% 11.34/1.99 thf(f35693,plain,(
% 11.34/1.99 spl41_482 | ~spl41_48 | ~spl41_146),
% 11.34/1.99 inference(avatar_split_clause,[],[f3708,f3694,f2510,f35691])).
% 11.34/1.99 thf(f35691,plain,(
% 11.34/1.99 spl41_482 <=> ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X1),vAPP(nat,nat,suc,X0)))) | ($true = vAPP(nat,$o,X1,zero_zero(nat))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_482])])).
% 11.34/1.99 thf(f3708,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X1),vAPP(nat,nat,suc,X0)))) | ($true = vAPP(nat,$o,X1,zero_zero(nat)))) ) | (~spl41_48 | ~spl41_146)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3702])).
% 11.34/1.99 thf(f3702,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X1),vAPP(nat,nat,suc,X0)))) | ($true = vAPP(nat,$o,X1,zero_zero(nat)))) ) | (~spl41_48 | ~spl41_146)),
% 11.34/1.99 inference(superposition,[],[f3695,f2511])).
% 11.34/1.99 thf(f35689,plain,(
% 11.34/1.99 spl41_481 | ~spl41_26 | ~spl41_145),
% 11.34/1.99 inference(avatar_split_clause,[],[f3691,f3685,f2369,f35687])).
% 11.34/1.99 thf(f35687,plain,(
% 11.34/1.99 spl41_481 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK38(X0),X1),X2)))) | ($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_481])])).
% 11.34/1.99 thf(f3685,plain,(
% 11.34/1.99 spl41_145 <=> ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_145])])).
% 11.34/1.99 thf(f3691,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK38(X0),X1),X2)))) | ($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2))) ) | (~spl41_26 | ~spl41_145)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3690])).
% 11.34/1.99 thf(f3690,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK38(X0),X1),X2)))) | ($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2))) ) | (~spl41_26 | ~spl41_145)),
% 11.34/1.99 inference(superposition,[],[f3686,f2370])).
% 11.34/1.99 thf(f3686,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))))) ) | ~spl41_145),
% 11.34/1.99 inference(avatar_component_clause,[],[f3685])).
% 11.34/1.99 thf(f35685,plain,(
% 11.34/1.99 spl41_480 | ~spl41_26 | ~spl41_137),
% 11.34/1.99 inference(avatar_split_clause,[],[f3619,f3598,f2369,f35683])).
% 11.34/1.99 thf(f35683,plain,(
% 11.34/1.99 spl41_480 <=> ! [X0 : $o > nat,X3 : $o,X2 : $o,X1 : $o > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP($o,nat,X0,X2)),vAPP($o,nat,X0,$true))) | ($true = vAPP($o,$o,X1,X2)) | ($true = vAPP($o,$o,X1,X3)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK40($o),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_480])])).
% 11.34/1.99 thf(f3619,plain,(
% 11.34/1.99 ( ! [X2 : $o,X3 : $o,X0 : $o > nat,X1 : $o > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP($o,nat,X0,X2)),vAPP($o,nat,X0,$true))) | ($true = vAPP($o,$o,X1,X2)) | ($true = vAPP($o,$o,X1,X3)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK40($o),X0),X1))) ) | (~spl41_26 | ~spl41_137)),
% 11.34/1.99 inference(superposition,[],[f3599,f2370])).
% 11.34/1.99 thf(f35681,plain,(
% 11.34/1.99 spl41_479),
% 11.34/1.99 inference(avatar_split_clause,[],[f1630,f35679])).
% 11.34/1.99 thf(f35679,plain,(
% 11.34/1.99 spl41_479 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_479])])).
% 11.34/1.99 thf(f1630,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.34/1.99 inference(binary_proxy_clausification,[],[f1626])).
% 11.34/1.99 thf(f1626,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)))) )),
% 11.34/1.99 inference(binary_proxy_clausification,[],[f1378])).
% 11.34/1.99 thf(f1378,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)))) )),
% 11.34/1.99 inference(cnf_transformation,[],[f628])).
% 11.34/1.99 thf(f628,plain,(
% 11.34/1.99 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)))),
% 11.34/1.99 inference(fool_elimination,[],[f627])).
% 11.34/1.99 thf(f627,plain,(
% 11.34/1.99 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))),
% 11.34/1.99 inference(rectify,[],[f7])).
% 11.34/1.99 thf(f7,axiom,(
% 11.34/1.99 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X3))),
% 11.34/1.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_nat__0__less__mult__iff)).
% 11.34/1.99 thf(f32176,plain,(
% 11.34/1.99 spl41_478 | ~spl41_48 | ~spl41_178),
% 11.34/1.99 inference(avatar_split_clause,[],[f4159,f4147,f2510,f32174])).
% 11.34/1.99 thf(f32174,plain,(
% 11.34/1.99 spl41_478 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_478])])).
% 11.34/1.99 thf(f4147,plain,(
% 11.34/1.99 spl41_178 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_178])])).
% 11.34/1.99 thf(f4159,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))) ) | (~spl41_48 | ~spl41_178)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4152])).
% 11.34/1.99 thf(f4152,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))) ) | (~spl41_48 | ~spl41_178)),
% 11.34/1.99 inference(superposition,[],[f4148,f2511])).
% 11.34/1.99 thf(f4148,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)))) ) | ~spl41_178),
% 11.34/1.99 inference(avatar_component_clause,[],[f4147])).
% 11.34/1.99 thf(f32172,plain,(
% 11.34/1.99 spl41_477 | ~spl41_44 | ~spl41_146),
% 11.34/1.99 inference(avatar_split_clause,[],[f3709,f3694,f2489,f32170])).
% 11.34/1.99 thf(f32170,plain,(
% 11.34/1.99 spl41_477 <=> ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X1),vAPP(nat,nat,suc,X0)))) | ($true = vAPP(nat,$o,X1,X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_477])])).
% 11.34/1.99 thf(f3709,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X1),vAPP(nat,nat,suc,X0)))) | ($true = vAPP(nat,$o,X1,X0))) ) | (~spl41_44 | ~spl41_146)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3701])).
% 11.34/1.99 thf(f3701,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X1),vAPP(nat,nat,suc,X0)))) | ($true = vAPP(nat,$o,X1,X0))) ) | (~spl41_44 | ~spl41_146)),
% 11.34/1.99 inference(superposition,[],[f3695,f2490])).
% 11.34/1.99 thf(f32168,plain,(
% 11.34/1.99 spl41_476 | ~spl41_26 | ~spl41_143),
% 11.34/1.99 inference(avatar_split_clause,[],[f3675,f3653,f2369,f32166])).
% 11.34/1.99 thf(f32166,plain,(
% 11.34/1.99 spl41_476 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (field(X0) = $false))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_476])])).
% 11.34/1.99 thf(f3653,plain,(
% 11.34/1.99 spl41_143 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (zero_zero(X0) = X1) | (field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_143])])).
% 11.34/1.99 thf(f3675,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_143)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3674])).
% 11.34/1.99 thf(f3674,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_143)),
% 11.34/1.99 inference(superposition,[],[f3654,f2370])).
% 11.34/1.99 thf(f3654,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((field(X0) != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))) ) | ~spl41_143),
% 11.34/1.99 inference(avatar_component_clause,[],[f3653])).
% 11.34/1.99 thf(f32164,plain,(
% 11.34/1.99 spl41_475 | ~spl41_26 | ~spl41_142),
% 11.34/1.99 inference(avatar_split_clause,[],[f3673,f3648,f2369,f32162])).
% 11.34/1.99 thf(f32162,plain,(
% 11.34/1.99 spl41_475 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (field(X0) = $false))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_475])])).
% 11.34/1.99 thf(f3648,plain,(
% 11.34/1.99 spl41_142 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (zero_zero(X0) = X1) | (field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_142])])).
% 11.34/1.99 thf(f3673,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_142)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3672])).
% 11.34/1.99 thf(f3672,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_142)),
% 11.34/1.99 inference(superposition,[],[f3649,f2370])).
% 11.34/1.99 thf(f3649,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((field(X0) != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))) ) | ~spl41_142),
% 11.34/1.99 inference(avatar_component_clause,[],[f3648])).
% 11.34/1.99 thf(f32160,plain,(
% 11.34/1.99 spl41_474 | ~spl41_26 | ~spl41_141),
% 11.34/1.99 inference(avatar_split_clause,[],[f3671,f3644,f2369,f32158])).
% 11.34/1.99 thf(f32158,plain,(
% 11.34/1.99 spl41_474 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (field(X0) = $false))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_474])])).
% 11.34/1.99 thf(f3644,plain,(
% 11.34/1.99 spl41_141 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (zero_zero(X0) = X1) | (field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_141])])).
% 11.34/1.99 thf(f3671,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_141)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3670])).
% 11.34/1.99 thf(f3670,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_141)),
% 11.34/1.99 inference(superposition,[],[f3645,f2370])).
% 11.34/1.99 thf(f3645,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((field(X0) != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)))) ) | ~spl41_141),
% 11.34/1.99 inference(avatar_component_clause,[],[f3644])).
% 11.34/1.99 thf(f32156,plain,(
% 11.34/1.99 spl41_473 | ~spl41_26 | ~spl41_140),
% 11.34/1.99 inference(avatar_split_clause,[],[f3669,f3640,f2369,f32154])).
% 11.34/1.99 thf(f32154,plain,(
% 11.34/1.99 spl41_473 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (field(X0) = $false))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_473])])).
% 11.34/1.99 thf(f3640,plain,(
% 11.34/1.99 spl41_140 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (zero_zero(X0) = X1) | (field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_140])])).
% 11.34/1.99 thf(f3669,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_140)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3668])).
% 11.34/1.99 thf(f3668,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_140)),
% 11.34/1.99 inference(superposition,[],[f3641,f2370])).
% 11.34/1.99 thf(f3641,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((field(X0) != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) ) | ~spl41_140),
% 11.34/1.99 inference(avatar_component_clause,[],[f3640])).
% 11.34/1.99 thf(f32152,plain,(
% 11.34/1.99 spl41_472 | ~spl41_26 | ~spl41_139),
% 11.34/1.99 inference(avatar_split_clause,[],[f3666,f3636,f2369,f32150])).
% 11.34/1.99 thf(f32150,plain,(
% 11.34/1.99 spl41_472 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (euclid191655569cancel(X0) = $false))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_472])])).
% 11.34/1.99 thf(f3636,plain,(
% 11.34/1.99 spl41_139 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (zero_zero(X0) = X1) | (euclid191655569cancel(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_139])])).
% 11.34/1.99 thf(f3666,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (euclid191655569cancel(X0) = $false)) ) | (~spl41_26 | ~spl41_139)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3665])).
% 11.34/1.99 thf(f3665,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (euclid191655569cancel(X0) = $false)) ) | (~spl41_26 | ~spl41_139)),
% 11.34/1.99 inference(superposition,[],[f3637,f2370])).
% 11.34/1.99 thf(f3637,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((euclid191655569cancel(X0) != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))) ) | ~spl41_139),
% 11.34/1.99 inference(avatar_component_clause,[],[f3636])).
% 11.34/1.99 thf(f32148,plain,(
% 11.34/1.99 spl41_471 | ~spl41_26 | ~spl41_138),
% 11.34/1.99 inference(avatar_split_clause,[],[f3662,f3632,f2369,f32146])).
% 11.34/1.99 thf(f32146,plain,(
% 11.34/1.99 spl41_471 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (euclid191655569cancel(X0) = $false))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_471])])).
% 11.34/1.99 thf(f3632,plain,(
% 11.34/1.99 spl41_138 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (zero_zero(X0) = X1) | (euclid191655569cancel(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_138])])).
% 11.34/1.99 thf(f3662,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (euclid191655569cancel(X0) = $false)) ) | (~spl41_26 | ~spl41_138)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3661])).
% 11.34/1.99 thf(f3661,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (euclid191655569cancel(X0) = $false)) ) | (~spl41_26 | ~spl41_138)),
% 11.34/1.99 inference(superposition,[],[f3633,f2370])).
% 11.34/1.99 thf(f3633,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((euclid191655569cancel(X0) != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) ) | ~spl41_138),
% 11.34/1.99 inference(avatar_component_clause,[],[f3632])).
% 11.34/1.99 thf(f32144,plain,(
% 11.34/1.99 spl41_470 | ~spl41_26 | ~spl41_134),
% 11.34/1.99 inference(avatar_split_clause,[],[f3439,f3424,f2369,f32142])).
% 11.34/1.99 thf(f32142,plain,(
% 11.34/1.99 spl41_470 <=> ! [X2 : $o,X0 : $o > $o,X1 : $o > nat] : ((zero_zero(nat) = vAPP($o,nat,X1,$true)) | ($true = vAPP($o,$o,X0,X2)) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X1),X0)) | ($false = vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_470])])).
% 11.34/1.99 thf(f3439,plain,(
% 11.34/1.99 ( ! [X2 : $o,X0 : $o > $o,X1 : $o > nat] : ((zero_zero(nat) = vAPP($o,nat,X1,$true)) | ($true = vAPP($o,$o,X0,X2)) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X1),X0)) | ($false = vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),X0),X1))) ) | (~spl41_26 | ~spl41_134)),
% 11.34/1.99 inference(superposition,[],[f3425,f2370])).
% 11.34/1.99 thf(f32140,plain,(
% 11.34/1.99 spl41_453 | spl41_469 | ~spl41_304 | ~spl41_438),
% 11.34/1.99 inference(avatar_split_clause,[],[f27869,f27191,f14610,f32137,f28047])).
% 11.34/1.99 thf(f32137,plain,(
% 11.34/1.99 spl41_469 <=> (k = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),n))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_469])])).
% 11.34/1.99 thf(f14610,plain,(
% 11.34/1.99 spl41_304 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_304])])).
% 11.34/1.99 thf(f27869,plain,(
% 11.34/1.99 (k = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),n)) | (zero_zero(nat) = n) | (~spl41_304 | ~spl41_438)),
% 11.34/1.99 inference(superposition,[],[f14611,f27193])).
% 11.34/1.99 thf(f14611,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1) | (zero_zero(nat) = X0)) ) | ~spl41_304),
% 11.34/1.99 inference(avatar_component_clause,[],[f14610])).
% 11.34/1.99 thf(f32135,plain,(
% 11.34/1.99 spl41_468 | ~spl41_116),
% 11.34/1.99 inference(avatar_split_clause,[],[f3267,f3246,f32133])).
% 11.34/1.99 thf(f32133,plain,(
% 11.34/1.99 spl41_468 <=> ! [X0 : $o,X1 : $o > nat] : (($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK38($o),X1),vAPP($o,sTfun($o,$o),vAND,X0))) | ($true != vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X1),vAPP($o,sTfun($o,$o),vAND,X0))) | ($false = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_468])])).
% 11.34/1.99 thf(f3246,plain,(
% 11.34/1.99 spl41_116 <=> ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true != vAPP(X1,$o,X0,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_116])])).
% 11.34/1.99 thf(f3267,plain,(
% 11.34/1.99 ( ! [X0 : $o,X1 : $o > nat] : (($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK38($o),X1),vAPP($o,sTfun($o,$o),vAND,X0))) | ($true != vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X1),vAPP($o,sTfun($o,$o),vAND,X0))) | ($false = X0)) ) | ~spl41_116),
% 11.34/1.99 inference(binary_proxy_clausification,[],[f3251])).
% 11.34/1.99 thf(f3251,plain,(
% 11.34/1.99 ( ! [X0 : $o,X1 : $o > nat] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,X0),vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK38($o),X1),vAPP($o,sTfun($o,$o),vAND,X0)))) | ($true != vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X1),vAPP($o,sTfun($o,$o),vAND,X0)))) ) | ~spl41_116),
% 11.34/1.99 inference(primitive_instantiation,[],[f3247])).
% 11.34/1.99 thf(f3247,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true != vAPP(X1,$o,X0,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0))) ) | ~spl41_116),
% 11.34/1.99 inference(avatar_component_clause,[],[f3246])).
% 11.34/1.99 thf(f32131,plain,(
% 11.34/1.99 spl41_467 | ~spl41_96),
% 11.34/1.99 inference(avatar_split_clause,[],[f3083,f3013,f32129])).
% 11.34/1.99 thf(f32129,plain,(
% 11.34/1.99 spl41_467 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))))) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_467])])).
% 11.34/1.99 thf(f3013,plain,(
% 11.34/1.99 spl41_96 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_96])])).
% 11.34/1.99 thf(f3083,plain,(
% 11.34/1.99 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))))) | (zero_zero(nat) = X0)) ) | ~spl41_96),
% 11.34/1.99 inference(leibniz_equality_elimination,[],[f3014])).
% 11.34/1.99 thf(f3014,plain,(
% 11.34/1.99 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl41_96),
% 11.34/1.99 inference(avatar_component_clause,[],[f3013])).
% 11.34/1.99 thf(f32127,plain,(
% 11.34/1.99 spl41_466 | ~spl41_95),
% 11.34/1.99 inference(avatar_split_clause,[],[f3054,f3009,f32125])).
% 11.34/1.99 thf(f32125,plain,(
% 11.34/1.99 spl41_466 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X2 : X0] : ((wellorder(X1) != $true) | (vAPP(sTfun(X0,X1),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X0),sK16(X1,X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))),X3) = X2))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_466])])).
% 11.34/1.99 thf(f3009,plain,(
% 11.34/1.99 spl41_95 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1 > $o,X2 : X1 > X0] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2))) | ($true != wellorder(X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_95])])).
% 11.34/1.99 thf(f3054,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0 > X1] : ((wellorder(X1) != $true) | (vAPP(sTfun(X0,X1),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X0),sK16(X1,X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))),X3) = X2)) ) | ~spl41_95),
% 11.34/1.99 inference(leibniz_equality_elimination,[],[f3010])).
% 11.34/1.99 thf(f3010,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2))) | ($true = vAPP(X1,$o,X3,X4)) | ($true != wellorder(X0))) ) | ~spl41_95),
% 11.34/1.99 inference(avatar_component_clause,[],[f3009])).
% 11.34/1.99 thf(f32123,plain,(
% 11.34/1.99 spl41_465 | ~spl41_94),
% 11.34/1.99 inference(avatar_split_clause,[],[f3026,f3005,f32121])).
% 11.34/1.99 thf(f32121,plain,(
% 11.34/1.99 spl41_465 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X2 : X0] : ((wellorder(X1) != $true) | (vAPP(sTfun(X0,X1),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X0),sK15(X1,X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))),X3) = X2))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_465])])).
% 11.34/1.99 thf(f3005,plain,(
% 11.34/1.99 spl41_94 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1 > $o,X2 : X1 > X0] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2))) | ($true != wellorder(X0)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_94])])).
% 11.34/1.99 thf(f3026,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0 > X1] : ((wellorder(X1) != $true) | (vAPP(sTfun(X0,X1),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X0),sK15(X1,X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))),X3) = X2)) ) | ~spl41_94),
% 11.34/1.99 inference(leibniz_equality_elimination,[],[f3006])).
% 11.34/1.99 thf(f3006,plain,(
% 11.34/1.99 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2))) | ($true = vAPP(X1,$o,X3,X4)) | ($true != wellorder(X0))) ) | ~spl41_94),
% 11.34/1.99 inference(avatar_component_clause,[],[f3005])).
% 11.34/1.99 thf(f31993,plain,(
% 11.34/1.99 ~spl41_421 | spl41_464 | ~spl41_38 | ~spl41_196),
% 11.34/1.99 inference(avatar_split_clause,[],[f4404,f4291,f2456,f31991,f26025])).
% 11.34/1.99 thf(f31991,plain,(
% 11.34/1.99 spl41_464 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_464])])).
% 11.34/1.99 thf(f2456,plain,(
% 11.34/1.99 spl41_38 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_38])])).
% 11.34/1.99 thf(f4291,plain,(
% 11.34/1.99 spl41_196 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (linordered_field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_196])])).
% 11.34/1.99 thf(f4404,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != linordered_field(nat))) ) | (~spl41_38 | ~spl41_196)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f4399])).
% 11.34/1.99 thf(f4399,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != linordered_field(nat))) ) | (~spl41_38 | ~spl41_196)),
% 11.34/1.99 inference(superposition,[],[f4292,f2457])).
% 11.34/1.99 thf(f2457,plain,(
% 11.34/1.99 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0))) ) | ~spl41_38),
% 11.34/1.99 inference(avatar_component_clause,[],[f2456])).
% 11.34/1.99 thf(f4292,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (linordered_field(X0) != $true)) ) | ~spl41_196),
% 11.34/1.99 inference(avatar_component_clause,[],[f4291])).
% 11.34/1.99 thf(f31989,plain,(
% 11.34/1.99 spl41_463 | ~spl41_26 | ~spl41_132),
% 11.34/1.99 inference(avatar_split_clause,[],[f3403,f3357,f2369,f31987])).
% 11.34/1.99 thf(f31987,plain,(
% 11.34/1.99 spl41_463 <=> ! [X2 : $o,X0 : $o > $o,X1 : $o > nat] : (($true != vAPP($o,$o,X0,$true)) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X1),X0)) | ($true = vAPP($o,$o,X0,X2)) | ($false = vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),X0),X1)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_463])])).
% 11.34/1.99 thf(f3403,plain,(
% 11.34/1.99 ( ! [X2 : $o,X0 : $o > $o,X1 : $o > nat] : (($true != vAPP($o,$o,X0,$true)) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X1),X0)) | ($true = vAPP($o,$o,X0,X2)) | ($false = vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),X0),X1))) ) | (~spl41_26 | ~spl41_132)),
% 11.34/1.99 inference(superposition,[],[f3358,f2370])).
% 11.34/1.99 thf(f31985,plain,(
% 11.34/1.99 spl41_462 | ~spl41_116),
% 11.34/1.99 inference(avatar_split_clause,[],[f3262,f3246,f31983])).
% 11.34/1.99 thf(f31983,plain,(
% 11.34/1.99 spl41_462 <=> ! [X0 : $tType,X2 : X0 > nat,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK38(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_462])])).
% 11.34/1.99 thf(f3262,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > nat,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK38(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))) ) | ~spl41_116),
% 11.34/1.99 inference(equality_proxy_clausification,[],[f3254])).
% 11.34/1.99 thf(f3254,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > nat,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK38(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))) ) | ~spl41_116),
% 11.34/1.99 inference(primitive_instantiation,[],[f3247])).
% 11.34/1.99 thf(f30723,plain,(
% 11.34/1.99 spl41_461 | ~spl41_26 | ~spl41_137),
% 11.34/1.99 inference(avatar_split_clause,[],[f3626,f3598,f2369,f30721])).
% 11.34/1.99 thf(f30721,plain,(
% 11.34/1.99 spl41_461 <=> ! [X0 : $tType,X4 : X0,X3 : X0 > $o,X2 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,X3,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X1),X3)))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_461])])).
% 11.34/1.99 thf(f3626,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > nat,X4 : X0] : (($true = vAPP(X0,$o,X3,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X1),X3))))) ) | (~spl41_26 | ~spl41_137)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3625])).
% 11.34/1.99 thf(f3625,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > nat,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,X3,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X1),X3))))) ) | (~spl41_26 | ~spl41_137)),
% 11.34/1.99 inference(superposition,[],[f3599,f2370])).
% 11.34/1.99 thf(f30719,plain,(
% 11.34/1.99 spl41_460 | ~spl41_26 | ~spl41_136),
% 11.34/1.99 inference(avatar_split_clause,[],[f3605,f3594,f2369,f30717])).
% 11.34/1.99 thf(f30717,plain,(
% 11.34/1.99 spl41_460 <=> ! [X0 : $tType,X3 : list(X0),X2 : list(X0) > $o,X1 : list(X0)] : (($true = vAPP(list(X0),$o,X2,X1)) | ($true = vAPP(list(X0),$o,X2,X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X1)),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X2)))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_460])])).
% 11.34/1.99 thf(f3594,plain,(
% 11.34/1.99 spl41_136 <=> ! [X0 : $tType,X4 : list(X0),X2 : list(X0),X1 : list(X0) > $o] : (($true = vAPP(list(X0),$o,X1,X2)) | ($true = vAPP(list(X0),$o,X1,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X4)),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1)))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_136])])).
% 11.34/1.99 thf(f3605,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : list(X0) > $o,X3 : list(X0),X1 : list(X0)] : (($true = vAPP(list(X0),$o,X2,X1)) | ($true = vAPP(list(X0),$o,X2,X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X1)),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X2))))) ) | (~spl41_26 | ~spl41_136)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3604])).
% 11.34/1.99 thf(f3604,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : list(X0) > $o,X3 : list(X0),X1 : list(X0)] : (($true != $true) | ($true = vAPP(list(X0),$o,X2,X1)) | ($true = vAPP(list(X0),$o,X2,X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X1)),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X2))))) ) | (~spl41_26 | ~spl41_136)),
% 11.34/1.99 inference(superposition,[],[f3595,f2370])).
% 11.34/1.99 thf(f3595,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0) > $o,X4 : list(X0)] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X4)),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1)))) | ($true = vAPP(list(X0),$o,X1,X4)) | ($true = vAPP(list(X0),$o,X1,X2))) ) | ~spl41_136),
% 11.34/1.99 inference(avatar_component_clause,[],[f3594])).
% 11.34/1.99 thf(f30660,plain,(
% 11.34/1.99 ~spl41_421 | spl41_459 | ~spl41_48 | ~spl41_150),
% 11.34/1.99 inference(avatar_split_clause,[],[f3865,f3842,f2510,f30658,f26025])).
% 11.34/1.99 thf(f30658,plain,(
% 11.34/1.99 spl41_459 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK11(nat),X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,suc,X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_459])])).
% 11.34/1.99 thf(f3865,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK11(nat),X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,suc,X0))) | ($true != linordered_field(nat))) ) | (~spl41_48 | ~spl41_150)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3860])).
% 11.34/1.99 thf(f3860,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK11(nat),X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,suc,X0))) | ($true != linordered_field(nat))) ) | (~spl41_48 | ~spl41_150)),
% 11.34/1.99 inference(superposition,[],[f3843,f2511])).
% 11.34/1.99 thf(f30656,plain,(
% 11.34/1.99 spl41_458 | ~spl41_41 | ~spl41_136),
% 11.34/1.99 inference(avatar_split_clause,[],[f3601,f3594,f2476,f30654])).
% 11.34/1.99 thf(f30654,plain,(
% 11.34/1.99 spl41_458 <=> ! [X0 : $tType,X3 : list(X0),X2 : list(X0) > $o,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X2)))) | ($true = vAPP(list(X0),$o,X2,vAPP(nat,list(X0),sK23(X0),X1))) | ($true = vAPP(list(X0),$o,X2,X3)))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_458])])).
% 11.34/1.99 thf(f2476,plain,(
% 11.34/1.99 spl41_41 <=> ! [X0 : $tType,X1 : nat] : (vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK23(X0),X1)) = X1)),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_41])])).
% 11.34/1.99 thf(f3601,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : list(X0) > $o,X3 : list(X0),X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X2)))) | ($true = vAPP(list(X0),$o,X2,vAPP(nat,list(X0),sK23(X0),X1))) | ($true = vAPP(list(X0),$o,X2,X3))) ) | (~spl41_41 | ~spl41_136)),
% 11.34/1.99 inference(superposition,[],[f3595,f2477])).
% 11.34/1.99 thf(f2477,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X1 : nat] : ((vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK23(X0),X1)) = X1)) ) | ~spl41_41),
% 11.34/1.99 inference(avatar_component_clause,[],[f2476])).
% 11.34/1.99 thf(f28066,plain,(
% 11.34/1.99 spl41_457 | ~spl41_14 | ~spl41_139),
% 11.34/1.99 inference(avatar_split_clause,[],[f3667,f3636,f2310,f28064])).
% 11.34/1.99 thf(f28064,plain,(
% 11.34/1.99 spl41_457 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_457])])).
% 11.34/1.99 thf(f2310,plain,(
% 11.34/1.99 spl41_14 <=> (euclid191655569cancel(nat) = $true)),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_14])])).
% 11.34/1.99 thf(f3667,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)))) ) | (~spl41_14 | ~spl41_139)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3664])).
% 11.34/1.99 thf(f3664,plain,(
% 11.34/1.99 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (zero_zero(nat) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)))) ) | (~spl41_14 | ~spl41_139)),
% 11.34/1.99 inference(superposition,[],[f3637,f2312])).
% 11.34/1.99 thf(f2312,plain,(
% 11.34/1.99 (euclid191655569cancel(nat) = $true) | ~spl41_14),
% 11.34/1.99 inference(avatar_component_clause,[],[f2310])).
% 11.34/1.99 thf(f28062,plain,(
% 11.34/1.99 spl41_456 | ~spl41_26 | ~spl41_132),
% 11.34/1.99 inference(avatar_split_clause,[],[f3406,f3357,f2369,f28060])).
% 11.34/1.99 thf(f28060,plain,(
% 11.34/1.99 spl41_456 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > nat,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),X1)) | ($true = vAPP(X0,$o,X1,X3)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X1),X2))))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_456])])).
% 11.34/1.99 thf(f3406,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),X1)) | ($true = vAPP(X0,$o,X1,X3)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X1),X2)))) ) | (~spl41_26 | ~spl41_132)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3405])).
% 11.34/1.99 thf(f3405,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),X1)) | ($true = vAPP(X0,$o,X1,X3)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X1),X2)))) ) | (~spl41_26 | ~spl41_132)),
% 11.34/1.99 inference(superposition,[],[f3358,f2370])).
% 11.34/1.99 thf(f28058,plain,(
% 11.34/1.99 spl41_455 | ~spl41_26 | ~spl41_130),
% 11.34/1.99 inference(avatar_split_clause,[],[f3385,f3349,f2369,f28056])).
% 11.34/1.99 thf(f28056,plain,(
% 11.34/1.99 spl41_455 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),X2)) | (field(X0) = $false))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_455])])).
% 11.34/1.99 thf(f3349,plain,(
% 11.34/1.99 spl41_130 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3)) | (field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_130])])).
% 11.34/1.99 thf(f3385,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),X2)) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_130)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3384])).
% 11.34/1.99 thf(f3384,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),X2)) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_130)),
% 11.34/1.99 inference(superposition,[],[f3350,f2370])).
% 11.34/1.99 thf(f3350,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((field(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3))) ) | ~spl41_130),
% 11.34/1.99 inference(avatar_component_clause,[],[f3349])).
% 11.34/1.99 thf(f28054,plain,(
% 11.34/1.99 spl41_453 | spl41_2 | ~spl41_454 | ~spl41_260 | ~spl41_438),
% 11.34/1.99 inference(avatar_split_clause,[],[f27868,f27191,f8710,f28051,f2250,f28047])).
% 11.34/1.99 thf(f28051,plain,(
% 11.34/1.99 spl41_454 <=> (zero_zero(nat) = vAPP(list(a),nat,size_size(list(a)),xs))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_454])])).
% 11.34/1.99 thf(f8710,plain,(
% 11.34/1.99 spl41_260 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | (zero_zero(nat) = X1) | (zero_zero(nat) = X0))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_260])])).
% 11.34/1.99 thf(f27868,plain,(
% 11.34/1.99 (zero_zero(nat) != vAPP(list(a),nat,size_size(list(a)),xs)) | (zero_zero(nat) = k) | (zero_zero(nat) = n) | (~spl41_260 | ~spl41_438)),
% 11.34/1.99 inference(superposition,[],[f8711,f27193])).
% 11.34/1.99 thf(f8711,plain,(
% 11.34/1.99 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | (zero_zero(nat) = X1) | (zero_zero(nat) = X0)) ) | ~spl41_260),
% 11.34/1.99 inference(avatar_component_clause,[],[f8710])).
% 11.34/1.99 thf(f28045,plain,(
% 11.34/1.99 spl41_452 | ~spl41_26 | ~spl41_129),
% 11.34/1.99 inference(avatar_split_clause,[],[f3383,f3345,f2369,f28043])).
% 11.34/1.99 thf(f28043,plain,(
% 11.34/1.99 spl41_452 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | (field(X0) = $false))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_452])])).
% 11.34/1.99 thf(f3345,plain,(
% 11.34/1.99 spl41_129 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | (field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_129])])).
% 11.34/1.99 thf(f3383,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_129)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3382])).
% 11.34/1.99 thf(f3382,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_129)),
% 11.34/1.99 inference(superposition,[],[f3346,f2370])).
% 11.34/1.99 thf(f3346,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((field(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)))) ) | ~spl41_129),
% 11.34/1.99 inference(avatar_component_clause,[],[f3345])).
% 11.34/1.99 thf(f28041,plain,(
% 11.34/1.99 spl41_451 | ~spl41_26 | ~spl41_128),
% 11.34/1.99 inference(avatar_split_clause,[],[f3381,f3341,f2369,f28039])).
% 11.34/1.99 thf(f28039,plain,(
% 11.34/1.99 spl41_451 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2)) | (field(X0) = $false))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_451])])).
% 11.34/1.99 thf(f3341,plain,(
% 11.34/1.99 spl41_128 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2)) | (field(X0) != $true))),
% 11.34/1.99 introduced(avatar_definition,[new_symbols(naming,[spl41_128])])).
% 11.34/1.99 thf(f3381,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2)) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_128)),
% 11.34/1.99 inference(trivial_inequality_removal,[],[f3380])).
% 11.34/1.99 thf(f3380,plain,(
% 11.34/1.99 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2)) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_128)),
% 11.34/2.00 inference(superposition,[],[f3342,f2370])).
% 11.34/2.00 thf(f3342,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((field(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2))) ) | ~spl41_128),
% 11.34/2.00 inference(avatar_component_clause,[],[f3341])).
% 11.34/2.00 thf(f28037,plain,(
% 11.34/2.00 spl41_450 | ~spl41_26 | ~spl41_127),
% 11.34/2.00 inference(avatar_split_clause,[],[f3379,f3337,f2369,f28035])).
% 11.34/2.00 thf(f28035,plain,(
% 11.34/2.00 spl41_450 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | (division_ring(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_450])])).
% 11.34/2.00 thf(f3337,plain,(
% 11.34/2.00 spl41_127 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | (division_ring(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_127])])).
% 11.34/2.00 thf(f3379,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | (division_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_127)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3378])).
% 11.34/2.00 thf(f3378,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | (division_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_127)),
% 11.34/2.00 inference(superposition,[],[f3338,f2370])).
% 11.34/2.00 thf(f3338,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((division_ring(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)))) ) | ~spl41_127),
% 11.34/2.00 inference(avatar_component_clause,[],[f3337])).
% 11.34/2.00 thf(f28033,plain,(
% 11.34/2.00 spl41_449 | ~spl41_26 | ~spl41_126),
% 11.34/2.00 inference(avatar_split_clause,[],[f3377,f3333,f2369,f28031])).
% 11.34/2.00 thf(f28031,plain,(
% 11.34/2.00 spl41_449 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (division_ring(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_449])])).
% 11.34/2.00 thf(f3333,plain,(
% 11.34/2.00 spl41_126 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (division_ring(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_126])])).
% 11.34/2.00 thf(f3377,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (division_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_126)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3376])).
% 11.34/2.00 thf(f3376,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (division_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_126)),
% 11.34/2.00 inference(superposition,[],[f3334,f2370])).
% 11.34/2.00 thf(f3334,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((division_ring(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3))) ) | ~spl41_126),
% 11.34/2.00 inference(avatar_component_clause,[],[f3333])).
% 11.34/2.00 thf(f28029,plain,(
% 11.34/2.00 spl41_448 | ~spl41_26 | ~spl41_125),
% 11.34/2.00 inference(avatar_split_clause,[],[f3374,f3329,f2369,f28027])).
% 11.34/2.00 thf(f28027,plain,(
% 11.34/2.00 spl41_448 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (ab_semigroup_mult(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_448])])).
% 11.34/2.00 thf(f3329,plain,(
% 11.34/2.00 spl41_125 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (ab_semigroup_mult(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_125])])).
% 11.34/2.00 thf(f3374,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (ab_semigroup_mult(X0) = $false)) ) | (~spl41_26 | ~spl41_125)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3373])).
% 11.34/2.00 thf(f3373,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (ab_semigroup_mult(X0) = $false)) ) | (~spl41_26 | ~spl41_125)),
% 11.34/2.00 inference(superposition,[],[f3330,f2370])).
% 11.34/2.00 thf(f3330,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((ab_semigroup_mult(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3))) ) | ~spl41_125),
% 11.34/2.00 inference(avatar_component_clause,[],[f3329])).
% 11.34/2.00 thf(f28025,plain,(
% 11.34/2.00 spl41_447 | ~spl41_26 | ~spl41_124),
% 11.34/2.00 inference(avatar_split_clause,[],[f3370,f3325,f2369,f28023])).
% 11.34/2.00 thf(f28023,plain,(
% 11.34/2.00 spl41_447 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (ab_semigroup_mult(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_447])])).
% 11.34/2.00 thf(f3325,plain,(
% 11.34/2.00 spl41_124 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (ab_semigroup_mult(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_124])])).
% 11.34/2.00 thf(f3370,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (ab_semigroup_mult(X0) = $false)) ) | (~spl41_26 | ~spl41_124)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3369])).
% 11.34/2.00 thf(f3369,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (ab_semigroup_mult(X0) = $false)) ) | (~spl41_26 | ~spl41_124)),
% 11.34/2.00 inference(superposition,[],[f3326,f2370])).
% 11.34/2.00 thf(f3326,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((ab_semigroup_mult(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)))) ) | ~spl41_124),
% 11.34/2.00 inference(avatar_component_clause,[],[f3325])).
% 11.34/2.00 thf(f28021,plain,(
% 11.34/2.00 spl41_446 | ~spl41_26 | ~spl41_122),
% 11.34/2.00 inference(avatar_split_clause,[],[f3362,f3317,f2369,f28019])).
% 11.34/2.00 thf(f28019,plain,(
% 11.34/2.00 spl41_446 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (semigroup_mult(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_446])])).
% 11.34/2.00 thf(f3317,plain,(
% 11.34/2.00 spl41_122 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (semigroup_mult(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_122])])).
% 11.34/2.00 thf(f3362,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (semigroup_mult(X0) = $false)) ) | (~spl41_26 | ~spl41_122)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3361])).
% 11.34/2.00 thf(f3361,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (semigroup_mult(X0) = $false)) ) | (~spl41_26 | ~spl41_122)),
% 11.34/2.00 inference(superposition,[],[f3318,f2370])).
% 11.34/2.00 thf(f3318,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((semigroup_mult(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3))) ) | ~spl41_122),
% 11.34/2.00 inference(avatar_component_clause,[],[f3317])).
% 11.34/2.00 thf(f28017,plain,(
% 11.34/2.00 spl41_445 | ~spl41_64),
% 11.34/2.00 inference(avatar_split_clause,[],[f2651,f2648,f28015])).
% 11.34/2.00 thf(f28015,plain,(
% 11.34/2.00 spl41_445 <=> ! [X0 : $tType,X1 : list(X0)] : (vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),vAPP(sTfun(list(X0),$o),sTfun(list(X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(list(X0),$o),sTfun(list(X0),$o)),bCOMB,vNOT),vAPP(list(X0),sTfun(list(X0),$o),vEQ(list(X0)),X1))) = X1)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_445])])).
% 11.34/2.00 thf(f2648,plain,(
% 11.34/2.00 spl41_64 <=> ! [X0 : $tType,X2 : list(X0),X1 : list(X0) > $o] : (($true = vAPP(list(X0),$o,X1,X2)) | ($true != vAPP(list(X0),$o,X1,vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_64])])).
% 11.34/2.00 thf(f2651,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X1 : list(X0)] : ((vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),vAPP(sTfun(list(X0),$o),sTfun(list(X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(list(X0),$o),sTfun(list(X0),$o)),bCOMB,vNOT),vAPP(list(X0),sTfun(list(X0),$o),vEQ(list(X0)),X1))) = X1)) ) | ~spl41_64),
% 11.34/2.00 inference(leibniz_equality_elimination,[],[f2649])).
% 11.34/2.00 thf(f2649,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0) > $o] : (($true != vAPP(list(X0),$o,X1,vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1))) | ($true = vAPP(list(X0),$o,X1,X2))) ) | ~spl41_64),
% 11.34/2.00 inference(avatar_component_clause,[],[f2648])).
% 11.34/2.00 thf(f27218,plain,(
% 11.34/2.00 spl41_444 | ~spl41_16 | ~spl41_38 | ~spl41_189),
% 11.34/2.00 inference(avatar_split_clause,[],[f4363,f4263,f2456,f2320,f27216])).
% 11.34/2.00 thf(f27216,plain,(
% 11.34/2.00 spl41_444 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_444])])).
% 11.34/2.00 thf(f2320,plain,(
% 11.34/2.00 spl41_16 <=> (ordered_semiring(nat) = $true)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_16])])).
% 11.34/2.00 thf(f4263,plain,(
% 11.34/2.00 spl41_189 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_semiring(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_189])])).
% 11.34/2.00 thf(f4363,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))) ) | (~spl41_16 | ~spl41_38 | ~spl41_189)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4362])).
% 11.34/2.00 thf(f4362,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))) ) | (~spl41_16 | ~spl41_38 | ~spl41_189)),
% 11.34/2.00 inference(forward_demodulation,[],[f4361,f2322])).
% 11.34/2.00 thf(f2322,plain,(
% 11.34/2.00 (ordered_semiring(nat) = $true) | ~spl41_16),
% 11.34/2.00 inference(avatar_component_clause,[],[f2320])).
% 11.34/2.00 thf(f4361,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (ordered_semiring(nat) != $true)) ) | (~spl41_38 | ~spl41_189)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4356])).
% 11.34/2.00 thf(f4356,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (ordered_semiring(nat) != $true)) ) | (~spl41_38 | ~spl41_189)),
% 11.34/2.00 inference(superposition,[],[f4264,f2457])).
% 11.34/2.00 thf(f4264,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_semiring(X0) != $true)) ) | ~spl41_189),
% 11.34/2.00 inference(avatar_component_clause,[],[f4263])).
% 11.34/2.00 thf(f27214,plain,(
% 11.34/2.00 spl41_443 | ~spl41_4 | ~spl41_38 | ~spl41_184),
% 11.34/2.00 inference(avatar_split_clause,[],[f4318,f4243,f2456,f2260,f27212])).
% 11.34/2.00 thf(f27212,plain,(
% 11.34/2.00 spl41_443 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_443])])).
% 11.34/2.00 thf(f2260,plain,(
% 11.34/2.00 spl41_4 <=> (ordere1490568538miring(nat) = $true)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_4])])).
% 11.34/2.00 thf(f4243,plain,(
% 11.34/2.00 spl41_184 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere1490568538miring(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_184])])).
% 11.34/2.00 thf(f4318,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))) ) | (~spl41_4 | ~spl41_38 | ~spl41_184)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4317])).
% 11.34/2.00 thf(f4317,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))) ) | (~spl41_4 | ~spl41_38 | ~spl41_184)),
% 11.34/2.00 inference(forward_demodulation,[],[f4316,f2262])).
% 11.34/2.00 thf(f2262,plain,(
% 11.34/2.00 (ordere1490568538miring(nat) = $true) | ~spl41_4),
% 11.34/2.00 inference(avatar_component_clause,[],[f2260])).
% 11.34/2.00 thf(f4316,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (ordere1490568538miring(nat) != $true)) ) | (~spl41_38 | ~spl41_184)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4311])).
% 11.34/2.00 thf(f4311,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (ordere1490568538miring(nat) != $true)) ) | (~spl41_38 | ~spl41_184)),
% 11.34/2.00 inference(superposition,[],[f4244,f2457])).
% 11.34/2.00 thf(f4244,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere1490568538miring(X0) != $true)) ) | ~spl41_184),
% 11.34/2.00 inference(avatar_component_clause,[],[f4243])).
% 11.34/2.00 thf(f27210,plain,(
% 11.34/2.00 spl41_442 | ~spl41_26 | ~spl41_121),
% 11.34/2.00 inference(avatar_split_clause,[],[f3315,f3309,f2369,f27208])).
% 11.34/2.00 thf(f27208,plain,(
% 11.34/2.00 spl41_442 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X2)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_442])])).
% 11.34/2.00 thf(f3315,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X2)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)))) ) | (~spl41_26 | ~spl41_121)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3314])).
% 11.34/2.00 thf(f3314,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X2)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)))) ) | (~spl41_26 | ~spl41_121)),
% 11.34/2.00 inference(superposition,[],[f3310,f2370])).
% 11.34/2.00 thf(f27206,plain,(
% 11.34/2.00 spl41_441 | ~spl41_35 | ~spl41_112),
% 11.34/2.00 inference(avatar_split_clause,[],[f3223,f3207,f2444,f27204])).
% 11.34/2.00 thf(f27204,plain,(
% 11.34/2.00 spl41_441 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK5,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK5,X0)))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_441])])).
% 11.34/2.00 thf(f3207,plain,(
% 11.34/2.00 spl41_112 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_112])])).
% 11.34/2.00 thf(f3223,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK5,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK5,X0)))) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_112)),
% 11.34/2.00 inference(superposition,[],[f3208,f2445])).
% 11.34/2.00 thf(f3208,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)))) ) | ~spl41_112),
% 11.34/2.00 inference(avatar_component_clause,[],[f3207])).
% 11.34/2.00 thf(f27202,plain,(
% 11.34/2.00 spl41_440 | ~spl41_34 | ~spl41_112),
% 11.34/2.00 inference(avatar_split_clause,[],[f3222,f3207,f2440,f27200])).
% 11.34/2.00 thf(f27200,plain,(
% 11.34/2.00 spl41_440 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK4,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK4,X0)))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_440])])).
% 11.34/2.00 thf(f3222,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK4,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK4,X0)))) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_112)),
% 11.34/2.00 inference(superposition,[],[f3208,f2441])).
% 11.34/2.00 thf(f27198,plain,(
% 11.34/2.00 spl41_438 | spl41_439 | ~spl41_60 | ~spl41_309),
% 11.34/2.00 inference(avatar_split_clause,[],[f15515,f15126,f2585,f27195,f27191])).
% 11.34/2.00 thf(f2585,plain,(
% 11.34/2.00 spl41_60 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs)) = $false)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_60])])).
% 11.34/2.00 thf(f15126,plain,(
% 11.34/2.00 spl41_309 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_309])])).
% 11.34/2.00 thf(f15515,plain,(
% 11.34/2.00 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(a),nat,size_size(list(a)),xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k))) | (vAPP(list(a),nat,size_size(list(a)),xs) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)) | (~spl41_60 | ~spl41_309)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f15153])).
% 11.34/2.00 thf(f15153,plain,(
% 11.34/2.00 ($true = $false) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(a),nat,size_size(list(a)),xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k))) | (vAPP(list(a),nat,size_size(list(a)),xs) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)) | (~spl41_60 | ~spl41_309)),
% 11.34/2.00 inference(superposition,[],[f15127,f2587])).
% 11.34/2.00 thf(f2587,plain,(
% 11.34/2.00 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs)) = $false) | ~spl41_60),
% 11.34/2.00 inference(avatar_component_clause,[],[f2585])).
% 11.34/2.00 thf(f15127,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (X0 = X1)) ) | ~spl41_309),
% 11.34/2.00 inference(avatar_component_clause,[],[f15126])).
% 11.34/2.00 thf(f27189,plain,(
% 11.34/2.00 spl41_437 | ~spl41_33 | ~spl41_112),
% 11.34/2.00 inference(avatar_split_clause,[],[f3221,f3207,f2436,f27187])).
% 11.34/2.00 thf(f27187,plain,(
% 11.34/2.00 spl41_437 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK3,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK3,X0)))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_437])])).
% 11.34/2.00 thf(f3221,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK3,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK3,X0)))) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_112)),
% 11.34/2.00 inference(superposition,[],[f3208,f2437])).
% 11.34/2.00 thf(f27185,plain,(
% 11.34/2.00 spl41_436 | ~spl41_78),
% 11.34/2.00 inference(avatar_split_clause,[],[f2803,f2800,f27183])).
% 11.34/2.00 thf(f27183,plain,(
% 11.34/2.00 spl41_436 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > nat] : (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))) = X2)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_436])])).
% 11.34/2.00 thf(f2800,plain,(
% 11.34/2.00 spl41_78 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > nat,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_78])])).
% 11.34/2.00 thf(f2803,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0 > nat] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))) = X2)) ) | ~spl41_78),
% 11.34/2.00 inference(leibniz_equality_elimination,[],[f2801])).
% 11.34/2.00 thf(f2801,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1))) | ($true = vAPP(X0,$o,X1,X3))) ) | ~spl41_78),
% 11.34/2.00 inference(avatar_component_clause,[],[f2800])).
% 11.34/2.00 thf(f27181,plain,(
% 11.34/2.00 ~spl41_421 | spl41_435 | ~spl41_48 | ~spl41_174),
% 11.34/2.00 inference(avatar_split_clause,[],[f4136,f3971,f2510,f27179,f26025])).
% 11.34/2.00 thf(f27179,plain,(
% 11.34/2.00 spl41_435 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,suc,X0)),X1))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_435])])).
% 11.34/2.00 thf(f4136,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,suc,X0)),X1))) | ($true != linordered_field(nat))) ) | (~spl41_48 | ~spl41_174)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4131])).
% 11.34/2.00 thf(f4131,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,suc,X0)),X1))) | ($true != linordered_field(nat))) ) | (~spl41_48 | ~spl41_174)),
% 11.34/2.00 inference(superposition,[],[f3972,f2511])).
% 11.34/2.00 thf(f27177,plain,(
% 11.34/2.00 ~spl41_421 | spl41_434 | ~spl41_48 | ~spl41_173),
% 11.34/2.00 inference(avatar_split_clause,[],[f4127,f3967,f2510,f27175,f26025])).
% 11.34/2.00 thf(f27175,plain,(
% 11.34/2.00 spl41_434 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK11(nat),X1),vAPP(nat,nat,suc,X0)))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_434])])).
% 11.34/2.00 thf(f4127,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK11(nat),X1),vAPP(nat,nat,suc,X0)))) | ($true != linordered_field(nat))) ) | (~spl41_48 | ~spl41_173)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4122])).
% 11.34/2.00 thf(f4122,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK11(nat),X1),vAPP(nat,nat,suc,X0)))) | ($true != linordered_field(nat))) ) | (~spl41_48 | ~spl41_173)),
% 11.34/2.00 inference(superposition,[],[f3968,f2511])).
% 11.34/2.00 thf(f26915,plain,(
% 11.34/2.00 ~spl41_421 | spl41_433 | ~spl41_48 | ~spl41_151),
% 11.34/2.00 inference(avatar_split_clause,[],[f3874,f3847,f2510,f26913,f26025])).
% 11.34/2.00 thf(f26913,plain,(
% 11.34/2.00 spl41_433 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK11(nat),X1),vAPP(nat,nat,suc,X0))),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_433])])).
% 11.34/2.00 thf(f3874,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK11(nat),X1),vAPP(nat,nat,suc,X0))),X1)) | ($true != linordered_field(nat))) ) | (~spl41_48 | ~spl41_151)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3869])).
% 11.34/2.00 thf(f3869,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK11(nat),X1),vAPP(nat,nat,suc,X0))),X1)) | ($true != linordered_field(nat))) ) | (~spl41_48 | ~spl41_151)),
% 11.34/2.00 inference(superposition,[],[f3848,f2511])).
% 11.34/2.00 thf(f26911,plain,(
% 11.34/2.00 spl41_432 | ~spl41_48 | ~spl41_144),
% 11.34/2.00 inference(avatar_split_clause,[],[f3683,f3657,f2510,f26909])).
% 11.34/2.00 thf(f26909,plain,(
% 11.34/2.00 spl41_432 <=> ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),vAPP(nat,nat,suc,X0)))),vAPP(nat,nat,suc,X0))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_432])])).
% 11.34/2.00 thf(f3657,plain,(
% 11.34/2.00 spl41_144 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_144])])).
% 11.34/2.00 thf(f3683,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),vAPP(nat,nat,suc,X0)))),vAPP(nat,nat,suc,X0))))) ) | (~spl41_48 | ~spl41_144)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3676])).
% 11.34/2.00 thf(f3676,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),vAPP(nat,nat,suc,X0)))),vAPP(nat,nat,suc,X0))))) ) | (~spl41_48 | ~spl41_144)),
% 11.34/2.00 inference(superposition,[],[f3658,f2511])).
% 11.34/2.00 thf(f3658,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))),X0)))) ) | ~spl41_144),
% 11.34/2.00 inference(avatar_component_clause,[],[f3657])).
% 11.34/2.00 thf(f26877,plain,(
% 11.34/2.00 spl41_274 | spl41_431 | ~spl41_134),
% 11.34/2.00 inference(avatar_split_clause,[],[f3584,f3424,f26875,f8769])).
% 11.34/2.00 thf(f8769,plain,(
% 11.34/2.00 spl41_274 <=> ! [X1 : $o] : ($false = X1)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_274])])).
% 11.34/2.00 thf(f26875,plain,(
% 11.34/2.00 spl41_431 <=> ! [X0 : $o > nat] : ((zero_zero(nat) = vAPP($o,nat,X0,vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),vNOT),X0))) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_431])])).
% 11.34/2.00 thf(f3584,plain,(
% 11.34/2.00 ( ! [X0 : $o > nat,X1 : $o] : ((zero_zero(nat) = vAPP($o,nat,X0,vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),vNOT),X0))) | ($false = X1) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT))) ) | ~spl41_134),
% 11.34/2.00 inference(not_proxy_clausification,[],[f3437])).
% 11.34/2.00 thf(f3437,plain,(
% 11.34/2.00 ( ! [X0 : $o > nat,X1 : $o] : ((zero_zero(nat) = vAPP($o,nat,X0,vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),vNOT),X0))) | ($true = vAPP($o,$o,vNOT,X1)) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT))) ) | ~spl41_134),
% 11.34/2.00 inference(primitive_instantiation,[],[f3425])).
% 11.34/2.00 thf(f26867,plain,(
% 11.34/2.00 spl41_430 | ~spl41_100),
% 11.34/2.00 inference(avatar_split_clause,[],[f3135,f3115,f26865])).
% 11.34/2.00 thf(f26865,plain,(
% 11.34/2.00 spl41_430 <=> ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_430])])).
% 11.34/2.00 thf(f3115,plain,(
% 11.34/2.00 spl41_100 <=> ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0))) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_100])])).
% 11.34/2.00 thf(f3135,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) ) | ~spl41_100),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f3130])).
% 11.34/2.00 thf(f3130,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) ) | ~spl41_100),
% 11.34/2.00 inference(primitive_instantiation,[],[f3116])).
% 11.34/2.00 thf(f3116,plain,(
% 11.34/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0))) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0))) ) | ~spl41_100),
% 11.34/2.00 inference(avatar_component_clause,[],[f3115])).
% 11.34/2.00 thf(f26596,plain,(
% 11.34/2.00 spl41_429 | ~spl41_12 | ~spl41_124),
% 11.34/2.00 inference(avatar_split_clause,[],[f3371,f3325,f2300,f26594])).
% 11.34/2.00 thf(f26594,plain,(
% 11.34/2.00 spl41_429 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_429])])).
% 11.34/2.00 thf(f2300,plain,(
% 11.34/2.00 spl41_12 <=> (ab_semigroup_mult(nat) = $true)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_12])])).
% 11.34/2.00 thf(f3371,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)))) ) | (~spl41_12 | ~spl41_124)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3368])).
% 11.34/2.00 thf(f3368,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)))) ) | (~spl41_12 | ~spl41_124)),
% 11.34/2.00 inference(superposition,[],[f3326,f2302])).
% 11.34/2.00 thf(f2302,plain,(
% 11.34/2.00 (ab_semigroup_mult(nat) = $true) | ~spl41_12),
% 11.34/2.00 inference(avatar_component_clause,[],[f2300])).
% 11.34/2.00 thf(f26592,plain,(
% 11.34/2.00 spl41_428 | ~spl41_5 | ~spl41_122),
% 11.34/2.00 inference(avatar_split_clause,[],[f3363,f3317,f2265,f26590])).
% 11.34/2.00 thf(f26590,plain,(
% 11.34/2.00 spl41_428 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X2))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_428])])).
% 11.34/2.00 thf(f2265,plain,(
% 11.34/2.00 spl41_5 <=> (semigroup_mult(nat) = $true)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_5])])).
% 11.34/2.00 thf(f3363,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X2))) ) | (~spl41_5 | ~spl41_122)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3360])).
% 11.34/2.00 thf(f3360,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X2))) ) | (~spl41_5 | ~spl41_122)),
% 11.34/2.00 inference(superposition,[],[f3318,f2267])).
% 11.34/2.00 thf(f2267,plain,(
% 11.34/2.00 (semigroup_mult(nat) = $true) | ~spl41_5),
% 11.34/2.00 inference(avatar_component_clause,[],[f2265])).
% 11.34/2.00 thf(f26588,plain,(
% 11.34/2.00 spl41_427 | ~spl41_26 | ~spl41_116),
% 11.34/2.00 inference(avatar_split_clause,[],[f3256,f3246,f2369,f26586])).
% 11.34/2.00 thf(f26586,plain,(
% 11.34/2.00 spl41_427 <=> ! [X0 : $o > nat,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true != vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),X1)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK38($o),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_427])])).
% 11.34/2.00 thf(f3256,plain,(
% 11.34/2.00 ( ! [X0 : $o > nat,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true != vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),X1)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK38($o),X0),X1))) ) | (~spl41_26 | ~spl41_116)),
% 11.34/2.00 inference(superposition,[],[f3247,f2370])).
% 11.34/2.00 thf(f26560,plain,(
% 11.34/2.00 spl41_426 | ~spl41_63 | ~spl41_120),
% 11.34/2.00 inference(avatar_split_clause,[],[f3302,f3298,f2643,f26558])).
% 11.34/2.00 thf(f26558,plain,(
% 11.34/2.00 spl41_426 <=> ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),k),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,suc,n)),X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_426])])).
% 11.34/2.00 thf(f3298,plain,(
% 11.34/2.00 spl41_120 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)),X2))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_120])])).
% 11.34/2.00 thf(f3302,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),k),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,suc,n)),X0))) ) | (~spl41_63 | ~spl41_120)),
% 11.34/2.00 inference(superposition,[],[f3299,f2645])).
% 11.34/2.00 thf(f3299,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)),X2))) ) | ~spl41_120),
% 11.34/2.00 inference(avatar_component_clause,[],[f3298])).
% 11.34/2.00 thf(f26517,plain,(
% 11.34/2.00 spl41_425 | ~spl41_26 | spl41_341),
% 11.34/2.00 inference(avatar_split_clause,[],[f18521,f18509,f2369,f26514])).
% 11.34/2.00 thf(f26514,plain,(
% 11.34/2.00 spl41_425 <=> ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_425])])).
% 11.34/2.00 thf(f18509,plain,(
% 11.34/2.00 spl41_341 <=> ($true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_341])])).
% 11.34/2.00 thf(f18521,plain,(
% 11.34/2.00 ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat))) | (~spl41_26 | spl41_341)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f18520])).
% 11.34/2.00 thf(f18520,plain,(
% 11.34/2.00 ($true != $true) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat))) | (~spl41_26 | spl41_341)),
% 11.34/2.00 inference(superposition,[],[f18511,f2370])).
% 11.34/2.00 thf(f18511,plain,(
% 11.34/2.00 ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat))) | spl41_341),
% 11.34/2.00 inference(avatar_component_clause,[],[f18509])).
% 11.34/2.00 thf(f26400,plain,(
% 11.34/2.00 spl41_424 | ~spl41_26 | ~spl41_119),
% 11.34/2.00 inference(avatar_split_clause,[],[f3294,f3287,f2369,f26398])).
% 11.34/2.00 thf(f26398,plain,(
% 11.34/2.00 spl41_424 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_424])])).
% 11.34/2.00 thf(f3287,plain,(
% 11.34/2.00 spl41_119 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_119])])).
% 11.34/2.00 thf(f3294,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_119)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3293])).
% 11.34/2.00 thf(f3293,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_119)),
% 11.34/2.00 inference(superposition,[],[f3288,f2370])).
% 11.34/2.00 thf(f3288,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl41_119),
% 11.34/2.00 inference(avatar_component_clause,[],[f3287])).
% 11.34/2.00 thf(f26036,plain,(
% 11.34/2.00 ~spl41_421 | spl41_423 | ~spl41_38 | ~spl41_170),
% 11.34/2.00 inference(avatar_split_clause,[],[f4103,f3955,f2456,f26034,f26025])).
% 11.34/2.00 thf(f26034,plain,(
% 11.34/2.00 spl41_423 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)),zero_zero(nat))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_423])])).
% 11.34/2.00 thf(f4103,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)),zero_zero(nat))) | ($true != linordered_field(nat))) ) | (~spl41_38 | ~spl41_170)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4098])).
% 11.34/2.00 thf(f4098,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)),zero_zero(nat))) | ($true != linordered_field(nat))) ) | (~spl41_38 | ~spl41_170)),
% 11.34/2.00 inference(superposition,[],[f3956,f2457])).
% 11.34/2.00 thf(f26031,plain,(
% 11.34/2.00 ~spl41_421 | spl41_422 | ~spl41_38 | ~spl41_167),
% 11.34/2.00 inference(avatar_split_clause,[],[f4088,f3941,f2456,f26029,f26025])).
% 11.34/2.00 thf(f26029,plain,(
% 11.34/2.00 spl41_422 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_422])])).
% 11.34/2.00 thf(f4088,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true != linordered_field(nat))) ) | (~spl41_38 | ~spl41_167)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4083])).
% 11.34/2.00 thf(f4083,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true != linordered_field(nat))) ) | (~spl41_38 | ~spl41_167)),
% 11.34/2.00 inference(superposition,[],[f3942,f2457])).
% 11.34/2.00 thf(f26023,plain,(
% 11.34/2.00 spl41_420 | ~spl41_24 | ~spl41_48 | ~spl41_162),
% 11.34/2.00 inference(avatar_split_clause,[],[f4045,f3921,f2510,f2360,f26021])).
% 11.34/2.00 thf(f26021,plain,(
% 11.34/2.00 spl41_420 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_420])])).
% 11.34/2.00 thf(f2360,plain,(
% 11.34/2.00 spl41_24 <=> (linord20386208strict(nat) = $true)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_24])])).
% 11.34/2.00 thf(f4045,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)))) ) | (~spl41_24 | ~spl41_48 | ~spl41_162)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4044])).
% 11.34/2.00 thf(f4044,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)))) ) | (~spl41_24 | ~spl41_48 | ~spl41_162)),
% 11.34/2.00 inference(forward_demodulation,[],[f4040,f2362])).
% 11.34/2.00 thf(f2362,plain,(
% 11.34/2.00 (linord20386208strict(nat) = $true) | ~spl41_24),
% 11.34/2.00 inference(avatar_component_clause,[],[f2360])).
% 11.34/2.00 thf(f4040,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1))) | (linord20386208strict(nat) != $true)) ) | (~spl41_48 | ~spl41_162)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4035])).
% 11.34/2.00 thf(f4035,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1))) | (linord20386208strict(nat) != $true)) ) | (~spl41_48 | ~spl41_162)),
% 11.34/2.00 inference(superposition,[],[f3922,f2511])).
% 11.34/2.00 thf(f26019,plain,(
% 11.34/2.00 spl41_419 | ~spl41_26 | ~spl41_118),
% 11.34/2.00 inference(avatar_split_clause,[],[f3285,f3275,f2369,f26017])).
% 11.34/2.00 thf(f26017,plain,(
% 11.34/2.00 spl41_419 <=> ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X0),X1)),X0)) | ($false = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_419])])).
% 11.34/2.00 thf(f3275,plain,(
% 11.34/2.00 spl41_118 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)),X1)) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_118])])).
% 11.34/2.00 thf(f3285,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X0),X1)),X0)) | ($false = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),X1))) ) | (~spl41_26 | ~spl41_118)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3284])).
% 11.34/2.00 thf(f3284,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X0),X1)),X0)) | ($false = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),X1))) ) | (~spl41_26 | ~spl41_118)),
% 11.34/2.00 inference(superposition,[],[f3276,f2370])).
% 11.34/2.00 thf(f3276,plain,(
% 11.34/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)),X1))) ) | ~spl41_118),
% 11.34/2.00 inference(avatar_component_clause,[],[f3275])).
% 11.34/2.00 thf(f26015,plain,(
% 11.34/2.00 spl41_418 | ~spl41_26 | ~spl41_117),
% 11.34/2.00 inference(avatar_split_clause,[],[f3282,f3269,f2369,f26013])).
% 11.34/2.00 thf(f26013,plain,(
% 11.34/2.00 spl41_418 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_418])])).
% 11.34/2.00 thf(f3269,plain,(
% 11.34/2.00 spl41_117 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0))) | (vAPP(nat,nat,suc,X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_117])])).
% 11.34/2.00 thf(f3282,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_117)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3281])).
% 11.34/2.00 thf(f3281,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,suc,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_117)),
% 11.34/2.00 inference(superposition,[],[f3270,f2370])).
% 11.34/2.00 thf(f3270,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (vAPP(nat,nat,suc,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)))) ) | ~spl41_117),
% 11.34/2.00 inference(avatar_component_clause,[],[f3269])).
% 11.34/2.00 thf(f25896,plain,(
% 11.34/2.00 spl41_417 | ~spl41_44 | ~spl41_45 | ~spl41_181),
% 11.34/2.00 inference(avatar_split_clause,[],[f4200,f4169,f2496,f2489,f25894])).
% 11.34/2.00 thf(f25894,plain,(
% 11.34/2.00 spl41_417 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,zero_zero(nat))))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_417])])).
% 11.34/2.00 thf(f2496,plain,(
% 11.34/2.00 spl41_45 <=> ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))) = X0)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_45])])).
% 11.34/2.00 thf(f4169,plain,(
% 11.34/2.00 spl41_181 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_181])])).
% 11.34/2.00 thf(f4200,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,zero_zero(nat)))))) ) | (~spl41_44 | ~spl41_45 | ~spl41_181)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4199])).
% 11.34/2.00 thf(f4199,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,zero_zero(nat)))))) ) | (~spl41_44 | ~spl41_45 | ~spl41_181)),
% 11.34/2.00 inference(forward_demodulation,[],[f4190,f2490])).
% 11.34/2.00 thf(f4190,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,zero_zero(nat))))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,suc,zero_zero(nat))))) ) | (~spl41_45 | ~spl41_181)),
% 11.34/2.00 inference(superposition,[],[f4170,f2497])).
% 11.34/2.00 thf(f2497,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))) = X0)) ) | ~spl41_45),
% 11.34/2.00 inference(avatar_component_clause,[],[f2496])).
% 11.34/2.00 thf(f4170,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) ) | ~spl41_181),
% 11.34/2.00 inference(avatar_component_clause,[],[f4169])).
% 11.34/2.00 thf(f25892,plain,(
% 11.34/2.00 spl41_416 | ~spl41_26 | ~spl41_116),
% 11.34/2.00 inference(avatar_split_clause,[],[f3259,f3246,f2369,f25890])).
% 11.34/2.00 thf(f25890,plain,(
% 11.34/2.00 spl41_416 <=> ! [X0 : $tType,X2 : X0 > nat,X1 : X0 > $o] : (($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),X1)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK38(X0),X2),X1))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_416])])).
% 11.34/2.00 thf(f3259,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0 > nat,X1 : X0 > $o] : (($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),X1)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK38(X0),X2),X1)))) ) | (~spl41_26 | ~spl41_116)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3258])).
% 11.34/2.00 thf(f3258,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0 > nat,X1 : X0 > $o] : (($true != $true) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X2),X1)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK38(X0),X2),X1)))) ) | (~spl41_26 | ~spl41_116)),
% 11.34/2.00 inference(superposition,[],[f3247,f2370])).
% 11.34/2.00 thf(f25888,plain,(
% 11.34/2.00 spl41_415),
% 11.34/2.00 inference(avatar_split_clause,[],[f1616,f25886])).
% 11.34/2.00 thf(f25886,plain,(
% 11.34/2.00 spl41_415 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_415])])).
% 11.34/2.00 thf(f1616,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1613])).
% 11.34/2.00 thf(f1613,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1415])).
% 11.34/2.00 thf(f1415,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.34/2.00 inference(cnf_transformation,[],[f1059])).
% 11.34/2.00 thf(f1059,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.34/2.00 inference(ennf_transformation,[],[f678])).
% 11.34/2.00 thf(f678,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))))),
% 11.34/2.00 inference(fool_elimination,[],[f677])).
% 11.34/2.00 thf(f677,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))),
% 11.34/2.00 inference(rectify,[],[f172])).
% 11.34/2.00 thf(f172,axiom,(
% 11.34/2.00 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X3) => ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X2),X3)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_div__eq__0__conv_H)).
% 11.34/2.00 thf(f25165,plain,(
% 11.34/2.00 ~spl41_315 | ~spl41_373),
% 11.34/2.00 inference(avatar_contradiction_clause,[],[f25164])).
% 11.34/2.00 thf(f25164,plain,(
% 11.34/2.00 $false | (~spl41_315 | ~spl41_373)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f25163])).
% 11.34/2.00 thf(f25163,plain,(
% 11.34/2.00 ($true = $false) | (~spl41_315 | ~spl41_373)),
% 11.34/2.00 inference(duplicate_literal_removal,[],[f25133])).
% 11.34/2.00 thf(f25133,plain,(
% 11.34/2.00 ($true = $false) | ($true = $false) | (~spl41_315 | ~spl41_373)),
% 11.34/2.00 inference(superposition,[],[f21663,f15671])).
% 11.34/2.00 thf(f15671,plain,(
% 11.34/2.00 ($false = vAPP($o,$o,sK9($o),$true)) | ~spl41_315),
% 11.34/2.00 inference(avatar_component_clause,[],[f15669])).
% 11.34/2.00 thf(f15669,plain,(
% 11.34/2.00 spl41_315 <=> ($false = vAPP($o,$o,sK9($o),$true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_315])])).
% 11.34/2.00 thf(f21663,plain,(
% 11.34/2.00 ( ! [X0 : $o] : (($true = vAPP($o,$o,sK9($o),X0)) | ($false = X0)) ) | ~spl41_373),
% 11.34/2.00 inference(avatar_component_clause,[],[f21662])).
% 11.34/2.00 thf(f21662,plain,(
% 11.34/2.00 spl41_373 <=> ! [X0 : $o] : (($true = vAPP($o,$o,sK9($o),X0)) | ($false = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_373])])).
% 11.34/2.00 thf(f25161,plain,(
% 11.34/2.00 ~spl41_315 | ~spl41_373),
% 11.34/2.00 inference(avatar_contradiction_clause,[],[f25160])).
% 11.34/2.00 thf(f25160,plain,(
% 11.34/2.00 $false | (~spl41_315 | ~spl41_373)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f25159])).
% 11.34/2.00 thf(f25159,plain,(
% 11.34/2.00 ($true = $false) | (~spl41_315 | ~spl41_373)),
% 11.34/2.00 inference(duplicate_literal_removal,[],[f25135])).
% 11.34/2.00 thf(f25135,plain,(
% 11.34/2.00 ($true = $false) | ($true = $false) | (~spl41_315 | ~spl41_373)),
% 11.34/2.00 inference(superposition,[],[f15671,f21663])).
% 11.34/2.00 thf(f25069,plain,(
% 11.34/2.00 spl41_274 | spl41_414 | ~spl41_132),
% 11.34/2.00 inference(avatar_split_clause,[],[f3409,f3357,f25067,f8769])).
% 11.34/2.00 thf(f25067,plain,(
% 11.34/2.00 spl41_414 <=> ! [X0 : $o > nat] : (($true = vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),vNOT),X0)) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_414])])).
% 11.34/2.00 thf(f3409,plain,(
% 11.34/2.00 ( ! [X0 : $o > nat,X1 : $o] : (($true = vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),vNOT),X0)) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT)) | ($false = X1)) ) | ~spl41_132),
% 11.34/2.00 inference(not_proxy_clausification,[],[f3408])).
% 11.34/2.00 thf(f3408,plain,(
% 11.34/2.00 ( ! [X0 : $o > nat,X1 : $o] : (($true = vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),vNOT),X0)) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT)) | ($true = vAPP($o,$o,vNOT,X1))) ) | ~spl41_132),
% 11.34/2.00 inference(not_proxy_clausification,[],[f3402])).
% 11.34/2.00 thf(f3402,plain,(
% 11.34/2.00 ( ! [X0 : $o > nat,X1 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,nat),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,nat),$o),sK39($o),vNOT),X0))) | ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT)) | ($true = vAPP($o,$o,vNOT,X1))) ) | ~spl41_132),
% 11.34/2.00 inference(primitive_instantiation,[],[f3358])).
% 11.34/2.00 thf(f25065,plain,(
% 11.34/2.00 spl41_413 | ~spl41_26 | ~spl41_115),
% 11.34/2.00 inference(avatar_split_clause,[],[f3244,f3235,f2369,f25063])).
% 11.34/2.00 thf(f25063,plain,(
% 11.34/2.00 spl41_413 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2))) | (field(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_413])])).
% 11.34/2.00 thf(f3235,plain,(
% 11.34/2.00 spl41_115 <=> ! [X0 : $tType,X2 : X0,X3 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X3))) | (field(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_115])])).
% 11.34/2.00 thf(f3244,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_115)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3243])).
% 11.34/2.00 thf(f3243,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2))) | (field(X0) = $false)) ) | (~spl41_26 | ~spl41_115)),
% 11.34/2.00 inference(superposition,[],[f3236,f2370])).
% 11.34/2.00 thf(f3236,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0] : ((field(X0) != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X3)))) ) | ~spl41_115),
% 11.34/2.00 inference(avatar_component_clause,[],[f3235])).
% 11.34/2.00 thf(f25061,plain,(
% 11.34/2.00 spl41_412 | ~spl41_26 | ~spl41_114),
% 11.34/2.00 inference(avatar_split_clause,[],[f3240,f3231,f2369,f25059])).
% 11.34/2.00 thf(f25059,plain,(
% 11.34/2.00 spl41_412 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2))) | (euclid191655569cancel(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_412])])).
% 11.34/2.00 thf(f3231,plain,(
% 11.34/2.00 spl41_114 <=> ! [X0 : $tType,X2 : X0,X3 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X3))) | (euclid191655569cancel(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_114])])).
% 11.34/2.00 thf(f3240,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2))) | (euclid191655569cancel(X0) = $false)) ) | (~spl41_26 | ~spl41_114)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3239])).
% 11.34/2.00 thf(f3239,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2))) | (euclid191655569cancel(X0) = $false)) ) | (~spl41_26 | ~spl41_114)),
% 11.34/2.00 inference(superposition,[],[f3232,f2370])).
% 11.34/2.00 thf(f3232,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0] : ((euclid191655569cancel(X0) != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X3)))) ) | ~spl41_114),
% 11.34/2.00 inference(avatar_component_clause,[],[f3231])).
% 11.34/2.00 thf(f25057,plain,(
% 11.34/2.00 spl41_411 | ~spl41_35 | ~spl41_92),
% 11.34/2.00 inference(avatar_split_clause,[],[f2991,f2980,f2444,f25055])).
% 11.34/2.00 thf(f25055,plain,(
% 11.34/2.00 spl41_411 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | (vAPP(nat,nat,sK5,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK5,X0))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_411])])).
% 11.34/2.00 thf(f2980,plain,(
% 11.34/2.00 spl41_92 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_92])])).
% 11.34/2.00 thf(f2991,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | (vAPP(nat,nat,sK5,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK5,X0))) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_92)),
% 11.34/2.00 inference(superposition,[],[f2981,f2445])).
% 11.34/2.00 thf(f2981,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | (X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl41_92),
% 11.34/2.00 inference(avatar_component_clause,[],[f2980])).
% 11.34/2.00 thf(f25053,plain,(
% 11.34/2.00 spl41_410 | ~spl41_34 | ~spl41_92),
% 11.34/2.00 inference(avatar_split_clause,[],[f2990,f2980,f2440,f25051])).
% 11.34/2.00 thf(f25051,plain,(
% 11.34/2.00 spl41_410 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | (vAPP(nat,nat,sK4,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK4,X0))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_410])])).
% 11.34/2.00 thf(f2990,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | (vAPP(nat,nat,sK4,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK4,X0))) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_92)),
% 11.34/2.00 inference(superposition,[],[f2981,f2441])).
% 11.34/2.00 thf(f25049,plain,(
% 11.34/2.00 spl41_409 | ~spl41_33 | ~spl41_92),
% 11.34/2.00 inference(avatar_split_clause,[],[f2989,f2980,f2436,f25047])).
% 11.34/2.00 thf(f25047,plain,(
% 11.34/2.00 spl41_409 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | (vAPP(nat,nat,sK3,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK3,X0))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_409])])).
% 11.34/2.00 thf(f2989,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | (vAPP(nat,nat,sK3,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK3,X0))) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_92)),
% 11.34/2.00 inference(superposition,[],[f2981,f2437])).
% 11.34/2.00 thf(f25045,plain,(
% 11.34/2.00 spl41_408),
% 11.34/2.00 inference(avatar_split_clause,[],[f1533,f25043])).
% 11.34/2.00 thf(f25043,plain,(
% 11.34/2.00 spl41_408 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (X1 = X2))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_408])])).
% 11.34/2.00 thf(f1533,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (X1 = X2)) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1532])).
% 11.34/2.00 thf(f1532,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1531])).
% 11.34/2.00 thf(f1531,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1466])).
% 11.34/2.00 thf(f1466,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.34/2.00 inference(cnf_transformation,[],[f1092])).
% 11.34/2.00 thf(f1092,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.34/2.00 inference(ennf_transformation,[],[f738])).
% 11.34/2.00 thf(f738,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)))),
% 11.34/2.00 inference(fool_elimination,[],[f737])).
% 11.34/2.00 thf(f737,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) = (X1 = X2)))),
% 11.34/2.00 inference(rectify,[],[f92])).
% 11.34/2.00 thf(f92,axiom,(
% 11.34/2.00 ! [X4 : nat,X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X4) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X2)) = (X2 = X3)))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_nat__mult__eq__cancel1)).
% 11.34/2.00 thf(f25021,plain,(
% 11.34/2.00 spl41_407),
% 11.34/2.00 inference(avatar_split_clause,[],[f1529,f25019])).
% 11.34/2.00 thf(f25019,plain,(
% 11.34/2.00 spl41_407 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((X1 = X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_407])])).
% 11.34/2.00 thf(f1529,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((X1 = X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1528])).
% 11.34/2.00 thf(f1528,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((X1 = X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1524])).
% 11.34/2.00 thf(f1524,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1467])).
% 11.34/2.00 thf(f1467,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.34/2.00 inference(cnf_transformation,[],[f1093])).
% 11.34/2.00 thf(f1093,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.34/2.00 inference(ennf_transformation,[],[f740])).
% 11.34/2.00 thf(f740,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))))),
% 11.34/2.00 inference(fool_elimination,[],[f739])).
% 11.34/2.00 thf(f739,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)) = (X1 = X2)))),
% 11.34/2.00 inference(rectify,[],[f189])).
% 11.34/2.00 thf(f189,axiom,(
% 11.34/2.00 ! [X4 : nat,X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X4) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),X4) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X4)) = (X2 = X3)))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_mult__cancel2__gr0)).
% 11.34/2.00 thf(f24528,plain,(
% 11.34/2.00 spl41_406 | ~spl41_48 | ~spl41_117),
% 11.34/2.00 inference(avatar_split_clause,[],[f3283,f3269,f2510,f24526])).
% 11.34/2.00 thf(f24526,plain,(
% 11.34/2.00 spl41_406 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,suc,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,vAPP(nat,nat,suc,X0)),zero_zero(nat)))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_406])])).
% 11.34/2.00 thf(f3283,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,suc,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,vAPP(nat,nat,suc,X0)),zero_zero(nat))))) ) | (~spl41_48 | ~spl41_117)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3279])).
% 11.34/2.00 thf(f3279,plain,(
% 11.34/2.00 ( ! [X0 : nat] : (($true != $true) | (vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,suc,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,vAPP(nat,nat,suc,X0)),zero_zero(nat))))) ) | (~spl41_48 | ~spl41_117)),
% 11.34/2.00 inference(superposition,[],[f3270,f2511])).
% 11.34/2.00 thf(f24524,plain,(
% 11.34/2.00 spl41_405 | ~spl41_26 | ~spl41_113),
% 11.34/2.00 inference(avatar_split_clause,[],[f3229,f3211,f2369,f24522])).
% 11.34/2.00 thf(f24522,plain,(
% 11.34/2.00 spl41_405 <=> ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X0),X1)))) | ($false = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_405])])).
% 11.34/2.00 thf(f3211,plain,(
% 11.34/2.00 spl41_113 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)))) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_113])])).
% 11.34/2.00 thf(f3229,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X0),X1)))) | ($false = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),X1))) ) | (~spl41_26 | ~spl41_113)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3228])).
% 11.34/2.00 thf(f3228,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X0),X1)))) | ($false = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),X1))) ) | (~spl41_26 | ~spl41_113)),
% 11.34/2.00 inference(superposition,[],[f3212,f2370])).
% 11.34/2.00 thf(f3212,plain,(
% 11.34/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0))))) ) | ~spl41_113),
% 11.34/2.00 inference(avatar_component_clause,[],[f3211])).
% 11.34/2.00 thf(f24520,plain,(
% 11.34/2.00 spl41_404 | ~spl41_26 | ~spl41_112),
% 11.34/2.00 inference(avatar_split_clause,[],[f3226,f3207,f2369,f24518])).
% 11.34/2.00 thf(f24518,plain,(
% 11.34/2.00 spl41_404 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_404])])).
% 11.34/2.00 thf(f3226,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) ) | (~spl41_26 | ~spl41_112)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3225])).
% 11.34/2.00 thf(f3225,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) ) | (~spl41_26 | ~spl41_112)),
% 11.34/2.00 inference(superposition,[],[f3208,f2370])).
% 11.34/2.00 thf(f24516,plain,(
% 11.34/2.00 spl41_403 | ~spl41_26 | ~spl41_111),
% 11.34/2.00 inference(avatar_split_clause,[],[f3219,f3203,f2369,f24514])).
% 11.34/2.00 thf(f24514,plain,(
% 11.34/2.00 spl41_403 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($true != vAPP(nat,$o,X1,zero_zero(nat))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK20,X1))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_403])])).
% 11.34/2.00 thf(f3203,plain,(
% 11.34/2.00 spl41_111 <=> ! [X0 : nat > $o,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_111])])).
% 11.34/2.00 thf(f3219,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($true != vAPP(nat,$o,X1,zero_zero(nat))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK20,X1)))) ) | (~spl41_26 | ~spl41_111)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3218])).
% 11.34/2.00 thf(f3218,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($true != vAPP(nat,$o,X1,zero_zero(nat))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK20,X1)))) ) | (~spl41_26 | ~spl41_111)),
% 11.34/2.00 inference(superposition,[],[f3204,f2370])).
% 11.34/2.00 thf(f3204,plain,(
% 11.34/2.00 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true = vAPP(nat,$o,X0,X3)) | ($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) ) | ~spl41_111),
% 11.34/2.00 inference(avatar_component_clause,[],[f3203])).
% 11.34/2.00 thf(f24356,plain,(
% 11.34/2.00 spl41_402 | ~spl41_22 | ~spl41_38 | ~spl41_158),
% 11.34/2.00 inference(avatar_split_clause,[],[f4012,f3905,f2456,f2350,f24354])).
% 11.34/2.00 thf(f24354,plain,(
% 11.34/2.00 spl41_402 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_402])])).
% 11.34/2.00 thf(f2350,plain,(
% 11.34/2.00 spl41_22 <=> (ordered_semiring_0(nat) = $true)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_22])])).
% 11.34/2.00 thf(f4012,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat)))) ) | (~spl41_22 | ~spl41_38 | ~spl41_158)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4011])).
% 11.34/2.00 thf(f4011,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat)))) ) | (~spl41_22 | ~spl41_38 | ~spl41_158)),
% 11.34/2.00 inference(forward_demodulation,[],[f4010,f2352])).
% 11.34/2.00 thf(f2352,plain,(
% 11.34/2.00 (ordered_semiring_0(nat) = $true) | ~spl41_22),
% 11.34/2.00 inference(avatar_component_clause,[],[f2350])).
% 11.34/2.00 thf(f4010,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | (ordered_semiring_0(nat) != $true)) ) | (~spl41_38 | ~spl41_158)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4005])).
% 11.34/2.00 thf(f4005,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | (ordered_semiring_0(nat) != $true)) ) | (~spl41_38 | ~spl41_158)),
% 11.34/2.00 inference(superposition,[],[f3906,f2457])).
% 11.34/2.00 thf(f24352,plain,(
% 11.34/2.00 spl41_401 | ~spl41_22 | ~spl41_38 | ~spl41_156),
% 11.34/2.00 inference(avatar_split_clause,[],[f4003,f3897,f2456,f2350,f24350])).
% 11.34/2.00 thf(f24350,plain,(
% 11.34/2.00 spl41_401 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),zero_zero(nat))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_401])])).
% 11.34/2.00 thf(f4003,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),zero_zero(nat)))) ) | (~spl41_22 | ~spl41_38 | ~spl41_156)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f4002])).
% 11.34/2.00 thf(f4002,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),zero_zero(nat)))) ) | (~spl41_22 | ~spl41_38 | ~spl41_156)),
% 11.34/2.00 inference(forward_demodulation,[],[f4001,f2352])).
% 11.34/2.00 thf(f4001,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),zero_zero(nat))) | (ordered_semiring_0(nat) != $true)) ) | (~spl41_38 | ~spl41_156)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3996])).
% 11.34/2.00 thf(f3996,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),zero_zero(nat))) | (ordered_semiring_0(nat) != $true)) ) | (~spl41_38 | ~spl41_156)),
% 11.34/2.00 inference(superposition,[],[f3898,f2457])).
% 11.34/2.00 thf(f24348,plain,(
% 11.34/2.00 spl41_400 | ~spl41_45 | ~spl41_120),
% 11.34/2.00 inference(avatar_split_clause,[],[f3304,f3298,f2496,f24346])).
% 11.34/2.00 thf(f24346,plain,(
% 11.34/2.00 spl41_400 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,zero_zero(nat)))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_400])])).
% 11.34/2.00 thf(f3304,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,zero_zero(nat)))))) ) | (~spl41_45 | ~spl41_120)),
% 11.34/2.00 inference(superposition,[],[f3299,f2497])).
% 11.34/2.00 thf(f24344,plain,(
% 11.34/2.00 spl41_399 | ~spl41_45 | ~spl41_120),
% 11.34/2.00 inference(avatar_split_clause,[],[f3303,f3298,f2496,f24342])).
% 11.34/2.00 thf(f24342,plain,(
% 11.34/2.00 spl41_399 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_399])])).
% 11.34/2.00 thf(f3303,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)))) ) | (~spl41_45 | ~spl41_120)),
% 11.34/2.00 inference(superposition,[],[f3299,f2497])).
% 11.34/2.00 thf(f24340,plain,(
% 11.34/2.00 spl41_398 | ~spl41_26 | ~spl41_110),
% 11.34/2.00 inference(avatar_split_clause,[],[f3201,f3195,f2369,f24338])).
% 11.34/2.00 thf(f24338,plain,(
% 11.34/2.00 spl41_398 <=> ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_398])])).
% 11.34/2.00 thf(f3195,plain,(
% 11.34/2.00 spl41_110 <=> ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_110])])).
% 11.34/2.00 thf(f3201,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) ) | (~spl41_26 | ~spl41_110)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3200])).
% 11.34/2.00 thf(f3200,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) ) | (~spl41_26 | ~spl41_110)),
% 11.34/2.00 inference(superposition,[],[f3196,f2370])).
% 11.34/2.00 thf(f3196,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)))) ) | ~spl41_110),
% 11.34/2.00 inference(avatar_component_clause,[],[f3195])).
% 11.34/2.00 thf(f24336,plain,(
% 11.34/2.00 spl41_397 | ~spl41_26 | ~spl41_109),
% 11.34/2.00 inference(avatar_split_clause,[],[f3199,f3191,f2369,f24334])).
% 11.34/2.00 thf(f24334,plain,(
% 11.34/2.00 spl41_397 <=> ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_397])])).
% 11.34/2.00 thf(f3191,plain,(
% 11.34/2.00 spl41_109 <=> ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_109])])).
% 11.34/2.00 thf(f3199,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) ) | (~spl41_26 | ~spl41_109)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3198])).
% 11.34/2.00 thf(f3198,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) ) | (~spl41_26 | ~spl41_109)),
% 11.34/2.00 inference(superposition,[],[f3192,f2370])).
% 11.34/2.00 thf(f3192,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)))) ) | ~spl41_109),
% 11.34/2.00 inference(avatar_component_clause,[],[f3191])).
% 11.34/2.00 thf(f24315,plain,(
% 11.34/2.00 spl41_396 | ~spl41_26 | spl41_315),
% 11.34/2.00 inference(avatar_split_clause,[],[f21010,f15669,f2369,f24313])).
% 11.34/2.00 thf(f24313,plain,(
% 11.34/2.00 spl41_396 <=> ! [X0 : $o] : (($false != vAPP($o,$o,sK9($o),X0)) | ($false = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_396])])).
% 11.34/2.00 thf(f21010,plain,(
% 11.34/2.00 ( ! [X0 : $o] : (($false != vAPP($o,$o,sK9($o),X0)) | ($false = X0)) ) | (~spl41_26 | spl41_315)),
% 11.34/2.00 inference(superposition,[],[f15670,f2370])).
% 11.34/2.00 thf(f15670,plain,(
% 11.34/2.00 ($false != vAPP($o,$o,sK9($o),$true)) | spl41_315),
% 11.34/2.00 inference(avatar_component_clause,[],[f15669])).
% 11.34/2.00 thf(f23658,plain,(
% 11.34/2.00 spl41_395 | ~spl41_116),
% 11.34/2.00 inference(avatar_split_clause,[],[f3261,f3246,f23656])).
% 11.34/2.00 thf(f23656,plain,(
% 11.34/2.00 spl41_395 <=> ! [X0 : $o > nat] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK38($o),X0),vNOT)) | ($true != vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_395])])).
% 11.34/2.00 thf(f3261,plain,(
% 11.34/2.00 ( ! [X0 : $o > nat] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK38($o),X0),vNOT)) | ($true != vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT))) ) | ~spl41_116),
% 11.34/2.00 inference(not_proxy_clausification,[],[f3255])).
% 11.34/2.00 thf(f3255,plain,(
% 11.34/2.00 ( ! [X0 : $o > nat] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK38($o),X0),vNOT))) | ($true != vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sP2($o),X0),vNOT))) ) | ~spl41_116),
% 11.34/2.00 inference(primitive_instantiation,[],[f3247])).
% 11.34/2.00 thf(f23647,plain,(
% 11.34/2.00 spl41_394 | ~spl41_26 | ~spl41_107),
% 11.34/2.00 inference(avatar_split_clause,[],[f3188,f3163,f2369,f23645])).
% 11.34/2.00 thf(f23645,plain,(
% 11.34/2.00 spl41_394 <=> ! [X0 : nat > nat > $o] : (($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_394])])).
% 11.34/2.00 thf(f3163,plain,(
% 11.34/2.00 spl41_107 <=> ! [X0 : nat > nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_107])])).
% 11.34/2.00 thf(f3188,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)))) ) | (~spl41_26 | ~spl41_107)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3187])).
% 11.34/2.00 thf(f3187,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != $true) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)))) ) | (~spl41_26 | ~spl41_107)),
% 11.34/2.00 inference(superposition,[],[f3164,f2370])).
% 11.34/2.00 thf(f3164,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) ) | ~spl41_107),
% 11.34/2.00 inference(avatar_component_clause,[],[f3163])).
% 11.34/2.00 thf(f23643,plain,(
% 11.34/2.00 spl41_393 | ~spl41_26 | ~spl41_106),
% 11.34/2.00 inference(avatar_split_clause,[],[f3185,f3159,f2369,f23641])).
% 11.34/2.00 thf(f23641,plain,(
% 11.34/2.00 spl41_393 <=> ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_393])])).
% 11.34/2.00 thf(f3159,plain,(
% 11.34/2.00 spl41_106 <=> ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_106])])).
% 11.34/2.00 thf(f3185,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) ) | (~spl41_26 | ~spl41_106)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3184])).
% 11.34/2.00 thf(f3184,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) ) | (~spl41_26 | ~spl41_106)),
% 11.34/2.00 inference(superposition,[],[f3160,f2370])).
% 11.34/2.00 thf(f3160,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)))) ) | ~spl41_106),
% 11.34/2.00 inference(avatar_component_clause,[],[f3159])).
% 11.34/2.00 thf(f23639,plain,(
% 11.34/2.00 spl41_392 | ~spl41_26 | ~spl41_105),
% 11.34/2.00 inference(avatar_split_clause,[],[f3183,f3155,f2369,f23637])).
% 11.34/2.00 thf(f23637,plain,(
% 11.34/2.00 spl41_392 <=> ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_392])])).
% 11.34/2.00 thf(f3155,plain,(
% 11.34/2.00 spl41_105 <=> ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_105])])).
% 11.34/2.00 thf(f3183,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) ) | (~spl41_26 | ~spl41_105)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3182])).
% 11.34/2.00 thf(f3182,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) ) | (~spl41_26 | ~spl41_105)),
% 11.34/2.00 inference(superposition,[],[f3156,f2370])).
% 11.34/2.00 thf(f3156,plain,(
% 11.34/2.00 ( ! [X0 : nat > nat > $o] : (($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)))) ) | ~spl41_105),
% 11.34/2.00 inference(avatar_component_clause,[],[f3155])).
% 11.34/2.00 thf(f23635,plain,(
% 11.34/2.00 spl41_391 | ~spl41_35 | ~spl41_98),
% 11.34/2.00 inference(avatar_split_clause,[],[f3105,f3023,f2444,f23633])).
% 11.34/2.00 thf(f23633,plain,(
% 11.34/2.00 spl41_391 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X1)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK5,X0))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_391])])).
% 11.34/2.00 thf(f3023,plain,(
% 11.34/2.00 spl41_98 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_98])])).
% 11.34/2.00 thf(f3105,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X1)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK5,X0))) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_98)),
% 11.34/2.00 inference(superposition,[],[f3024,f2445])).
% 11.34/2.00 thf(f3024,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl41_98),
% 11.34/2.00 inference(avatar_component_clause,[],[f3023])).
% 11.34/2.00 thf(f23631,plain,(
% 11.34/2.00 spl41_390 | ~spl41_34 | ~spl41_98),
% 11.34/2.00 inference(avatar_split_clause,[],[f3104,f3023,f2440,f23629])).
% 11.34/2.00 thf(f23629,plain,(
% 11.34/2.00 spl41_390 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X1)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK4,X0))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_390])])).
% 11.34/2.00 thf(f3104,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X1)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK4,X0))) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_98)),
% 11.34/2.00 inference(superposition,[],[f3024,f2441])).
% 11.34/2.00 thf(f23627,plain,(
% 11.34/2.00 spl41_389 | ~spl41_33 | ~spl41_98),
% 11.34/2.00 inference(avatar_split_clause,[],[f3103,f3023,f2436,f23625])).
% 11.34/2.00 thf(f23625,plain,(
% 11.34/2.00 spl41_389 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X1)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK3,X0))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_389])])).
% 11.34/2.00 thf(f3103,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X1)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,sK3,X0))) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_98)),
% 11.34/2.00 inference(superposition,[],[f3024,f2437])).
% 11.34/2.00 thf(f23623,plain,(
% 11.34/2.00 spl41_388 | ~spl41_35 | ~spl41_98),
% 11.34/2.00 inference(avatar_split_clause,[],[f3102,f3023,f2444,f23621])).
% 11.34/2.00 thf(f23621,plain,(
% 11.34/2.00 spl41_388 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK5,X0)),X1)) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_388])])).
% 11.34/2.00 thf(f3102,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK5,X0)),X1)) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_98)),
% 11.34/2.00 inference(superposition,[],[f3024,f2445])).
% 11.34/2.00 thf(f23619,plain,(
% 11.34/2.00 spl41_387 | ~spl41_34 | ~spl41_98),
% 11.34/2.00 inference(avatar_split_clause,[],[f3101,f3023,f2440,f23617])).
% 11.34/2.00 thf(f23617,plain,(
% 11.34/2.00 spl41_387 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK4,X0)),X1)) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_387])])).
% 11.34/2.00 thf(f3101,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK4,X0)),X1)) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_98)),
% 11.34/2.00 inference(superposition,[],[f3024,f2441])).
% 11.34/2.00 thf(f23615,plain,(
% 11.34/2.00 spl41_386 | ~spl41_33 | ~spl41_98),
% 11.34/2.00 inference(avatar_split_clause,[],[f3100,f3023,f2436,f23613])).
% 11.34/2.00 thf(f23613,plain,(
% 11.34/2.00 spl41_386 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK3,X0)),X1)) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_386])])).
% 11.34/2.00 thf(f3100,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK3,X0)),X1)) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_98)),
% 11.34/2.00 inference(superposition,[],[f3024,f2437])).
% 11.34/2.00 thf(f22843,plain,(
% 11.34/2.00 spl41_385 | ~spl41_26 | ~spl41_102),
% 11.34/2.00 inference(avatar_split_clause,[],[f3144,f3137,f2369,f22841])).
% 11.34/2.00 thf(f22841,plain,(
% 11.34/2.00 spl41_385 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_385])])).
% 11.34/2.00 thf(f3137,plain,(
% 11.34/2.00 spl41_102 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_102])])).
% 11.34/2.00 thf(f3144,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_102)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3143])).
% 11.34/2.00 thf(f3143,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,suc,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_102)),
% 11.34/2.00 inference(superposition,[],[f3138,f2370])).
% 11.34/2.00 thf(f3138,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (vAPP(nat,nat,suc,X0) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) ) | ~spl41_102),
% 11.34/2.00 inference(avatar_component_clause,[],[f3137])).
% 11.34/2.00 thf(f22839,plain,(
% 11.34/2.00 spl41_384 | ~spl41_26 | ~spl41_95),
% 11.34/2.00 inference(avatar_split_clause,[],[f3062,f3009,f2369,f22837])).
% 11.34/2.00 thf(f22837,plain,(
% 11.34/2.00 spl41_384 <=> ! [X0 : $tType,X3 : $o,X2 : $o > X0,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X3)) | ($true != wellorder(X0)) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK16(X0,$o),X1),X2)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_384])])).
% 11.34/2.00 thf(f3062,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $o > X0,X3 : $o,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X3)) | ($true != wellorder(X0)) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK16(X0,$o),X1),X2))) ) | (~spl41_26 | ~spl41_95)),
% 11.34/2.00 inference(superposition,[],[f3010,f2370])).
% 11.34/2.00 thf(f22835,plain,(
% 11.34/2.00 spl41_383 | ~spl41_26 | ~spl41_94),
% 11.34/2.00 inference(avatar_split_clause,[],[f3034,f3005,f2369,f22833])).
% 11.34/2.00 thf(f22833,plain,(
% 11.34/2.00 spl41_383 <=> ! [X0 : $tType,X3 : $o,X2 : $o > X0,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X3)) | ($true != wellorder(X0)) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK15(X0,$o),X1),X2)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_383])])).
% 11.34/2.00 thf(f3034,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $o > X0,X3 : $o,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X3)) | ($true != wellorder(X0)) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK15(X0,$o),X1),X2))) ) | (~spl41_26 | ~spl41_94)),
% 11.34/2.00 inference(superposition,[],[f3006,f2370])).
% 11.34/2.00 thf(f22830,plain,(
% 11.34/2.00 ~spl41_277 | ~spl41_315),
% 11.34/2.00 inference(avatar_contradiction_clause,[],[f22829])).
% 11.34/2.00 thf(f22829,plain,(
% 11.34/2.00 $false | (~spl41_277 | ~spl41_315)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f22828])).
% 11.34/2.00 thf(f22828,plain,(
% 11.34/2.00 ($true = $false) | (~spl41_277 | ~spl41_315)),
% 11.34/2.00 inference(forward_demodulation,[],[f12781,f15671])).
% 11.34/2.00 thf(f12781,plain,(
% 11.34/2.00 ($true = vAPP($o,$o,sK9($o),$true)) | ~spl41_277),
% 11.34/2.00 inference(avatar_component_clause,[],[f12780])).
% 11.34/2.00 thf(f12780,plain,(
% 11.34/2.00 spl41_277 <=> ($true = vAPP($o,$o,sK9($o),$true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_277])])).
% 11.34/2.00 thf(f22807,plain,(
% 11.34/2.00 spl41_382 | ~spl41_26 | spl41_277),
% 11.34/2.00 inference(avatar_split_clause,[],[f21669,f12780,f2369,f22805])).
% 11.34/2.00 thf(f22805,plain,(
% 11.34/2.00 spl41_382 <=> ! [X0 : $o] : (($false = vAPP($o,$o,sK9($o),X0)) | ($false = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_382])])).
% 11.34/2.00 thf(f21669,plain,(
% 11.34/2.00 ( ! [X0 : $o] : (($false = vAPP($o,$o,sK9($o),X0)) | ($false = X0)) ) | (~spl41_26 | spl41_277)),
% 11.34/2.00 inference(duplicate_literal_removal,[],[f13712])).
% 11.34/2.00 thf(f13712,plain,(
% 11.34/2.00 ( ! [X0 : $o] : (($false = vAPP($o,$o,sK9($o),X0)) | ($false = X0) | ($false = X0)) ) | (~spl41_26 | spl41_277)),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f13707])).
% 11.34/2.00 thf(f13707,plain,(
% 11.34/2.00 ( ! [X0 : $o] : ((vAPP($o,$o,sK9($o),X0) != X0) | ($false = X0)) ) | (~spl41_26 | spl41_277)),
% 11.34/2.00 inference(superposition,[],[f12782,f2370])).
% 11.34/2.00 thf(f12782,plain,(
% 11.34/2.00 ($true != vAPP($o,$o,sK9($o),$true)) | spl41_277),
% 11.34/2.00 inference(avatar_component_clause,[],[f12780])).
% 11.34/2.00 thf(f22803,plain,(
% 11.34/2.00 spl41_381 | ~spl41_35 | ~spl41_93),
% 11.34/2.00 inference(avatar_split_clause,[],[f2999,f2984,f2444,f22801])).
% 11.34/2.00 thf(f22801,plain,(
% 11.34/2.00 spl41_381 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK5,X0))) = X1) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_381])])).
% 11.34/2.00 thf(f2984,plain,(
% 11.34/2.00 spl41_93 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_93])])).
% 11.34/2.00 thf(f2999,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK5,X0))) = X1) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_93)),
% 11.34/2.00 inference(superposition,[],[f2985,f2445])).
% 11.34/2.00 thf(f2985,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X1)) ) | ~spl41_93),
% 11.34/2.00 inference(avatar_component_clause,[],[f2984])).
% 11.34/2.00 thf(f22799,plain,(
% 11.34/2.00 spl41_380 | ~spl41_34 | ~spl41_93),
% 11.34/2.00 inference(avatar_split_clause,[],[f2998,f2984,f2440,f22797])).
% 11.34/2.00 thf(f22797,plain,(
% 11.34/2.00 spl41_380 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK4,X0))) = X1) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_380])])).
% 11.34/2.00 thf(f2998,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK4,X0))) = X1) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_93)),
% 11.34/2.00 inference(superposition,[],[f2985,f2441])).
% 11.34/2.00 thf(f22795,plain,(
% 11.34/2.00 spl41_379 | ~spl41_33 | ~spl41_93),
% 11.34/2.00 inference(avatar_split_clause,[],[f2997,f2984,f2436,f22793])).
% 11.34/2.00 thf(f22793,plain,(
% 11.34/2.00 spl41_379 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK3,X0))) = X1) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_379])])).
% 11.34/2.00 thf(f2997,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),vAPP(nat,nat,sK3,X0))) = X1) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_93)),
% 11.34/2.00 inference(superposition,[],[f2985,f2437])).
% 11.34/2.00 thf(f22791,plain,(
% 11.34/2.00 spl41_378 | ~spl41_59),
% 11.34/2.00 inference(avatar_split_clause,[],[f2617,f2566,f22789])).
% 11.34/2.00 thf(f22789,plain,(
% 11.34/2.00 spl41_378 <=> ! [X0 : nat] : (vAPP(sTfun(nat,$o),nat,sK14,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_378])])).
% 11.34/2.00 thf(f2566,plain,(
% 11.34/2.00 spl41_59 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_59])])).
% 11.34/2.00 thf(f2617,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(sTfun(nat,$o),nat,sK14,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl41_59),
% 11.34/2.00 inference(leibniz_equality_elimination,[],[f2567])).
% 11.34/2.00 thf(f2567,plain,(
% 11.34/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0))) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl41_59),
% 11.34/2.00 inference(avatar_component_clause,[],[f2566])).
% 11.34/2.00 thf(f22787,plain,(
% 11.34/2.00 spl41_377 | ~spl41_58),
% 11.34/2.00 inference(avatar_split_clause,[],[f2607,f2562,f22785])).
% 11.34/2.00 thf(f22785,plain,(
% 11.34/2.00 spl41_377 <=> ! [X0 : nat] : (vAPP(sTfun(nat,$o),nat,sK13,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_377])])).
% 11.34/2.00 thf(f2562,plain,(
% 11.34/2.00 spl41_58 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_58])])).
% 11.34/2.00 thf(f2607,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(sTfun(nat,$o),nat,sK13,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl41_58),
% 11.34/2.00 inference(leibniz_equality_elimination,[],[f2563])).
% 11.34/2.00 thf(f2563,plain,(
% 11.34/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0))) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl41_58),
% 11.34/2.00 inference(avatar_component_clause,[],[f2562])).
% 11.34/2.00 thf(f22677,plain,(
% 11.34/2.00 spl41_376 | ~spl41_26 | ~spl41_100),
% 11.34/2.00 inference(avatar_split_clause,[],[f3133,f3115,f2369,f22675])).
% 11.34/2.00 thf(f22675,plain,(
% 11.34/2.00 spl41_376 <=> ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_376])])).
% 11.34/2.00 thf(f3133,plain,(
% 11.34/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)))) ) | (~spl41_26 | ~spl41_100)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3132])).
% 11.34/2.00 thf(f3132,plain,(
% 11.34/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)))) ) | (~spl41_26 | ~spl41_100)),
% 11.34/2.00 inference(superposition,[],[f3116,f2370])).
% 11.34/2.00 thf(f22673,plain,(
% 11.34/2.00 spl41_375 | ~spl41_48 | ~spl41_99),
% 11.34/2.00 inference(avatar_split_clause,[],[f3123,f3111,f2510,f22671])).
% 11.34/2.00 thf(f22671,plain,(
% 11.34/2.00 spl41_375 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,suc,X0)) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,vAPP(nat,nat,suc,X0)),zero_zero(nat)))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_375])])).
% 11.34/2.00 thf(f3111,plain,(
% 11.34/2.00 spl41_99 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1) | (vAPP(nat,nat,suc,X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_99])])).
% 11.34/2.00 thf(f3123,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,suc,X0)) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,vAPP(nat,nat,suc,X0)),zero_zero(nat))))) ) | (~spl41_48 | ~spl41_99)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3119])).
% 11.34/2.00 thf(f3119,plain,(
% 11.34/2.00 ( ! [X0 : nat] : (($true != $true) | (vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,suc,X0)) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,vAPP(nat,nat,suc,X0)),zero_zero(nat))))) ) | (~spl41_48 | ~spl41_99)),
% 11.34/2.00 inference(superposition,[],[f3112,f2511])).
% 11.34/2.00 thf(f3112,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (vAPP(nat,nat,suc,X0) = X1) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1)) ) | ~spl41_99),
% 11.34/2.00 inference(avatar_component_clause,[],[f3111])).
% 11.34/2.00 thf(f22643,plain,(
% 11.34/2.00 spl41_374 | ~spl41_26 | ~spl41_99),
% 11.34/2.00 inference(avatar_split_clause,[],[f3122,f3111,f2369,f22641])).
% 11.34/2.00 thf(f22641,plain,(
% 11.34/2.00 spl41_374 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = X1) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_374])])).
% 11.34/2.00 thf(f3122,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = X1) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_99)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3121])).
% 11.34/2.00 thf(f3121,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,suc,X0) = X1) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_99)),
% 11.34/2.00 inference(superposition,[],[f3112,f2370])).
% 11.34/2.00 thf(f21664,plain,(
% 11.34/2.00 spl41_373 | ~spl41_26 | ~spl41_277),
% 11.34/2.00 inference(avatar_split_clause,[],[f16785,f12780,f2369,f21662])).
% 11.34/2.00 thf(f16785,plain,(
% 11.34/2.00 ( ! [X0 : $o] : (($true = vAPP($o,$o,sK9($o),X0)) | ($false = X0)) ) | (~spl41_26 | ~spl41_277)),
% 11.34/2.00 inference(duplicate_literal_removal,[],[f16783])).
% 11.34/2.00 thf(f16783,plain,(
% 11.34/2.00 ( ! [X0 : $o] : (($true = vAPP($o,$o,sK9($o),X0)) | ($false = X0) | ($false = X0)) ) | (~spl41_26 | ~spl41_277)),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f16763])).
% 11.34/2.00 thf(f16763,plain,(
% 11.34/2.00 ( ! [X0 : $o] : ((vAPP($o,$o,sK9($o),X0) = X0) | ($false = X0)) ) | (~spl41_26 | ~spl41_277)),
% 11.34/2.00 inference(superposition,[],[f12781,f2370])).
% 11.34/2.00 thf(f21072,plain,(
% 11.34/2.00 spl41_255 | spl41_372 | ~spl41_111),
% 11.34/2.00 inference(avatar_split_clause,[],[f3220,f3203,f21070,f6357])).
% 11.34/2.00 thf(f6357,plain,(
% 11.34/2.00 spl41_255 <=> ! [X0 : nat] : (zero_zero(nat) = X0)),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_255])])).
% 11.34/2.00 thf(f21070,plain,(
% 11.34/2.00 spl41_372 <=> ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_372])])).
% 11.34/2.00 thf(f3220,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))) | (zero_zero(nat) = X1) | (zero_zero(nat) = X0)) ) | ~spl41_111),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f3216])).
% 11.34/2.00 thf(f3216,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)) | (zero_zero(nat) = X0)) ) | ~spl41_111),
% 11.34/2.00 inference(leibniz_equality_elimination,[],[f3204])).
% 11.34/2.00 thf(f21068,plain,(
% 11.34/2.00 spl41_371 | ~spl41_26 | ~spl41_96),
% 11.34/2.00 inference(avatar_split_clause,[],[f3089,f3013,f2369,f21066])).
% 11.34/2.00 thf(f21066,plain,(
% 11.34/2.00 spl41_371 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_371])])).
% 11.34/2.00 thf(f3089,plain,(
% 11.34/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,zero_zero(nat)))) ) | (~spl41_26 | ~spl41_96)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3088])).
% 11.34/2.00 thf(f3088,plain,(
% 11.34/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,zero_zero(nat)))) ) | (~spl41_26 | ~spl41_96)),
% 11.34/2.00 inference(superposition,[],[f3014,f2370])).
% 11.34/2.00 thf(f21064,plain,(
% 11.34/2.00 spl41_370 | ~spl41_26 | ~spl41_95),
% 11.34/2.00 inference(avatar_split_clause,[],[f3065,f3009,f2369,f21062])).
% 11.34/2.00 thf(f21062,plain,(
% 11.34/2.00 spl41_370 <=> ! [X0 : $tType,X2 : $tType,X4 : X0,X3 : X0 > X2,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK16(X2,X0),X1),X3))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_370])])).
% 11.34/2.00 thf(f3065,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK16(X2,X0),X1),X3)))) ) | (~spl41_26 | ~spl41_95)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3064])).
% 11.34/2.00 thf(f3064,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0 > $o,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK16(X2,X0),X1),X3)))) ) | (~spl41_26 | ~spl41_95)),
% 11.34/2.00 inference(superposition,[],[f3010,f2370])).
% 11.34/2.00 thf(f21056,plain,(
% 11.34/2.00 spl41_369 | ~spl41_26 | ~spl41_94),
% 11.34/2.00 inference(avatar_split_clause,[],[f3037,f3005,f2369,f21054])).
% 11.34/2.00 thf(f21054,plain,(
% 11.34/2.00 spl41_369 <=> ! [X0 : $tType,X2 : $tType,X4 : X0,X3 : X0 > X2,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK15(X2,X0),X1),X3))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_369])])).
% 11.34/2.00 thf(f3037,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK15(X2,X0),X1),X3)))) ) | (~spl41_26 | ~spl41_94)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3036])).
% 11.34/2.00 thf(f3036,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0 > $o,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK15(X2,X0),X1),X3)))) ) | (~spl41_26 | ~spl41_94)),
% 11.34/2.00 inference(superposition,[],[f3006,f2370])).
% 11.34/2.00 thf(f21052,plain,(
% 11.34/2.00 spl41_368 | ~spl41_35 | ~spl41_84),
% 11.34/2.00 inference(avatar_split_clause,[],[f2932,f2854,f2444,f21050])).
% 11.34/2.00 thf(f21050,plain,(
% 11.34/2.00 spl41_368 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK5,X0)),X1)) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_368])])).
% 11.34/2.00 thf(f2854,plain,(
% 11.34/2.00 spl41_84 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_84])])).
% 11.34/2.00 thf(f2932,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK5,X0)),X1)) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_84)),
% 11.34/2.00 inference(superposition,[],[f2855,f2445])).
% 11.34/2.00 thf(f2855,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl41_84),
% 11.34/2.00 inference(avatar_component_clause,[],[f2854])).
% 11.34/2.00 thf(f21048,plain,(
% 11.34/2.00 spl41_367 | ~spl41_34 | ~spl41_84),
% 11.34/2.00 inference(avatar_split_clause,[],[f2931,f2854,f2440,f21046])).
% 11.34/2.00 thf(f21046,plain,(
% 11.34/2.00 spl41_367 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK4,X0)),X1)) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_367])])).
% 11.34/2.00 thf(f2931,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK4,X0)),X1)) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_84)),
% 11.34/2.00 inference(superposition,[],[f2855,f2441])).
% 11.34/2.00 thf(f21044,plain,(
% 11.34/2.00 spl41_366 | ~spl41_33 | ~spl41_84),
% 11.34/2.00 inference(avatar_split_clause,[],[f2930,f2854,f2436,f21042])).
% 11.34/2.00 thf(f21042,plain,(
% 11.34/2.00 spl41_366 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK3,X0)),X1)) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_366])])).
% 11.34/2.00 thf(f2930,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK3,X0)),X1)) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_84)),
% 11.34/2.00 inference(superposition,[],[f2855,f2437])).
% 11.34/2.00 thf(f21040,plain,(
% 11.34/2.00 spl41_365),
% 11.34/2.00 inference(avatar_split_clause,[],[f2153,f21038])).
% 11.34/2.00 thf(f21038,plain,(
% 11.34/2.00 spl41_365 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)) | (semiri1923998003cancel(X0) != $true) | (X1 = X3) | (zero_zero(X0) = X2))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_365])])).
% 11.34/2.00 thf(f2153,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)) | (semiri1923998003cancel(X0) != $true) | (X1 = X3) | (zero_zero(X0) = X2)) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2152])).
% 11.34/2.00 thf(f2152,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)) | (semiri1923998003cancel(X0) != $true) | (X1 = X3) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2151])).
% 11.34/2.00 thf(f2151,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)) | (semiri1923998003cancel(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f2150])).
% 11.34/2.00 thf(f2150,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)) | (semiri1923998003cancel(X0) != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2149])).
% 11.34/2.00 thf(f2149,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | (semiri1923998003cancel(X0) != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1246])).
% 11.34/2.00 thf(f1246,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) | (semiri1923998003cancel(X0) != $true)) )),
% 11.34/2.00 inference(cnf_transformation,[],[f887])).
% 11.34/2.00 thf(f887,plain,(
% 11.34/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) | (semiri1923998003cancel(X0) != $true))),
% 11.34/2.00 inference(ennf_transformation,[],[f376])).
% 11.34/2.00 thf(f376,plain,(
% 11.34/2.00 ! [X0 : $tType] : ((semiri1923998003cancel(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))))),
% 11.34/2.00 inference(fool_elimination,[],[f375])).
% 11.34/2.00 thf(f375,plain,(
% 11.34/2.00 ! [X0 : $tType] : (semiri1923998003cancel(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)) = (X1 = X3) | (zero_zero(X0) = X2)))),
% 11.34/2.00 inference(rectify,[],[f117])).
% 11.34/2.00 thf(f117,axiom,(
% 11.34/2.00 ! [X0 : $tType] : (semiri1923998003cancel(X0) => ! [X9 : X0,X10 : X0,X11 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)) = (X9 = X11) | (zero_zero(X0) = X10)))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_mult__cancel__right)).
% 11.34/2.00 thf(f21036,plain,(
% 11.34/2.00 spl41_364),
% 11.34/2.00 inference(avatar_split_clause,[],[f2142,f21034])).
% 11.34/2.00 thf(f21034,plain,(
% 11.34/2.00 spl41_364 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) | (semiri1923998003cancel(X0) != $true) | (X2 = X3) | (zero_zero(X0) = X1))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_364])])).
% 11.34/2.00 thf(f2142,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) | (semiri1923998003cancel(X0) != $true) | (X2 = X3) | (zero_zero(X0) = X1)) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2141])).
% 11.34/2.00 thf(f2141,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) | (semiri1923998003cancel(X0) != $true) | (X2 = X3) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2140])).
% 11.34/2.00 thf(f2140,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) | (semiri1923998003cancel(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f2139])).
% 11.34/2.00 thf(f2139,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) | (semiri1923998003cancel(X0) != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2138])).
% 11.34/2.00 thf(f2138,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (semiri1923998003cancel(X0) != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1247])).
% 11.34/2.00 thf(f1247,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | (semiri1923998003cancel(X0) != $true)) )),
% 11.34/2.00 inference(cnf_transformation,[],[f888])).
% 11.34/2.00 thf(f888,plain,(
% 11.34/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | (semiri1923998003cancel(X0) != $true))),
% 11.34/2.00 inference(ennf_transformation,[],[f378])).
% 11.34/2.00 thf(f378,plain,(
% 11.34/2.00 ! [X0 : $tType] : ((semiri1923998003cancel(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))))),
% 11.34/2.00 inference(fool_elimination,[],[f377])).
% 11.34/2.00 thf(f377,plain,(
% 11.34/2.00 ! [X0 : $tType] : (semiri1923998003cancel(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = (X2 = X3) | (zero_zero(X0) = X1)))),
% 11.34/2.00 inference(rectify,[],[f116])).
% 11.34/2.00 thf(f116,axiom,(
% 11.34/2.00 ! [X0 : $tType] : (semiri1923998003cancel(X0) => ! [X10 : X0,X9 : X0,X11 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)) = (X9 = X11) | (zero_zero(X0) = X10)))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_mult__cancel__left)).
% 11.34/2.00 thf(f21032,plain,(
% 11.34/2.00 spl41_363),
% 11.34/2.00 inference(avatar_split_clause,[],[f1944,f21030])).
% 11.34/2.00 thf(f21030,plain,(
% 11.34/2.00 spl41_363 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((X1 = X3) | (field(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)) | (zero_zero(X0) = X2))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_363])])).
% 11.34/2.00 thf(f1944,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((X1 = X3) | (field(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)) | (zero_zero(X0) = X2)) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1943])).
% 11.34/2.00 thf(f1943,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((X1 = X3) | (field(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1942])).
% 11.34/2.00 thf(f1942,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((X1 = X3) | (field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1941])).
% 11.34/2.00 thf(f1941,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)) | (field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1933])).
% 11.34/2.00 thf(f1933,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) | (field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1305])).
% 11.34/2.00 thf(f1305,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))) | (field(X0) != $true)) )),
% 11.34/2.00 inference(cnf_transformation,[],[f967])).
% 11.34/2.00 thf(f967,plain,(
% 11.34/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))) | (field(X0) != $true))),
% 11.34/2.00 inference(ennf_transformation,[],[f492])).
% 11.34/2.00 thf(f492,plain,(
% 11.34/2.00 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))))),
% 11.34/2.00 inference(fool_elimination,[],[f491])).
% 11.34/2.00 thf(f491,plain,(
% 11.34/2.00 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)) = (X1 = X3) | (zero_zero(X0) = X2)))),
% 11.34/2.00 inference(rectify,[],[f122])).
% 11.34/2.00 thf(f122,axiom,(
% 11.34/2.00 ! [X0 : $tType] : (field(X0) => ! [X9 : X0,X10 : X0,X11 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X11),X10) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X10)) = (X9 = X11) | (zero_zero(X0) = X10)))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_divide__cancel__right)).
% 11.34/2.00 thf(f21028,plain,(
% 11.34/2.00 spl41_362),
% 11.34/2.00 inference(avatar_split_clause,[],[f1932,f21026])).
% 11.34/2.00 thf(f21026,plain,(
% 11.34/2.00 spl41_362 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((X2 = X3) | (field(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)) | (zero_zero(X0) = X1))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_362])])).
% 11.34/2.00 thf(f1932,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((X2 = X3) | (field(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)) | (zero_zero(X0) = X1)) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1931])).
% 11.34/2.00 thf(f1931,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((X2 = X3) | (field(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1930])).
% 11.34/2.00 thf(f1930,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((X2 = X3) | (field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1929])).
% 11.34/2.00 thf(f1929,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | (field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1921])).
% 11.34/2.00 thf(f1921,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | (field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1306])).
% 11.34/2.00 thf(f1306,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | (field(X0) != $true)) )),
% 11.34/2.00 inference(cnf_transformation,[],[f968])).
% 11.34/2.00 thf(f968,plain,(
% 11.34/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | (field(X0) != $true))),
% 11.34/2.00 inference(ennf_transformation,[],[f494])).
% 11.34/2.00 thf(f494,plain,(
% 11.34/2.00 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))))),
% 11.34/2.00 inference(fool_elimination,[],[f493])).
% 11.34/2.00 thf(f493,plain,(
% 11.34/2.00 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)) = (X2 = X3) | (zero_zero(X0) = X1)))),
% 11.34/2.00 inference(rectify,[],[f121])).
% 11.34/2.00 thf(f121,axiom,(
% 11.34/2.00 ! [X0 : $tType] : (field(X0) => ! [X10 : X0,X9 : X0,X11 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X10),X9) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X10),X11)) = (X9 = X11) | (zero_zero(X0) = X10)))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_divide__cancel__left)).
% 11.34/2.00 thf(f21024,plain,(
% 11.34/2.00 spl41_361),
% 11.34/2.00 inference(avatar_split_clause,[],[f1766,f21022])).
% 11.34/2.00 thf(f21022,plain,(
% 11.34/2.00 spl41_361 <=> ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_361])])).
% 11.34/2.00 thf(f1766,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1360])).
% 11.34/2.00 thf(f1360,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))) )),
% 11.34/2.00 inference(cnf_transformation,[],[f822])).
% 11.34/2.00 thf(f822,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))),
% 11.34/2.00 inference(rectify,[],[f18])).
% 11.34/2.00 thf(f18,axiom,(
% 11.34/2.00 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X2)))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Suc__less__eq)).
% 11.34/2.00 thf(f21020,plain,(
% 11.34/2.00 spl41_360),
% 11.34/2.00 inference(avatar_split_clause,[],[f1765,f21018])).
% 11.34/2.00 thf(f21018,plain,(
% 11.34/2.00 spl41_360 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_360])])).
% 11.34/2.00 thf(f1765,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1360])).
% 11.34/2.00 thf(f21009,plain,(
% 11.34/2.00 spl41_359),
% 11.34/2.00 inference(avatar_split_clause,[],[f1764,f21007])).
% 11.34/2.00 thf(f21007,plain,(
% 11.34/2.00 spl41_359 <=> ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_359])])).
% 11.34/2.00 thf(f1764,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1361])).
% 11.34/2.00 thf(f1361,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 11.34/2.00 inference(cnf_transformation,[],[f823])).
% 11.34/2.00 thf(f823,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))),
% 11.34/2.00 inference(rectify,[],[f217])).
% 11.34/2.00 thf(f217,axiom,(
% 11.34/2.00 ! [X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,X2)),vAPP(nat,nat,suc,X3)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Suc__le__mono)).
% 11.34/2.00 thf(f21005,plain,(
% 11.34/2.00 spl41_358),
% 11.34/2.00 inference(avatar_split_clause,[],[f1763,f21003])).
% 11.34/2.00 thf(f21003,plain,(
% 11.34/2.00 spl41_358 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_358])])).
% 11.34/2.00 thf(f1763,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1361])).
% 11.34/2.00 thf(f21001,plain,(
% 11.34/2.00 spl41_357),
% 11.34/2.00 inference(avatar_split_clause,[],[f1577,f20999])).
% 11.34/2.00 thf(f20999,plain,(
% 11.34/2.00 spl41_357 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((X1 = X2) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_357])])).
% 11.34/2.00 thf(f1577,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((X1 = X2) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1576])).
% 11.34/2.00 thf(f1576,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((X1 = X2) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1572])).
% 11.34/2.00 thf(f1572,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1432])).
% 11.34/2.00 thf(f1432,plain,(
% 11.34/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))) )),
% 11.34/2.00 inference(cnf_transformation,[],[f704])).
% 11.34/2.00 thf(f704,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)))),
% 11.34/2.00 inference(fool_elimination,[],[f703])).
% 11.34/2.00 thf(f703,plain,(
% 11.34/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X2)) = (X1 = X2))),
% 11.34/2.00 inference(rectify,[],[f82])).
% 11.34/2.00 thf(f82,axiom,(
% 11.34/2.00 ! [X4 : nat,X3 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X4)),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X4)),X2)) = (X2 = X3))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Suc__mult__cancel1)).
% 11.34/2.00 thf(f20098,plain,(
% 11.34/2.00 spl41_356 | ~spl41_26 | ~spl41_302),
% 11.34/2.00 inference(avatar_split_clause,[],[f15041,f14602,f2369,f20096])).
% 11.34/2.00 thf(f20096,plain,(
% 11.34/2.00 spl41_356 <=> ! [X0 : $tType] : ((linordered_field(X0) = $false) | (canoni770627133id_add(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_356])])).
% 11.34/2.00 thf(f14602,plain,(
% 11.34/2.00 spl41_302 <=> ! [X0 : $tType] : ((canoni770627133id_add(X0) != $true) | (linordered_field(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_302])])).
% 11.34/2.00 thf(f15041,plain,(
% 11.34/2.00 ( ! [X0 : $tType] : ((linordered_field(X0) = $false) | (canoni770627133id_add(X0) = $false)) ) | (~spl41_26 | ~spl41_302)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f15040])).
% 11.34/2.00 thf(f15040,plain,(
% 11.34/2.00 ( ! [X0 : $tType] : (($true != $true) | (linordered_field(X0) = $false) | (canoni770627133id_add(X0) = $false)) ) | (~spl41_26 | ~spl41_302)),
% 11.34/2.00 inference(superposition,[],[f14603,f2370])).
% 11.34/2.00 thf(f14603,plain,(
% 11.34/2.00 ( ! [X0 : $tType] : ((canoni770627133id_add(X0) != $true) | (linordered_field(X0) = $false)) ) | ~spl41_302),
% 11.34/2.00 inference(avatar_component_clause,[],[f14602])).
% 11.34/2.00 thf(f19835,plain,(
% 11.34/2.00 spl41_355 | ~spl41_48 | ~spl41_102),
% 11.34/2.00 inference(avatar_split_clause,[],[f3145,f3137,f2510,f19833])).
% 11.34/2.00 thf(f19833,plain,(
% 11.34/2.00 spl41_355 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,suc,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,suc,X0))))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_355])])).
% 11.34/2.00 thf(f3145,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,suc,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,suc,X0)))) ) | (~spl41_48 | ~spl41_102)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3141])).
% 11.34/2.00 thf(f3141,plain,(
% 11.34/2.00 ( ! [X0 : nat] : (($true != $true) | (vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,suc,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,suc,X0)))) ) | (~spl41_48 | ~spl41_102)),
% 11.34/2.00 inference(superposition,[],[f3138,f2511])).
% 11.34/2.00 thf(f19831,plain,(
% 11.34/2.00 spl41_354 | ~spl41_96),
% 11.34/2.00 inference(avatar_split_clause,[],[f3092,f3013,f19829])).
% 11.34/2.00 thf(f19829,plain,(
% 11.34/2.00 spl41_354 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | (X0 = X1))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_354])])).
% 11.34/2.00 thf(f3092,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | (X0 = X1)) ) | ~spl41_96),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f3091])).
% 11.34/2.00 thf(f3091,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_96),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f3086])).
% 11.34/2.00 thf(f3086,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_96),
% 11.34/2.00 inference(primitive_instantiation,[],[f3014])).
% 11.34/2.00 thf(f19827,plain,(
% 11.34/2.00 spl41_353 | ~spl41_95),
% 11.34/2.00 inference(avatar_split_clause,[],[f3070,f3009,f19825])).
% 11.34/2.00 thf(f19825,plain,(
% 11.34/2.00 spl41_353 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : X0 > X2,X1 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK16(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | (X1 = X4) | ($true != wellorder(X2)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_353])])).
% 11.34/2.00 thf(f3070,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK16(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | (X1 = X4) | ($true != wellorder(X2))) ) | ~spl41_95),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f3069])).
% 11.34/2.00 thf(f3069,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK16(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4)) | ($true != wellorder(X2))) ) | ~spl41_95),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f3060])).
% 11.34/2.00 thf(f3060,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK16(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4)) | ($true != wellorder(X2))) ) | ~spl41_95),
% 11.34/2.00 inference(primitive_instantiation,[],[f3010])).
% 11.34/2.00 thf(f19823,plain,(
% 11.34/2.00 spl41_352 | ~spl41_94),
% 11.34/2.00 inference(avatar_split_clause,[],[f3042,f3005,f19821])).
% 11.34/2.00 thf(f19821,plain,(
% 11.34/2.00 spl41_352 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : X0 > X2,X1 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK15(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | (X1 = X4) | ($true != wellorder(X2)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_352])])).
% 11.34/2.00 thf(f3042,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK15(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | (X1 = X4) | ($true != wellorder(X2))) ) | ~spl41_94),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f3041])).
% 11.34/2.00 thf(f3041,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK15(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4)) | ($true != wellorder(X2))) ) | ~spl41_94),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f3032])).
% 11.34/2.00 thf(f3032,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK15(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4)) | ($true != wellorder(X2))) ) | ~spl41_94),
% 11.34/2.00 inference(primitive_instantiation,[],[f3006])).
% 11.34/2.00 thf(f19819,plain,(
% 11.34/2.00 spl41_351 | ~spl41_26 | ~spl41_93),
% 11.34/2.00 inference(avatar_split_clause,[],[f3002,f2984,f2369,f19817])).
% 11.34/2.00 thf(f19817,plain,(
% 11.34/2.00 spl41_351 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_351])])).
% 11.34/2.00 thf(f3002,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) ) | (~spl41_26 | ~spl41_93)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f3001])).
% 11.34/2.00 thf(f3001,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) ) | (~spl41_26 | ~spl41_93)),
% 11.34/2.00 inference(superposition,[],[f2985,f2370])).
% 11.34/2.00 thf(f19815,plain,(
% 11.34/2.00 spl41_350 | ~spl41_26 | ~spl41_91),
% 11.34/2.00 inference(avatar_split_clause,[],[f2988,f2976,f2369,f19813])).
% 11.34/2.00 thf(f19813,plain,(
% 11.34/2.00 spl41_350 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (linordered_idom(X0) = $false))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_350])])).
% 11.34/2.00 thf(f2976,plain,(
% 11.34/2.00 spl41_91 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | (linordered_idom(X0) != $true))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_91])])).
% 11.34/2.00 thf(f2988,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (linordered_idom(X0) = $false)) ) | (~spl41_26 | ~spl41_91)),
% 11.34/2.00 inference(trivial_inequality_removal,[],[f2987])).
% 11.34/2.00 thf(f2987,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (linordered_idom(X0) = $false)) ) | (~spl41_26 | ~spl41_91)),
% 11.34/2.00 inference(superposition,[],[f2977,f2370])).
% 11.34/2.00 thf(f2977,plain,(
% 11.34/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((linordered_idom(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))) ) | ~spl41_91),
% 11.34/2.00 inference(avatar_component_clause,[],[f2976])).
% 11.34/2.00 thf(f19811,plain,(
% 11.34/2.00 spl41_349),
% 11.34/2.00 inference(avatar_split_clause,[],[f2193,f19809])).
% 11.34/2.00 thf(f19809,plain,(
% 11.34/2.00 spl41_349 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat))))) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_349])])).
% 11.34/2.00 thf(f2193,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat))))) | (zero_zero(nat) = X0)) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2192])).
% 11.34/2.00 thf(f2192,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2191])).
% 11.34/2.00 thf(f2191,plain,(
% 11.34/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f2185])).
% 11.34/2.00 thf(f2185,plain,(
% 11.34/2.00 ( ! [X0 : nat] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1202])).
% 11.34/2.00 thf(f1202,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))))) )),
% 11.34/2.00 inference(cnf_transformation,[],[f302])).
% 11.34/2.00 thf(f302,plain,(
% 11.34/2.00 ! [X0 : nat] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))))),
% 11.34/2.00 inference(fool_elimination,[],[f301])).
% 11.34/2.00 thf(f301,plain,(
% 11.34/2.00 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))) = (vAPP(nat,nat,suc,zero_zero(nat)) = X0) | (zero_zero(nat) = X0))),
% 11.34/2.00 inference(rectify,[],[f200])).
% 11.34/2.00 thf(f200,axiom,(
% 11.34/2.00 ! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))) = (vAPP(nat,nat,suc,zero_zero(nat)) = X2) | (zero_zero(nat) = X2))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_nat__lessSucSuc0__conv)).
% 11.34/2.00 thf(f19805,plain,(
% 11.34/2.00 spl41_348),
% 11.34/2.00 inference(avatar_split_clause,[],[f2178,f19803])).
% 11.34/2.00 thf(f19803,plain,(
% 11.34/2.00 spl41_348 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0)) | (zero_zero(nat) = X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_348])])).
% 11.34/2.00 thf(f2178,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0)) | (zero_zero(nat) = X0)) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2177])).
% 11.34/2.00 thf(f2177,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 11.34/2.00 inference(not_proxy_clausification,[],[f2176])).
% 11.34/2.00 thf(f2176,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0)) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f2175])).
% 11.34/2.00 thf(f2175,plain,(
% 11.34/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0)) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.34/2.00 inference(not_proxy_clausification,[],[f2174])).
% 11.34/2.00 thf(f2174,plain,(
% 11.34/2.00 ( ! [X0 : nat] : (($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0)) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f2173])).
% 11.34/2.00 thf(f2173,plain,(
% 11.34/2.00 ( ! [X0 : nat] : (($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1203])).
% 11.34/2.00 thf(f1203,plain,(
% 11.34/2.00 ( ! [X0 : nat] : ((vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0))) )),
% 11.34/2.00 inference(cnf_transformation,[],[f304])).
% 11.34/2.00 thf(f304,plain,(
% 11.34/2.00 ! [X0 : nat] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0))),
% 11.34/2.00 inference(fool_elimination,[],[f303])).
% 11.34/2.00 thf(f303,plain,(
% 11.34/2.00 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X0) = (vAPP(nat,nat,suc,zero_zero(nat)) != X0) & (zero_zero(nat) != X0))),
% 11.34/2.00 inference(rectify,[],[f227])).
% 11.34/2.00 thf(f227,axiom,(
% 11.34/2.00 ! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero(nat)))),X2) = (vAPP(nat,nat,suc,zero_zero(nat)) != X2) & (zero_zero(nat) != X2))),
% 11.34/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_nat__geSucSuc0__conv)).
% 11.34/2.00 thf(f19801,plain,(
% 11.34/2.00 spl41_347),
% 11.34/2.00 inference(avatar_split_clause,[],[f1712,f19799])).
% 11.34/2.00 thf(f19799,plain,(
% 11.34/2.00 spl41_347 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | (vAPP(nat,nat,suc,zero_zero(nat)) != X1) | (vAPP(nat,nat,suc,zero_zero(nat)) != X0))),
% 11.34/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_347])])).
% 11.34/2.00 thf(f1712,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | (vAPP(nat,nat,suc,zero_zero(nat)) != X1) | (vAPP(nat,nat,suc,zero_zero(nat)) != X0)) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1711])).
% 11.34/2.00 thf(f1711,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | (vAPP(nat,nat,suc,zero_zero(nat)) != X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) )),
% 11.34/2.00 inference(equality_proxy_clausification,[],[f1710])).
% 11.34/2.00 thf(f1710,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) )),
% 11.34/2.00 inference(binary_proxy_clausification,[],[f1709])).
% 11.34/2.00 thf(f1709,plain,(
% 11.34/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1702])).
% 11.45/2.00 thf(f1702,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1368])).
% 11.45/2.00 thf(f1368,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f608])).
% 11.45/2.00 thf(f608,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)))),
% 11.45/2.00 inference(fool_elimination,[],[f607])).
% 11.45/2.00 thf(f607,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) = (vAPP(nat,nat,suc,zero_zero(nat)) = X1) & (vAPP(nat,nat,suc,zero_zero(nat)) = X0))),
% 11.45/2.00 inference(rectify,[],[f10])).
% 11.45/2.00 thf(f10,axiom,(
% 11.45/2.00 ! [X3 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),X2) = vAPP(nat,nat,suc,zero_zero(nat))) = (vAPP(nat,nat,suc,zero_zero(nat)) = X2) & (vAPP(nat,nat,suc,zero_zero(nat)) = X3))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_one__eq__mult__iff)).
% 11.45/2.00 thf(f19797,plain,(
% 11.45/2.00 spl41_346),
% 11.45/2.00 inference(avatar_split_clause,[],[f1638,f19795])).
% 11.45/2.00 thf(f19795,plain,(
% 11.45/2.00 spl41_346 <=> ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | (X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_346])])).
% 11.45/2.00 thf(f1638,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | (X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1637])).
% 11.45/2.00 thf(f1637,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1636])).
% 11.45/2.00 thf(f1636,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1376])).
% 11.45/2.00 thf(f1376,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f624])).
% 11.45/2.00 thf(f624,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)))),
% 11.45/2.00 inference(fool_elimination,[],[f623])).
% 11.45/2.00 thf(f623,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1)) = (X0 = X1) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))),
% 11.45/2.00 inference(rectify,[],[f72])).
% 11.45/2.00 thf(f72,axiom,(
% 11.45/2.00 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,suc,X2)) = (X2 = X3) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__Suc__eq)).
% 11.45/2.00 thf(f18933,plain,(
% 11.45/2.00 spl41_345 | ~spl41_26 | ~spl41_89),
% 11.45/2.00 inference(avatar_split_clause,[],[f2974,f2964,f2369,f18931])).
% 11.45/2.00 thf(f18931,plain,(
% 11.45/2.00 spl41_345 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK14,X1))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_345])])).
% 11.45/2.00 thf(f2964,plain,(
% 11.45/2.00 spl41_89 <=> ! [X0 : nat > $o,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK14,X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_89])])).
% 11.45/2.00 thf(f2974,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK14,X1)))) ) | (~spl41_26 | ~spl41_89)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2973])).
% 11.45/2.00 thf(f2973,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK14,X1)))) ) | (~spl41_26 | ~spl41_89)),
% 11.45/2.00 inference(superposition,[],[f2965,f2370])).
% 11.45/2.00 thf(f2965,plain,(
% 11.45/2.00 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK14,X0))) | ($true = vAPP(nat,$o,X0,X3)) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl41_89),
% 11.45/2.00 inference(avatar_component_clause,[],[f2964])).
% 11.45/2.00 thf(f18929,plain,(
% 11.45/2.00 spl41_344 | ~spl41_26 | ~spl41_88),
% 11.45/2.00 inference(avatar_split_clause,[],[f2968,f2960,f2369,f18927])).
% 11.45/2.00 thf(f18927,plain,(
% 11.45/2.00 spl41_344 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK13,X1))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_344])])).
% 11.45/2.00 thf(f2960,plain,(
% 11.45/2.00 spl41_88 <=> ! [X0 : nat > $o,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK13,X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_88])])).
% 11.45/2.00 thf(f2968,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK13,X1)))) ) | (~spl41_26 | ~spl41_88)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2967])).
% 11.45/2.00 thf(f2967,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK13,X1)))) ) | (~spl41_26 | ~spl41_88)),
% 11.45/2.00 inference(superposition,[],[f2961,f2370])).
% 11.45/2.00 thf(f2961,plain,(
% 11.45/2.00 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK13,X0))) | ($true = vAPP(nat,$o,X0,X3)) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl41_88),
% 11.45/2.00 inference(avatar_component_clause,[],[f2960])).
% 11.45/2.00 thf(f18925,plain,(
% 11.45/2.00 spl41_343 | ~spl41_26 | ~spl41_78),
% 11.45/2.00 inference(avatar_split_clause,[],[f2811,f2800,f2369,f18923])).
% 11.45/2.00 thf(f18923,plain,(
% 11.45/2.00 spl41_343 <=> ! [X2 : $o,X0 : $o > nat,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X2)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK40($o),X0),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_343])])).
% 11.45/2.00 thf(f2811,plain,(
% 11.45/2.00 ( ! [X2 : $o,X0 : $o > nat,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X2)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK40($o),X0),X1))) ) | (~spl41_26 | ~spl41_78)),
% 11.45/2.00 inference(superposition,[],[f2801,f2370])).
% 11.45/2.00 thf(f18516,plain,(
% 11.45/2.00 ~spl41_341 | ~spl41_342 | ~spl41_107),
% 11.45/2.00 inference(avatar_split_clause,[],[f3189,f3163,f18513,f18509])).
% 11.45/2.00 thf(f18513,plain,(
% 11.45/2.00 spl41_342 <=> (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,vEQ(nat)) = vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,vEQ(nat)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_342])])).
% 11.45/2.00 thf(f3189,plain,(
% 11.45/2.00 (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,vEQ(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,vEQ(nat))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat))) | ~spl41_107),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f3186])).
% 11.45/2.00 thf(f3186,plain,(
% 11.45/2.00 ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,vEQ(nat)))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat))) | ~spl41_107),
% 11.45/2.00 inference(primitive_instantiation,[],[f3164])).
% 11.45/2.00 thf(f18501,plain,(
% 11.45/2.00 spl41_340 | ~spl41_26 | spl41_329),
% 11.45/2.00 inference(avatar_split_clause,[],[f16829,f16820,f2369,f18498])).
% 11.45/2.00 thf(f18498,plain,(
% 11.45/2.00 spl41_340 <=> ($false = linordered_ring($o))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_340])])).
% 11.45/2.00 thf(f16820,plain,(
% 11.45/2.00 spl41_329 <=> ($true = linordered_ring($o))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_329])])).
% 11.45/2.00 thf(f16829,plain,(
% 11.45/2.00 ($false = linordered_ring($o)) | (~spl41_26 | spl41_329)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f16828])).
% 11.45/2.00 thf(f16828,plain,(
% 11.45/2.00 ($true != $true) | ($false = linordered_ring($o)) | (~spl41_26 | spl41_329)),
% 11.45/2.00 inference(superposition,[],[f16822,f2370])).
% 11.45/2.00 thf(f16822,plain,(
% 11.45/2.00 ($true != linordered_ring($o)) | spl41_329),
% 11.45/2.00 inference(avatar_component_clause,[],[f16820])).
% 11.45/2.00 thf(f18496,plain,(
% 11.45/2.00 spl41_339 | ~spl41_48 | ~spl41_104),
% 11.45/2.00 inference(avatar_split_clause,[],[f3177,f3151,f2510,f18494])).
% 11.45/2.00 thf(f18494,plain,(
% 11.45/2.00 spl41_339 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X0)) = X1)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_339])])).
% 11.45/2.00 thf(f3151,plain,(
% 11.45/2.00 spl41_104 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_104])])).
% 11.45/2.00 thf(f3177,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X0)) = X1)) ) | (~spl41_48 | ~spl41_104)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3172])).
% 11.45/2.00 thf(f3172,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X0)) = X1)) ) | (~spl41_48 | ~spl41_104)),
% 11.45/2.00 inference(superposition,[],[f3152,f2511])).
% 11.45/2.00 thf(f3152,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1)) ) | ~spl41_104),
% 11.45/2.00 inference(avatar_component_clause,[],[f3151])).
% 11.45/2.00 thf(f18492,plain,(
% 11.45/2.00 spl41_338 | ~spl41_48 | ~spl41_103),
% 11.45/2.00 inference(avatar_split_clause,[],[f3171,f3147,f2510,f18490])).
% 11.45/2.00 thf(f18490,plain,(
% 11.45/2.00 spl41_338 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,suc,X0)) = X1)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_338])])).
% 11.45/2.00 thf(f3147,plain,(
% 11.45/2.00 spl41_103 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_103])])).
% 11.45/2.00 thf(f3171,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,suc,X0)) = X1)) ) | (~spl41_48 | ~spl41_103)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3166])).
% 11.45/2.00 thf(f3166,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,suc,X0)) = X1)) ) | (~spl41_48 | ~spl41_103)),
% 11.45/2.00 inference(superposition,[],[f3148,f2511])).
% 11.45/2.00 thf(f3148,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1)) ) | ~spl41_103),
% 11.45/2.00 inference(avatar_component_clause,[],[f3147])).
% 11.45/2.00 thf(f18397,plain,(
% 11.45/2.00 spl41_255 | spl41_337 | ~spl41_96),
% 11.45/2.00 inference(avatar_split_clause,[],[f3082,f3013,f18394,f6357])).
% 11.45/2.00 thf(f18394,plain,(
% 11.45/2.00 spl41_337 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_337])])).
% 11.45/2.00 thf(f3082,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))) | (zero_zero(nat) = X0)) ) | ~spl41_96),
% 11.45/2.00 inference(leibniz_equality_elimination,[],[f3014])).
% 11.45/2.00 thf(f18392,plain,(
% 11.45/2.00 spl41_336 | ~spl41_44 | ~spl41_93),
% 11.45/2.00 inference(avatar_split_clause,[],[f3003,f2984,f2489,f18390])).
% 11.45/2.00 thf(f18390,plain,(
% 11.45/2.00 spl41_336 <=> ! [X0 : nat] : (vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_336])])).
% 11.45/2.00 thf(f3003,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)))) ) | (~spl41_44 | ~spl41_93)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3000])).
% 11.45/2.00 thf(f3000,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | (vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)))) ) | (~spl41_44 | ~spl41_93)),
% 11.45/2.00 inference(superposition,[],[f2985,f2490])).
% 11.45/2.00 thf(f18388,plain,(
% 11.45/2.00 spl41_335 | ~spl41_26 | ~spl41_87),
% 11.45/2.00 inference(avatar_split_clause,[],[f2958,f2946,f2369,f18386])).
% 11.45/2.00 thf(f18386,plain,(
% 11.45/2.00 spl41_335 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2) | (division_ring(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_335])])).
% 11.45/2.00 thf(f2946,plain,(
% 11.45/2.00 spl41_87 <=> ! [X0 : $tType,X1 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),X1) = X3) | (zero_zero(X0) = X1) | (division_ring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_87])])).
% 11.45/2.00 thf(f2958,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2) | (division_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_87)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2957])).
% 11.45/2.00 thf(f2957,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2) | (division_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_87)),
% 11.45/2.00 inference(superposition,[],[f2947,f2370])).
% 11.45/2.00 thf(f2947,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X3 : X0,X1 : X0] : ((division_ring(X0) != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),X1) = X3)) ) | ~spl41_87),
% 11.45/2.00 inference(avatar_component_clause,[],[f2946])).
% 11.45/2.00 thf(f18384,plain,(
% 11.45/2.00 spl41_334 | ~spl41_26 | ~spl41_86),
% 11.45/2.00 inference(avatar_split_clause,[],[f2955,f2942,f2369,f18382])).
% 11.45/2.00 thf(f18382,plain,(
% 11.45/2.00 spl41_334 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2) | (semidom_divide(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_334])])).
% 11.45/2.00 thf(f2942,plain,(
% 11.45/2.00 spl41_86 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2) | (zero_zero(X0) = X1) | (semidom_divide(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_86])])).
% 11.45/2.00 thf(f2955,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2) | (semidom_divide(X0) = $false)) ) | (~spl41_26 | ~spl41_86)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2954])).
% 11.45/2.00 thf(f2954,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2) | (semidom_divide(X0) = $false)) ) | (~spl41_26 | ~spl41_86)),
% 11.45/2.00 inference(superposition,[],[f2943,f2370])).
% 11.45/2.00 thf(f2943,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((semidom_divide(X0) != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2)) ) | ~spl41_86),
% 11.45/2.00 inference(avatar_component_clause,[],[f2942])).
% 11.45/2.00 thf(f18380,plain,(
% 11.45/2.00 spl41_333 | ~spl41_26 | ~spl41_85),
% 11.45/2.00 inference(avatar_split_clause,[],[f2951,f2938,f2369,f18378])).
% 11.45/2.00 thf(f18378,plain,(
% 11.45/2.00 spl41_333 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X1) = X2) | (semidom_divide(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_333])])).
% 11.45/2.00 thf(f2938,plain,(
% 11.45/2.00 spl41_85 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X1) = X2) | (zero_zero(X0) = X1) | (semidom_divide(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_85])])).
% 11.45/2.00 thf(f2951,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X1) = X2) | (semidom_divide(X0) = $false)) ) | (~spl41_26 | ~spl41_85)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2950])).
% 11.45/2.00 thf(f2950,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X1) = X2) | (semidom_divide(X0) = $false)) ) | (~spl41_26 | ~spl41_85)),
% 11.45/2.00 inference(superposition,[],[f2939,f2370])).
% 11.45/2.00 thf(f2939,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((semidom_divide(X0) != $true) | (zero_zero(X0) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X1) = X2)) ) | ~spl41_85),
% 11.45/2.00 inference(avatar_component_clause,[],[f2938])).
% 11.45/2.00 thf(f18376,plain,(
% 11.45/2.00 spl41_332),
% 11.45/2.00 inference(avatar_split_clause,[],[f1737,f18374])).
% 11.45/2.00 thf(f18374,plain,(
% 11.45/2.00 spl41_332 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (zero_zero(nat) = X1))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_332])])).
% 11.45/2.00 thf(f1737,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (zero_zero(nat) = X1)) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1736])).
% 11.45/2.00 thf(f1736,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1735])).
% 11.45/2.00 thf(f1735,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1734])).
% 11.45/2.00 thf(f1734,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1365])).
% 11.45/2.00 thf(f1365,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f602])).
% 11.45/2.00 thf(f602,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(fool_elimination,[],[f601])).
% 11.45/2.00 thf(f601,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) | (zero_zero(nat) = X1))),
% 11.45/2.00 inference(rectify,[],[f171])).
% 11.45/2.00 thf(f171,axiom,(
% 11.45/2.00 ! [X2 : nat,X3 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X2),X3)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) | (zero_zero(nat) = X3))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_div__eq__0__conv)).
% 11.45/2.00 thf(f16849,plain,(
% 11.45/2.00 spl41_331 | ~spl41_26 | spl41_326),
% 11.45/2.00 inference(avatar_split_clause,[],[f16815,f16807,f2369,f16846])).
% 11.45/2.00 thf(f16846,plain,(
% 11.45/2.00 spl41_331 <=> ($false = wellorder($o))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_331])])).
% 11.45/2.00 thf(f16807,plain,(
% 11.45/2.00 spl41_326 <=> ($true = wellorder($o))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_326])])).
% 11.45/2.00 thf(f16815,plain,(
% 11.45/2.00 ($false = wellorder($o)) | (~spl41_26 | spl41_326)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f16814])).
% 11.45/2.00 thf(f16814,plain,(
% 11.45/2.00 ($true != $true) | ($false = wellorder($o)) | (~spl41_26 | spl41_326)),
% 11.45/2.00 inference(superposition,[],[f16809,f2370])).
% 11.45/2.00 thf(f16809,plain,(
% 11.45/2.00 ($true != wellorder($o)) | spl41_326),
% 11.45/2.00 inference(avatar_component_clause,[],[f16807])).
% 11.45/2.00 thf(f16827,plain,(
% 11.45/2.00 spl41_328 | ~spl41_329 | ~spl41_330 | ~spl41_26 | ~spl41_76 | ~spl41_248),
% 11.45/2.00 inference(avatar_split_clause,[],[f9147,f6251,f2784,f2369,f16824,f16820,f16817])).
% 11.45/2.00 thf(f16817,plain,(
% 11.45/2.00 spl41_328 <=> ! [X0 : $o] : ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),times_times($o),X0),X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_328])])).
% 11.45/2.00 thf(f16824,plain,(
% 11.45/2.00 spl41_330 <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_330])])).
% 11.45/2.00 thf(f2784,plain,(
% 11.45/2.00 spl41_76 <=> ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0))) | (linordered_ring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_76])])).
% 11.45/2.00 thf(f9147,plain,(
% 11.45/2.00 ( ! [X0 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$false)) | ($true != linordered_ring($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),times_times($o),X0),X0))) ) | (~spl41_26 | ~spl41_76 | ~spl41_248)),
% 11.45/2.00 inference(forward_demodulation,[],[f2791,f6253])).
% 11.45/2.00 thf(f2791,plain,(
% 11.45/2.00 ( ! [X0 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),zero_zero($o))) | ($true != linordered_ring($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),times_times($o),X0),X0))) ) | (~spl41_26 | ~spl41_76)),
% 11.45/2.00 inference(superposition,[],[f2785,f2370])).
% 11.45/2.00 thf(f2785,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0))) | (linordered_ring(X0) != $true)) ) | ~spl41_76),
% 11.45/2.00 inference(avatar_component_clause,[],[f2784])).
% 11.45/2.00 thf(f16813,plain,(
% 11.45/2.00 ~spl41_326 | spl41_327 | ~spl41_252 | ~spl41_38 | ~spl41_148),
% 11.45/2.00 inference(avatar_split_clause,[],[f3761,f3724,f2456,f6270,f16811,f16807])).
% 11.45/2.00 thf(f16811,plain,(
% 11.45/2.00 spl41_327 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_327])])).
% 11.45/2.00 thf(f6270,plain,(
% 11.45/2.00 spl41_252 <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_252])])).
% 11.45/2.00 thf(f3761,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$true)) | ($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($true != wellorder($o))) ) | (~spl41_38 | ~spl41_148)),
% 11.45/2.00 inference(forward_demodulation,[],[f3731,f2457])).
% 11.45/2.00 thf(f3731,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK15($o,nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)))))) | ($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($true != wellorder($o))) ) | (~spl41_38 | ~spl41_148)),
% 11.45/2.00 inference(superposition,[],[f3725,f2457])).
% 11.45/2.00 thf(f16805,plain,(
% 11.45/2.00 spl41_325 | ~spl41_44 | ~spl41_112),
% 11.45/2.00 inference(avatar_split_clause,[],[f3227,f3207,f2489,f16803])).
% 11.45/2.00 thf(f16803,plain,(
% 11.45/2.00 spl41_325 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_325])])).
% 11.45/2.00 thf(f3227,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)))) ) | (~spl41_44 | ~spl41_112)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3224])).
% 11.45/2.00 thf(f3224,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)))) ) | (~spl41_44 | ~spl41_112)),
% 11.45/2.00 inference(superposition,[],[f3208,f2490])).
% 11.45/2.00 thf(f16801,plain,(
% 11.45/2.00 spl41_324 | ~spl41_26 | ~spl41_84),
% 11.45/2.00 inference(avatar_split_clause,[],[f2935,f2854,f2369,f16799])).
% 11.45/2.00 thf(f16799,plain,(
% 11.45/2.00 spl41_324 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_324])])).
% 11.45/2.00 thf(f2935,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) ) | (~spl41_26 | ~spl41_84)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2934])).
% 11.45/2.00 thf(f2934,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) ) | (~spl41_26 | ~spl41_84)),
% 11.45/2.00 inference(superposition,[],[f2855,f2370])).
% 11.45/2.00 thf(f16797,plain,(
% 11.45/2.00 spl41_323 | ~spl41_26 | ~spl41_82),
% 11.45/2.00 inference(avatar_split_clause,[],[f2915,f2846,f2369,f16795])).
% 11.45/2.00 thf(f16795,plain,(
% 11.45/2.00 spl41_323 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0)))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_323])])).
% 11.45/2.00 thf(f2846,plain,(
% 11.45/2.00 spl41_82 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_82])])).
% 11.45/2.00 thf(f2915,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))))) ) | (~spl41_26 | ~spl41_82)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2914])).
% 11.45/2.00 thf(f2914,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))))) ) | (~spl41_26 | ~spl41_82)),
% 11.45/2.00 inference(superposition,[],[f2847,f2370])).
% 11.45/2.00 thf(f2847,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0)))) | ($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) ) | ~spl41_82),
% 11.45/2.00 inference(avatar_component_clause,[],[f2846])).
% 11.45/2.00 thf(f16793,plain,(
% 11.45/2.00 spl41_322 | ~spl41_26 | ~spl41_81),
% 11.45/2.00 inference(avatar_split_clause,[],[f2902,f2842,f2369,f16791])).
% 11.45/2.00 thf(f16791,plain,(
% 11.45/2.00 spl41_322 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,X0)))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_322])])).
% 11.45/2.00 thf(f2842,plain,(
% 11.45/2.00 spl41_81 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,X0)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_81])])).
% 11.45/2.00 thf(f2902,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,X0))))) ) | (~spl41_26 | ~spl41_81)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2901])).
% 11.45/2.00 thf(f2901,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,X0))))) ) | (~spl41_26 | ~spl41_81)),
% 11.45/2.00 inference(superposition,[],[f2843,f2370])).
% 11.45/2.00 thf(f2843,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,X0)))) | ($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) ) | ~spl41_81),
% 11.45/2.00 inference(avatar_component_clause,[],[f2842])).
% 11.45/2.00 thf(f16789,plain,(
% 11.45/2.00 spl41_321 | ~spl41_26 | ~spl41_80),
% 11.45/2.00 inference(avatar_split_clause,[],[f2885,f2838,f2369,f16787])).
% 11.45/2.00 thf(f16787,plain,(
% 11.45/2.00 spl41_321 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,X0)))) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_321])])).
% 11.45/2.00 thf(f2838,plain,(
% 11.45/2.00 spl41_80 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,X0)))) | ($true != vAPP(nat,$o,X0,X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_80])])).
% 11.45/2.00 thf(f2885,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,X0)))) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl41_26 | ~spl41_80)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2884])).
% 11.45/2.00 thf(f2884,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,X0)))) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl41_26 | ~spl41_80)),
% 11.45/2.00 inference(superposition,[],[f2839,f2370])).
% 11.45/2.00 thf(f2839,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,X0)))) | ($true = vAPP(nat,$o,X0,zero_zero(nat)))) ) | ~spl41_80),
% 11.45/2.00 inference(avatar_component_clause,[],[f2838])).
% 11.45/2.00 thf(f16762,plain,(
% 11.45/2.00 spl41_320 | ~spl41_26 | ~spl41_79),
% 11.45/2.00 inference(avatar_split_clause,[],[f2866,f2832,f2369,f16760])).
% 11.45/2.00 thf(f16760,plain,(
% 11.45/2.00 spl41_320 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,X0)))) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_320])])).
% 11.45/2.00 thf(f2832,plain,(
% 11.45/2.00 spl41_79 <=> ! [X2 : nat,X0 : nat > $o] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,X0)))) | ($true != vAPP(nat,$o,X0,X2)) | ($true = vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_79])])).
% 11.45/2.00 thf(f2866,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,X0)))) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl41_26 | ~spl41_79)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2865])).
% 11.45/2.00 thf(f2865,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,X0)))) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl41_26 | ~spl41_79)),
% 11.45/2.00 inference(superposition,[],[f2833,f2370])).
% 11.45/2.00 thf(f2833,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat > $o] : (($true != vAPP(nat,$o,X0,X2)) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,X0)))) | ($true = vAPP(nat,$o,X0,zero_zero(nat)))) ) | ~spl41_79),
% 11.45/2.00 inference(avatar_component_clause,[],[f2832])).
% 11.45/2.00 thf(f16758,plain,(
% 11.45/2.00 spl41_319),
% 11.45/2.00 inference(avatar_split_clause,[],[f1690,f16756])).
% 11.45/2.00 thf(f16756,plain,(
% 11.45/2.00 spl41_319 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_319])])).
% 11.45/2.00 thf(f1690,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.00 inference(not_proxy_clausification,[],[f1687])).
% 11.45/2.00 thf(f1687,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0))) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1370])).
% 11.45/2.00 thf(f1370,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0)) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f612])).
% 11.45/2.00 thf(f612,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0)) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(fool_elimination,[],[f611])).
% 11.45/2.00 thf(f611,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0)))),
% 11.45/2.00 inference(rectify,[],[f71])).
% 11.45/2.00 thf(f71,axiom,(
% 11.45/2.00 ! [X3 : nat,X2 : nat] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),vAPP(nat,nat,suc,X3)))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_not__less__eq)).
% 11.45/2.00 thf(f16754,plain,(
% 11.45/2.00 spl41_318),
% 11.45/2.00 inference(avatar_split_clause,[],[f1689,f16752])).
% 11.45/2.00 thf(f1689,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.00 inference(not_proxy_clausification,[],[f1688])).
% 11.45/2.00 thf(f1688,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,suc,X0))) | ($true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1370])).
% 11.45/2.00 thf(f16750,plain,(
% 11.45/2.00 spl41_317),
% 11.45/2.00 inference(avatar_split_clause,[],[f1605,f16748])).
% 11.45/2.00 thf(f16748,plain,(
% 11.45/2.00 spl41_317 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) | (zero_zero(nat) = X0) | (X1 = X2))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_317])])).
% 11.45/2.00 thf(f1605,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) | (zero_zero(nat) = X0) | (X1 = X2)) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1604])).
% 11.45/2.00 thf(f1604,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) | (zero_zero(nat) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1603])).
% 11.45/2.00 thf(f1603,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1602])).
% 11.45/2.00 thf(f1602,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1601])).
% 11.45/2.00 thf(f1601,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1429])).
% 11.45/2.00 thf(f1429,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f698])).
% 11.45/2.00 thf(f698,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))),
% 11.45/2.00 inference(fool_elimination,[],[f697])).
% 11.45/2.00 thf(f697,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)) = (zero_zero(nat) = X0) | (X1 = X2))),
% 11.45/2.00 inference(rectify,[],[f22])).
% 11.45/2.00 thf(f22,axiom,(
% 11.45/2.00 ! [X4 : nat,X3 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X2)) = (zero_zero(nat) = X4) | (X2 = X3))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_mult__cancel1)).
% 11.45/2.00 thf(f16746,plain,(
% 11.45/2.00 spl41_316),
% 11.45/2.00 inference(avatar_split_clause,[],[f1594,f16744])).
% 11.45/2.00 thf(f16744,plain,(
% 11.45/2.00 spl41_316 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1)) | (zero_zero(nat) = X1) | (X0 = X2))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_316])])).
% 11.45/2.00 thf(f1594,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1)) | (zero_zero(nat) = X1) | (X0 = X2)) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1593])).
% 11.45/2.00 thf(f1593,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1)) | (zero_zero(nat) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1592])).
% 11.45/2.00 thf(f1592,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1591])).
% 11.45/2.00 thf(f1591,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1590])).
% 11.45/2.00 thf(f1590,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1430])).
% 11.45/2.00 thf(f1430,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f700])).
% 11.45/2.00 thf(f700,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)))),
% 11.45/2.00 inference(fool_elimination,[],[f699])).
% 11.45/2.00 thf(f699,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1)) = (zero_zero(nat) = X1) | (X0 = X2))),
% 11.45/2.00 inference(rectify,[],[f21])).
% 11.45/2.00 thf(f21,axiom,(
% 11.45/2.00 ! [X3 : nat,X4 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),X4) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X4)) = (zero_zero(nat) = X4) | (X2 = X3))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_mult__cancel2)).
% 11.45/2.00 thf(f15696,plain,(
% 11.45/2.00 ~spl41_252 | ~spl41_258),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f15695])).
% 11.45/2.00 thf(f15695,plain,(
% 11.45/2.00 $false | (~spl41_252 | ~spl41_258)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f15694])).
% 11.45/2.00 thf(f15694,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_252 | ~spl41_258)),
% 11.45/2.00 inference(forward_demodulation,[],[f6271,f8412])).
% 11.45/2.00 thf(f8412,plain,(
% 11.45/2.00 ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$true)) | ~spl41_258),
% 11.45/2.00 inference(avatar_component_clause,[],[f8410])).
% 11.45/2.00 thf(f8410,plain,(
% 11.45/2.00 spl41_258 <=> ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_258])])).
% 11.45/2.00 thf(f6271,plain,(
% 11.45/2.00 ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$true)) | ~spl41_252),
% 11.45/2.00 inference(avatar_component_clause,[],[f6270])).
% 11.45/2.00 thf(f15672,plain,(
% 11.45/2.00 spl41_315 | ~spl41_26 | spl41_277),
% 11.45/2.00 inference(avatar_split_clause,[],[f13710,f12780,f2369,f15669])).
% 11.45/2.00 thf(f13710,plain,(
% 11.45/2.00 ($false = vAPP($o,$o,sK9($o),$true)) | (~spl41_26 | spl41_277)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f13709])).
% 11.45/2.00 thf(f13709,plain,(
% 11.45/2.00 ($true != $true) | ($false = vAPP($o,$o,sK9($o),$true)) | (~spl41_26 | spl41_277)),
% 11.45/2.00 inference(superposition,[],[f12782,f2370])).
% 11.45/2.00 thf(f15148,plain,(
% 11.45/2.00 spl41_314 | ~spl41_26 | ~spl41_37 | ~spl41_44 | ~spl41_80),
% 11.45/2.00 inference(avatar_split_clause,[],[f2894,f2838,f2489,f2452,f2369,f15146])).
% 11.45/2.00 thf(f15146,plain,(
% 11.45/2.00 spl41_314 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_314])])).
% 11.45/2.00 thf(f2452,plain,(
% 11.45/2.00 spl41_37 <=> ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_37])])).
% 11.45/2.00 thf(f2894,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)))))) ) | (~spl41_26 | ~spl41_37 | ~spl41_44 | ~spl41_80)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2893])).
% 11.45/2.00 thf(f2893,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = $false) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)))))) ) | (~spl41_26 | ~spl41_37 | ~spl41_44 | ~spl41_80)),
% 11.45/2.00 inference(forward_demodulation,[],[f2887,f2466])).
% 11.45/2.00 thf(f2466,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | (~spl41_26 | ~spl41_37)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2465])).
% 11.45/2.00 thf(f2465,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | (~spl41_26 | ~spl41_37)),
% 11.45/2.00 inference(superposition,[],[f2453,f2370])).
% 11.45/2.00 thf(f2453,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | ~spl41_37),
% 11.45/2.00 inference(avatar_component_clause,[],[f2452])).
% 11.45/2.00 thf(f2887,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | (~spl41_44 | ~spl41_80)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2881])).
% 11.45/2.00 thf(f2881,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | (~spl41_44 | ~spl41_80)),
% 11.45/2.00 inference(superposition,[],[f2839,f2490])).
% 11.45/2.00 thf(f15144,plain,(
% 11.45/2.00 spl41_313 | ~spl41_26 | ~spl41_37 | ~spl41_44 | ~spl41_79),
% 11.45/2.00 inference(avatar_split_clause,[],[f2875,f2832,f2489,f2452,f2369,f15142])).
% 11.45/2.00 thf(f15142,plain,(
% 11.45/2.00 spl41_313 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_313])])).
% 11.45/2.00 thf(f2875,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)))))) ) | (~spl41_26 | ~spl41_37 | ~spl41_44 | ~spl41_79)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2874])).
% 11.45/2.00 thf(f2874,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = $false) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0)))))) ) | (~spl41_26 | ~spl41_37 | ~spl41_44 | ~spl41_79)),
% 11.45/2.00 inference(forward_demodulation,[],[f2868,f2466])).
% 11.45/2.00 thf(f2868,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | (~spl41_44 | ~spl41_79)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2862])).
% 11.45/2.00 thf(f2862,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | (~spl41_44 | ~spl41_79)),
% 11.45/2.00 inference(superposition,[],[f2833,f2490])).
% 11.45/2.00 thf(f15140,plain,(
% 11.45/2.00 spl41_312 | ~spl41_26 | ~spl41_78),
% 11.45/2.00 inference(avatar_split_clause,[],[f2814,f2800,f2369,f15138])).
% 11.45/2.00 thf(f15138,plain,(
% 11.45/2.00 spl41_312 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > nat,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_312])])).
% 11.45/2.00 thf(f2814,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1)))) ) | (~spl41_26 | ~spl41_78)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2813])).
% 11.45/2.00 thf(f2813,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,X1,X3)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1)))) ) | (~spl41_26 | ~spl41_78)),
% 11.45/2.00 inference(superposition,[],[f2801,f2370])).
% 11.45/2.00 thf(f15136,plain,(
% 11.45/2.00 spl41_311),
% 11.45/2.00 inference(avatar_split_clause,[],[f2215,f15134])).
% 11.45/2.00 thf(f15134,plain,(
% 11.45/2.00 spl41_311 <=> ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) | (vAPP(nat,nat,suc,zero_zero(nat)) = X0) | (zero_zero(nat) = X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_311])])).
% 11.45/2.00 thf(f2215,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) | (vAPP(nat,nat,suc,zero_zero(nat)) = X0) | (zero_zero(nat) = X0)) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2214])).
% 11.45/2.00 thf(f2214,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) | (vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2213])).
% 11.45/2.00 thf(f2213,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f2212])).
% 11.45/2.00 thf(f2212,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1199])).
% 11.45/2.00 thf(f1199,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f296])).
% 11.45/2.00 thf(f296,plain,(
% 11.45/2.00 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)))),
% 11.45/2.00 inference(fool_elimination,[],[f295])).
% 11.45/2.00 thf(f295,plain,(
% 11.45/2.00 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))) = (vAPP(nat,nat,suc,zero_zero(nat)) = X0) | (zero_zero(nat) = X0))),
% 11.45/2.00 inference(rectify,[],[f228])).
% 11.45/2.00 thf(f228,axiom,(
% 11.45/2.00 ! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,suc,zero_zero(nat))) = (vAPP(nat,nat,suc,zero_zero(nat)) = X2) | (zero_zero(nat) = X2))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_nat__leSuc0__conv)).
% 11.45/2.00 thf(f15132,plain,(
% 11.45/2.00 spl41_310),
% 11.45/2.00 inference(avatar_split_clause,[],[f2206,f15130])).
% 11.45/2.00 thf(f15130,plain,(
% 11.45/2.00 spl41_310 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | (vAPP(nat,nat,suc,zero_zero(nat)) = X0) | (zero_zero(nat) = X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_310])])).
% 11.45/2.00 thf(f2206,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | (vAPP(nat,nat,suc,zero_zero(nat)) = X0) | (zero_zero(nat) = X0)) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2205])).
% 11.45/2.00 thf(f2205,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | (vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 11.45/2.00 inference(not_proxy_clausification,[],[f2204])).
% 11.45/2.00 thf(f2204,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | (vAPP(nat,nat,suc,zero_zero(nat)) = X0) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2203])).
% 11.45/2.00 thf(f2203,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.45/2.00 inference(not_proxy_clausification,[],[f2202])).
% 11.45/2.00 thf(f2202,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f2194])).
% 11.45/2.00 thf(f2194,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1201])).
% 11.45/2.00 thf(f1201,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f300])).
% 11.45/2.00 thf(f300,plain,(
% 11.45/2.00 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))))),
% 11.45/2.00 inference(fool_elimination,[],[f299])).
% 11.45/2.00 thf(f299,plain,(
% 11.45/2.00 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0) = (vAPP(nat,nat,suc,zero_zero(nat)) != X0) & (zero_zero(nat) != X0))),
% 11.45/2.00 inference(rectify,[],[f201])).
% 11.45/2.00 thf(f201,axiom,(
% 11.45/2.00 ! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X2) = (vAPP(nat,nat,suc,zero_zero(nat)) != X2) & (zero_zero(nat) != X2))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_nat__grSuc0__conv)).
% 11.45/2.00 thf(f15128,plain,(
% 11.45/2.00 spl41_309),
% 11.45/2.00 inference(avatar_split_clause,[],[f1758,f15126])).
% 11.45/2.00 thf(f1758,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1757])).
% 11.45/2.00 thf(f1757,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1756])).
% 11.45/2.00 thf(f1756,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 11.45/2.00 inference(not_proxy_clausification,[],[f1755])).
% 11.45/2.00 thf(f1755,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1362])).
% 11.45/2.00 thf(f1362,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f596])).
% 11.45/2.00 thf(f596,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))),
% 11.45/2.00 inference(fool_elimination,[],[f595])).
% 11.45/2.00 thf(f595,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : ((X0 != X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))),
% 11.45/2.00 inference(rectify,[],[f40])).
% 11.45/2.00 thf(f40,axiom,(
% 11.45/2.00 ! [X3 : nat,X2 : nat] : ((X2 != X3) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_nat__neq__iff)).
% 11.45/2.00 thf(f15035,plain,(
% 11.45/2.00 spl41_308 | ~spl41_78),
% 11.45/2.00 inference(avatar_split_clause,[],[f2819,f2800,f15033])).
% 11.45/2.00 thf(f15033,plain,(
% 11.45/2.00 spl41_308 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > nat,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | (X1 = X3))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_308])])).
% 11.45/2.00 thf(f2819,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | (X1 = X3)) ) | ~spl41_78),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2818])).
% 11.45/2.00 thf(f2818,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) ) | ~spl41_78),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2809])).
% 11.45/2.00 thf(f2809,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) ) | ~spl41_78),
% 11.45/2.00 inference(primitive_instantiation,[],[f2801])).
% 11.45/2.00 thf(f15031,plain,(
% 11.45/2.00 spl41_307 | ~spl41_26 | ~spl41_77),
% 11.45/2.00 inference(avatar_split_clause,[],[f2798,f2788,f2369,f15029])).
% 11.45/2.00 thf(f15029,plain,(
% 11.45/2.00 spl41_307 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1))) | (linordered_ring(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_307])])).
% 11.45/2.00 thf(f2788,plain,(
% 11.45/2.00 spl41_77 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1))) | (linordered_ring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_77])])).
% 11.45/2.00 thf(f2798,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1))) | (linordered_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_77)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2797])).
% 11.45/2.00 thf(f2797,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1))) | (linordered_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_77)),
% 11.45/2.00 inference(superposition,[],[f2789,f2370])).
% 11.45/2.00 thf(f2789,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((linordered_ring(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)))) ) | ~spl41_77),
% 11.45/2.00 inference(avatar_component_clause,[],[f2788])).
% 11.45/2.00 thf(f15027,plain,(
% 11.45/2.00 spl41_306 | ~spl41_26 | ~spl41_76),
% 11.45/2.00 inference(avatar_split_clause,[],[f2796,f2784,f2369,f15025])).
% 11.45/2.00 thf(f15025,plain,(
% 11.45/2.00 spl41_306 <=> ! [X0 : $tType,X1 : X0] : ((linordered_ring(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_306])])).
% 11.45/2.00 thf(f2796,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((linordered_ring(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_76)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2795])).
% 11.45/2.00 thf(f2795,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (linordered_ring(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_76)),
% 11.45/2.00 inference(superposition,[],[f2785,f2370])).
% 11.45/2.00 thf(f14616,plain,(
% 11.45/2.00 spl41_305 | ~spl41_17 | ~spl41_86),
% 11.45/2.00 inference(avatar_split_clause,[],[f2956,f2942,f2325,f14614])).
% 11.45/2.00 thf(f2325,plain,(
% 11.45/2.00 spl41_17 <=> (semidom_divide(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_17])])).
% 11.45/2.00 thf(f2956,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1)) ) | (~spl41_17 | ~spl41_86)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2953])).
% 11.45/2.00 thf(f2953,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (zero_zero(nat) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1)) ) | (~spl41_17 | ~spl41_86)),
% 11.45/2.00 inference(superposition,[],[f2943,f2327])).
% 11.45/2.00 thf(f2327,plain,(
% 11.45/2.00 (semidom_divide(nat) = $true) | ~spl41_17),
% 11.45/2.00 inference(avatar_component_clause,[],[f2325])).
% 11.45/2.00 thf(f14612,plain,(
% 11.45/2.00 spl41_304 | ~spl41_17 | ~spl41_85),
% 11.45/2.00 inference(avatar_split_clause,[],[f2952,f2938,f2325,f14610])).
% 11.45/2.00 thf(f2952,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1)) ) | (~spl41_17 | ~spl41_85)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2949])).
% 11.45/2.00 thf(f2949,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (zero_zero(nat) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1)) ) | (~spl41_17 | ~spl41_85)),
% 11.45/2.00 inference(superposition,[],[f2939,f2327])).
% 11.45/2.00 thf(f14608,plain,(
% 11.45/2.00 spl41_303 | ~spl41_26 | ~spl41_75),
% 11.45/2.00 inference(avatar_split_clause,[],[f2781,f2767,f2369,f14606])).
% 11.45/2.00 thf(f14606,plain,(
% 11.45/2.00 spl41_303 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_303])])).
% 11.45/2.00 thf(f2767,plain,(
% 11.45/2.00 spl41_75 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_75])])).
% 11.45/2.00 thf(f2781,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_75)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2780])).
% 11.45/2.00 thf(f2780,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl41_26 | ~spl41_75)),
% 11.45/2.00 inference(superposition,[],[f2768,f2370])).
% 11.45/2.00 thf(f2768,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1))) ) | ~spl41_75),
% 11.45/2.00 inference(avatar_component_clause,[],[f2767])).
% 11.45/2.00 thf(f14604,plain,(
% 11.45/2.00 spl41_302 | ~spl41_46 | ~spl41_268),
% 11.45/2.00 inference(avatar_split_clause,[],[f12890,f8745,f2500,f14602])).
% 11.45/2.00 thf(f2500,plain,(
% 11.45/2.00 spl41_46 <=> ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (canoni770627133id_add(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_46])])).
% 11.45/2.00 thf(f8745,plain,(
% 11.45/2.00 spl41_268 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK10(X0),X1)),X1)) | (linordered_field(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_268])])).
% 11.45/2.00 thf(f12890,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((canoni770627133id_add(X0) != $true) | (linordered_field(X0) = $false)) ) | (~spl41_46 | ~spl41_268)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f12805])).
% 11.45/2.00 thf(f12805,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : (($true != $true) | (canoni770627133id_add(X0) != $true) | (linordered_field(X0) = $false)) ) | (~spl41_46 | ~spl41_268)),
% 11.45/2.00 inference(superposition,[],[f2501,f8746])).
% 11.45/2.00 thf(f8746,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK10(X0),X1)),X1)) | (linordered_field(X0) = $false)) ) | ~spl41_268),
% 11.45/2.00 inference(avatar_component_clause,[],[f8745])).
% 11.45/2.00 thf(f2501,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (canoni770627133id_add(X0) != $true)) ) | ~spl41_46),
% 11.45/2.00 inference(avatar_component_clause,[],[f2500])).
% 11.45/2.00 thf(f13725,plain,(
% 11.45/2.00 spl41_301 | ~spl41_38 | ~spl41_116),
% 11.45/2.00 inference(avatar_split_clause,[],[f3260,f3246,f2456,f13723])).
% 11.45/2.00 thf(f13723,plain,(
% 11.45/2.00 spl41_301 <=> ! [X0 : nat > nat] : ($true != vAPP(sTfun(nat,$o),$o,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),$o),sP2(nat),X0),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_301])])).
% 11.45/2.00 thf(f3260,plain,(
% 11.45/2.00 ( ! [X0 : nat > nat] : (($true != vAPP(sTfun(nat,$o),$o,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),$o),sP2(nat),X0),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat))))) ) | (~spl41_38 | ~spl41_116)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3257])).
% 11.45/2.00 thf(f3257,plain,(
% 11.45/2.00 ( ! [X0 : nat > nat] : (($true != $true) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),$o),sP2(nat),X0),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat))))) ) | (~spl41_38 | ~spl41_116)),
% 11.45/2.00 inference(superposition,[],[f3247,f2457])).
% 11.45/2.00 thf(f13717,plain,(
% 11.45/2.00 spl41_274 | spl41_300 | ~spl41_95),
% 11.45/2.00 inference(avatar_split_clause,[],[f3068,f3009,f13715,f8769])).
% 11.45/2.00 thf(f13715,plain,(
% 11.45/2.00 spl41_300 <=> ! [X0 : $tType,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK16(X0,$o),vNOT),X1)) | ($true != wellorder(X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_300])])).
% 11.45/2.00 thf(f3068,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK16(X0,$o),vNOT),X1)) | ($false = X2) | ($true != wellorder(X0))) ) | ~spl41_95),
% 11.45/2.00 inference(not_proxy_clausification,[],[f3067])).
% 11.45/2.00 thf(f3067,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK16(X0,$o),vNOT),X1)) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != wellorder(X0))) ) | ~spl41_95),
% 11.45/2.00 inference(not_proxy_clausification,[],[f3061])).
% 11.45/2.00 thf(f3061,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK16(X0,$o),vNOT),X1))) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != wellorder(X0))) ) | ~spl41_95),
% 11.45/2.00 inference(primitive_instantiation,[],[f3010])).
% 11.45/2.00 thf(f13702,plain,(
% 11.45/2.00 spl41_274 | spl41_299 | ~spl41_94),
% 11.45/2.00 inference(avatar_split_clause,[],[f3040,f3005,f13700,f8769])).
% 11.45/2.00 thf(f13700,plain,(
% 11.45/2.00 spl41_299 <=> ! [X0 : $tType,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK15(X0,$o),vNOT),X1)) | ($true != wellorder(X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_299])])).
% 11.45/2.00 thf(f3040,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK15(X0,$o),vNOT),X1)) | ($false = X2) | ($true != wellorder(X0))) ) | ~spl41_94),
% 11.45/2.00 inference(not_proxy_clausification,[],[f3039])).
% 11.45/2.00 thf(f3039,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK15(X0,$o),vNOT),X1)) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != wellorder(X0))) ) | ~spl41_94),
% 11.45/2.00 inference(not_proxy_clausification,[],[f3033])).
% 11.45/2.00 thf(f3033,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK15(X0,$o),vNOT),X1))) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != wellorder(X0))) ) | ~spl41_94),
% 11.45/2.00 inference(primitive_instantiation,[],[f3006])).
% 11.45/2.00 thf(f13698,plain,(
% 11.45/2.00 spl41_298 | ~spl41_26 | ~spl41_72),
% 11.45/2.00 inference(avatar_split_clause,[],[f2753,f2694,f2369,f13696])).
% 11.45/2.00 thf(f13696,plain,(
% 11.45/2.00 spl41_298 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK20,X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_298])])).
% 11.45/2.00 thf(f2694,plain,(
% 11.45/2.00 spl41_72 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_72])])).
% 11.45/2.00 thf(f2753,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK20,X0)))) ) | (~spl41_26 | ~spl41_72)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2752])).
% 11.45/2.00 thf(f2752,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK20,X0)))) ) | (~spl41_26 | ~spl41_72)),
% 11.45/2.00 inference(superposition,[],[f2695,f2370])).
% 11.45/2.00 thf(f2695,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) ) | ~spl41_72),
% 11.45/2.00 inference(avatar_component_clause,[],[f2694])).
% 11.45/2.00 thf(f13694,plain,(
% 11.45/2.00 spl41_297 | ~spl41_26 | ~spl41_71),
% 11.45/2.00 inference(avatar_split_clause,[],[f2741,f2690,f2369,f13692])).
% 11.45/2.00 thf(f13692,plain,(
% 11.45/2.00 spl41_297 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_297])])).
% 11.45/2.00 thf(f2690,plain,(
% 11.45/2.00 spl41_71 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_71])])).
% 11.45/2.00 thf(f2741,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,zero_zero(nat)))) ) | (~spl41_26 | ~spl41_71)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2740])).
% 11.45/2.00 thf(f2740,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,zero_zero(nat)))) ) | (~spl41_26 | ~spl41_71)),
% 11.45/2.00 inference(superposition,[],[f2691,f2370])).
% 11.45/2.00 thf(f2691,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0))) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl41_71),
% 11.45/2.00 inference(avatar_component_clause,[],[f2690])).
% 11.45/2.00 thf(f13690,plain,(
% 11.45/2.00 spl41_296 | ~spl41_26 | ~spl41_70),
% 11.45/2.00 inference(avatar_split_clause,[],[f2729,f2686,f2369,f13688])).
% 11.45/2.00 thf(f13688,plain,(
% 11.45/2.00 spl41_296 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK18,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_296])])).
% 11.45/2.00 thf(f2686,plain,(
% 11.45/2.00 spl41_70 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK18,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_70])])).
% 11.45/2.00 thf(f2729,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK18,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,zero_zero(nat)))) ) | (~spl41_26 | ~spl41_70)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2728])).
% 11.45/2.00 thf(f2728,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK18,X0))) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,zero_zero(nat)))) ) | (~spl41_26 | ~spl41_70)),
% 11.45/2.00 inference(superposition,[],[f2687,f2370])).
% 11.45/2.00 thf(f2687,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,zero_zero(nat))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK18,X0))) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl41_70),
% 11.45/2.00 inference(avatar_component_clause,[],[f2686])).
% 11.45/2.00 thf(f13686,plain,(
% 11.45/2.00 spl41_295 | ~spl41_26 | ~spl41_68),
% 11.45/2.00 inference(avatar_split_clause,[],[f2718,f2678,f2369,f13684])).
% 11.45/2.00 thf(f13684,plain,(
% 11.45/2.00 spl41_295 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($true != vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK17,X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_295])])).
% 11.45/2.00 thf(f2678,plain,(
% 11.45/2.00 spl41_68 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK17,X0))) | ($true != vAPP(nat,$o,X0,X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_68])])).
% 11.45/2.00 thf(f2718,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($true != vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK17,X0)))) ) | (~spl41_26 | ~spl41_68)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2717])).
% 11.45/2.00 thf(f2717,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($true != vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK17,X0)))) ) | (~spl41_26 | ~spl41_68)),
% 11.45/2.00 inference(superposition,[],[f2679,f2370])).
% 11.45/2.00 thf(f2679,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK17,X0))) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($true != vAPP(nat,$o,X0,X1))) ) | ~spl41_68),
% 11.45/2.00 inference(avatar_component_clause,[],[f2678])).
% 11.45/2.00 thf(f13682,plain,(
% 11.45/2.00 spl41_294 | ~spl41_26 | ~spl41_67),
% 11.45/2.00 inference(avatar_split_clause,[],[f2710,f2674,f2369,f13680])).
% 11.45/2.00 thf(f13680,plain,(
% 11.45/2.00 spl41_294 <=> ! [X0 : $tType] : ((times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))) | (ab_semigroup_mult(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_294])])).
% 11.45/2.00 thf(f2674,plain,(
% 11.45/2.00 spl41_67 <=> ! [X0 : $tType] : ((times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))) | (ab_semigroup_mult(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_67])])).
% 11.45/2.00 thf(f2710,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))) | (ab_semigroup_mult(X0) = $false)) ) | (~spl41_26 | ~spl41_67)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2709])).
% 11.45/2.00 thf(f2709,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : (($true != $true) | (times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))) | (ab_semigroup_mult(X0) = $false)) ) | (~spl41_26 | ~spl41_67)),
% 11.45/2.00 inference(superposition,[],[f2675,f2370])).
% 11.45/2.00 thf(f2675,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((ab_semigroup_mult(X0) != $true) | (times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0)))) ) | ~spl41_67),
% 11.45/2.00 inference(avatar_component_clause,[],[f2674])).
% 11.45/2.00 thf(f13678,plain,(
% 11.45/2.00 spl41_293 | ~spl41_26 | ~spl41_66),
% 11.45/2.00 inference(avatar_split_clause,[],[f2703,f2670,f2369,f13676])).
% 11.45/2.00 thf(f13676,plain,(
% 11.45/2.00 spl41_293 <=> ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_293])])).
% 11.45/2.00 thf(f2670,plain,(
% 11.45/2.00 spl41_66 <=> ! [X2 : nat,X0 : nat > $o] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0))) | ($true != vAPP(nat,$o,X0,X2)) | ($true = vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_66])])).
% 11.45/2.00 thf(f2703,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0)))) ) | (~spl41_26 | ~spl41_66)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2702])).
% 11.45/2.00 thf(f2702,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0)))) ) | (~spl41_26 | ~spl41_66)),
% 11.45/2.00 inference(superposition,[],[f2671,f2370])).
% 11.45/2.00 thf(f2671,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat > $o] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0))) | ($true != vAPP(nat,$o,X0,X2)) | ($true = vAPP(nat,$o,X0,zero_zero(nat)))) ) | ~spl41_66),
% 11.45/2.00 inference(avatar_component_clause,[],[f2670])).
% 11.45/2.00 thf(f13326,plain,(
% 11.45/2.00 spl41_292 | ~spl41_30 | ~spl41_134),
% 11.45/2.00 inference(avatar_split_clause,[],[f3582,f3424,f2416,f13324])).
% 11.45/2.00 thf(f13324,plain,(
% 11.45/2.00 spl41_292 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),$o),sP2(nat),suc),X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_292])])).
% 11.45/2.00 thf(f2416,plain,(
% 11.45/2.00 spl41_30 <=> ! [X0 : nat] : (zero_zero(nat) != vAPP(nat,nat,suc,X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_30])])).
% 11.45/2.00 thf(f3582,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),$o),sP2(nat),suc),X0))) ) | (~spl41_30 | ~spl41_134)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3462])).
% 11.45/2.00 thf(f3462,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : ((zero_zero(nat) != zero_zero(nat)) | ($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),$o),sP2(nat),suc),X0))) ) | (~spl41_30 | ~spl41_134)),
% 11.45/2.00 inference(superposition,[],[f2417,f3425])).
% 11.45/2.00 thf(f2417,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) != vAPP(nat,nat,suc,X0))) ) | ~spl41_30),
% 11.45/2.00 inference(avatar_component_clause,[],[f2416])).
% 11.45/2.00 thf(f13322,plain,(
% 11.45/2.00 spl41_291 | ~spl41_48 | ~spl41_97),
% 11.45/2.00 inference(avatar_split_clause,[],[f3098,f3019,f2510,f13320])).
% 11.45/2.00 thf(f13320,plain,(
% 11.45/2.00 spl41_291 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_291])])).
% 11.45/2.00 thf(f3019,plain,(
% 11.45/2.00 spl41_97 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_97])])).
% 11.45/2.00 thf(f3098,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))))) ) | (~spl41_48 | ~spl41_97)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3094])).
% 11.45/2.00 thf(f3094,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))))) ) | (~spl41_48 | ~spl41_97)),
% 11.45/2.00 inference(superposition,[],[f3020,f2511])).
% 11.45/2.00 thf(f3020,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))) ) | ~spl41_97),
% 11.45/2.00 inference(avatar_component_clause,[],[f3019])).
% 11.45/2.00 thf(f13318,plain,(
% 11.45/2.00 spl41_290 | ~spl41_82),
% 11.45/2.00 inference(avatar_split_clause,[],[f2920,f2846,f13316])).
% 11.45/2.00 thf(f13316,plain,(
% 11.45/2.00 spl41_290 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0) | (X0 = X1) | (zero_zero(nat) != X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_290])])).
% 11.45/2.00 thf(f2920,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0) | (X0 = X1) | (zero_zero(nat) != X0)) ) | ~spl41_82),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2919])).
% 11.45/2.00 thf(f2919,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_82),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2918])).
% 11.45/2.00 thf(f2918,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_82),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2911])).
% 11.45/2.00 thf(f2911,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_82),
% 11.45/2.00 inference(primitive_instantiation,[],[f2847])).
% 11.45/2.00 thf(f13314,plain,(
% 11.45/2.00 spl41_289 | ~spl41_81),
% 11.45/2.00 inference(avatar_split_clause,[],[f2907,f2842,f13312])).
% 11.45/2.00 thf(f13312,plain,(
% 11.45/2.00 spl41_289 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0) | (X0 = X1) | (zero_zero(nat) != X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_289])])).
% 11.45/2.00 thf(f2907,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0) | (X0 = X1) | (zero_zero(nat) != X0)) ) | ~spl41_81),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2906])).
% 11.45/2.00 thf(f2906,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_81),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2905])).
% 11.45/2.00 thf(f2905,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_81),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2898])).
% 11.45/2.00 thf(f2898,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_81),
% 11.45/2.00 inference(primitive_instantiation,[],[f2843])).
% 11.45/2.00 thf(f13310,plain,(
% 11.45/2.00 spl41_288 | ~spl41_64),
% 11.45/2.00 inference(avatar_split_clause,[],[f2658,f2648,f13308])).
% 11.45/2.00 thf(f13308,plain,(
% 11.45/2.00 spl41_288 <=> ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : ((vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),vAPP(list(X0),sTfun(list(X0),$o),vEQ(list(X0)),X1)) != X1) | (X1 = X2))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_288])])).
% 11.45/2.00 thf(f2658,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : ((vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),vAPP(list(X0),sTfun(list(X0),$o),vEQ(list(X0)),X1)) != X1) | (X1 = X2)) ) | ~spl41_64),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2657])).
% 11.45/2.00 thf(f2657,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : ((vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),vAPP(list(X0),sTfun(list(X0),$o),vEQ(list(X0)),X1)) != X1) | ($true = vAPP(list(X0),$o,vAPP(list(X0),sTfun(list(X0),$o),vEQ(list(X0)),X1),X2))) ) | ~spl41_64),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2654])).
% 11.45/2.00 thf(f2654,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (($true != vAPP(list(X0),$o,vAPP(list(X0),sTfun(list(X0),$o),vEQ(list(X0)),X1),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),vAPP(list(X0),sTfun(list(X0),$o),vEQ(list(X0)),X1)))) | ($true = vAPP(list(X0),$o,vAPP(list(X0),sTfun(list(X0),$o),vEQ(list(X0)),X1),X2))) ) | ~spl41_64),
% 11.45/2.00 inference(primitive_instantiation,[],[f2649])).
% 11.45/2.00 thf(f13306,plain,(
% 11.45/2.00 spl41_287 | ~spl41_221 | ~spl41_268),
% 11.45/2.00 inference(avatar_split_clause,[],[f12903,f8745,f4793,f13303])).
% 11.45/2.00 thf(f13303,plain,(
% 11.45/2.00 spl41_287 <=> ($false = linordered_field(nat))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_287])])).
% 11.45/2.00 thf(f4793,plain,(
% 11.45/2.00 spl41_221 <=> ! [X0 : nat] : ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_221])])).
% 11.45/2.00 thf(f12903,plain,(
% 11.45/2.00 ($false = linordered_field(nat)) | (~spl41_221 | ~spl41_268)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f12792])).
% 11.45/2.00 thf(f12792,plain,(
% 11.45/2.00 ($true = $false) | ($false = linordered_field(nat)) | (~spl41_221 | ~spl41_268)),
% 11.45/2.00 inference(superposition,[],[f8746,f4794])).
% 11.45/2.00 thf(f4794,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | ~spl41_221),
% 11.45/2.00 inference(avatar_component_clause,[],[f4793])).
% 11.45/2.00 thf(f13301,plain,(
% 11.45/2.00 spl41_286),
% 11.45/2.00 inference(avatar_split_clause,[],[f2164,f13299])).
% 11.45/2.00 thf(f13299,plain,(
% 11.45/2.00 spl41_286 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) | (semiri1193490041visors(X0) != $true) | (zero_zero(X0) = X2) | (zero_zero(X0) = X1))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_286])])).
% 11.45/2.00 thf(f2164,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) | (semiri1193490041visors(X0) != $true) | (zero_zero(X0) = X2) | (zero_zero(X0) = X1)) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2163])).
% 11.45/2.00 thf(f2163,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) | (semiri1193490041visors(X0) != $true) | (zero_zero(X0) = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2162])).
% 11.45/2.00 thf(f2162,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) | (semiri1193490041visors(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f2161])).
% 11.45/2.00 thf(f2161,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) | (semiri1193490041visors(X0) != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2160])).
% 11.45/2.00 thf(f2160,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (semiri1193490041visors(X0) != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1225])).
% 11.45/2.00 thf(f1225,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2))) | (semiri1193490041visors(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f864])).
% 11.45/2.00 thf(f864,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2))) | (semiri1193490041visors(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f340])).
% 11.45/2.00 thf(f340,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((semiri1193490041visors(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2))))),
% 11.45/2.00 inference(fool_elimination,[],[f339])).
% 11.45/2.00 thf(f339,plain,(
% 11.45/2.00 ! [X0 : $tType] : (semiri1193490041visors(X0) => ! [X1 : X0,X2 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) = (zero_zero(X0) = X2) | (zero_zero(X0) = X1)))),
% 11.45/2.00 inference(rectify,[],[f115])).
% 11.45/2.00 thf(f115,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (semiri1193490041visors(X0) => ! [X9 : X0,X11 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)) = (zero_zero(X0) = X11) | (zero_zero(X0) = X9)))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_mult__eq__0__iff)).
% 11.45/2.00 thf(f13297,plain,(
% 11.45/2.00 spl41_285),
% 11.45/2.00 inference(avatar_split_clause,[],[f1956,f13295])).
% 11.45/2.00 thf(f13295,plain,(
% 11.45/2.00 spl41_285 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X2) | (field(X0) != $true) | (zero_zero(X0) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)) | (zero_zero(X0) = X1))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_285])])).
% 11.45/2.00 thf(f1956,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X2) | (field(X0) != $true) | (zero_zero(X0) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)) | (zero_zero(X0) = X1)) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1955])).
% 11.45/2.00 thf(f1955,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X2) | (field(X0) != $true) | (zero_zero(X0) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1954])).
% 11.45/2.00 thf(f1954,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = X2) | (field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1953])).
% 11.45/2.00 thf(f1953,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)) | (field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1945])).
% 11.45/2.00 thf(f1945,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2))) | (field(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1301])).
% 11.45/2.00 thf(f1301,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f963])).
% 11.45/2.00 thf(f963,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f484])).
% 11.45/2.00 thf(f484,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))))),
% 11.45/2.00 inference(fool_elimination,[],[f483])).
% 11.45/2.00 thf(f483,plain,(
% 11.45/2.00 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)) = (zero_zero(X0) = X2) | (zero_zero(X0) = X1)))),
% 11.45/2.00 inference(rectify,[],[f119])).
% 11.45/2.00 thf(f119,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (field(X0) => ! [X9 : X0,X11 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X11)) = (zero_zero(X0) = X11) | (zero_zero(X0) = X9)))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_divide__eq__0__iff)).
% 11.45/2.00 thf(f13181,plain,(
% 11.45/2.00 spl41_284 | ~spl41_26 | ~spl41_65),
% 11.45/2.00 inference(avatar_split_clause,[],[f2666,f2660,f2369,f13179])).
% 11.45/2.00 thf(f13179,plain,(
% 11.45/2.00 spl41_284 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK12,X0)) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_284])])).
% 11.45/2.00 thf(f2660,plain,(
% 11.45/2.00 spl41_65 <=> ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK12,X0)) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_65])])).
% 11.45/2.00 thf(f2666,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK12,X0)) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) ) | (~spl41_26 | ~spl41_65)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2665])).
% 11.45/2.00 thf(f2665,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | (vAPP(nat,nat,suc,vAPP(nat,nat,sK12,X0)) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) ) | (~spl41_26 | ~spl41_65)),
% 11.45/2.00 inference(superposition,[],[f2661,f2370])).
% 11.45/2.00 thf(f2661,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (vAPP(nat,nat,suc,vAPP(nat,nat,sK12,X0)) = X0)) ) | ~spl41_65),
% 11.45/2.00 inference(avatar_component_clause,[],[f2660])).
% 11.45/2.00 thf(f13012,plain,(
% 11.45/2.00 spl41_283 | ~spl41_38 | ~spl41_100),
% 11.45/2.00 inference(avatar_split_clause,[],[f3134,f3115,f2456,f13010])).
% 11.45/2.00 thf(f13010,plain,(
% 11.45/2.00 spl41_283 <=> ! [X0 : nat] : ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_283])])).
% 11.45/2.00 thf(f3134,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat))))) ) | (~spl41_38 | ~spl41_100)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3131])).
% 11.45/2.00 thf(f3131,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat))))) ) | (~spl41_38 | ~spl41_100)),
% 11.45/2.00 inference(superposition,[],[f3116,f2457])).
% 11.45/2.00 thf(f13008,plain,(
% 11.45/2.00 spl41_282 | ~spl41_26 | ~spl41_64),
% 11.45/2.00 inference(avatar_split_clause,[],[f2656,f2648,f2369,f13006])).
% 11.45/2.00 thf(f13006,plain,(
% 11.45/2.00 spl41_282 <=> ! [X0 : $tType,X2 : list(X0),X1 : list(X0) > $o] : (($true = vAPP(list(X0),$o,X1,X2)) | ($false = vAPP(list(X0),$o,X1,vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_282])])).
% 11.45/2.00 thf(f2656,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0) > $o] : (($true = vAPP(list(X0),$o,X1,X2)) | ($false = vAPP(list(X0),$o,X1,vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1)))) ) | (~spl41_26 | ~spl41_64)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2655])).
% 11.45/2.00 thf(f2655,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0) > $o] : (($true != $true) | ($true = vAPP(list(X0),$o,X1,X2)) | ($false = vAPP(list(X0),$o,X1,vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1)))) ) | (~spl41_26 | ~spl41_64)),
% 11.45/2.00 inference(superposition,[],[f2649,f2370])).
% 11.45/2.00 thf(f12949,plain,(
% 11.45/2.00 spl41_281 | ~spl41_80),
% 11.45/2.00 inference(avatar_split_clause,[],[f2892,f2838,f12947])).
% 11.45/2.00 thf(f12947,plain,(
% 11.45/2.00 spl41_281 <=> ! [X0 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_281])])).
% 11.45/2.00 thf(f2892,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl41_80),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2876])).
% 11.45/2.00 thf(f2876,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat))) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl41_80),
% 11.45/2.00 inference(leibniz_equality_elimination,[],[f2839])).
% 11.45/2.00 thf(f12945,plain,(
% 11.45/2.00 spl41_280 | ~spl41_79),
% 11.45/2.00 inference(avatar_split_clause,[],[f2873,f2832,f12943])).
% 11.45/2.00 thf(f12943,plain,(
% 11.45/2.00 spl41_280 <=> ! [X0 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_280])])).
% 11.45/2.00 thf(f2873,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) = X0) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl41_79),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2857])).
% 11.45/2.00 thf(f2857,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat))) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl41_79),
% 11.45/2.00 inference(leibniz_equality_elimination,[],[f2833])).
% 11.45/2.00 thf(f12941,plain,(
% 11.45/2.00 spl41_279 | ~spl41_12 | ~spl41_67),
% 11.45/2.00 inference(avatar_split_clause,[],[f2711,f2674,f2300,f12938])).
% 11.45/2.00 thf(f12938,plain,(
% 11.45/2.00 spl41_279 <=> (times_times(nat) = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,times_times(nat)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_279])])).
% 11.45/2.00 thf(f2711,plain,(
% 11.45/2.00 (times_times(nat) = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,times_times(nat))) | (~spl41_12 | ~spl41_67)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2708])).
% 11.45/2.00 thf(f2708,plain,(
% 11.45/2.00 ($true != $true) | (times_times(nat) = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,times_times(nat))) | (~spl41_12 | ~spl41_67)),
% 11.45/2.00 inference(superposition,[],[f2675,f2302])).
% 11.45/2.00 thf(f12787,plain,(
% 11.45/2.00 ~spl41_277 | spl41_278 | spl41_252 | ~spl41_267),
% 11.45/2.00 inference(avatar_split_clause,[],[f12713,f8741,f6270,f12784,f12780])).
% 11.45/2.00 thf(f12784,plain,(
% 11.45/2.00 spl41_278 <=> ($false = linordered_field($o))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_278])])).
% 11.45/2.00 thf(f8741,plain,(
% 11.45/2.00 spl41_267 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK9(X0),X1))) | (linordered_field(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_267])])).
% 11.45/2.00 thf(f12713,plain,(
% 11.45/2.00 ($false = linordered_field($o)) | ($true != vAPP($o,$o,sK9($o),$true)) | (spl41_252 | ~spl41_267)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f12662])).
% 11.45/2.00 thf(f12662,plain,(
% 11.45/2.00 ($true != $true) | ($false = linordered_field($o)) | ($true != vAPP($o,$o,sK9($o),$true)) | (spl41_252 | ~spl41_267)),
% 11.45/2.00 inference(constrained_superposition,[],[f6272,f8742])).
% 11.45/2.00 thf(f8742,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK9(X0),X1))) | (linordered_field(X0) = $false)) ) | ~spl41_267),
% 11.45/2.00 inference(avatar_component_clause,[],[f8741])).
% 11.45/2.00 thf(f6272,plain,(
% 11.45/2.00 ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$true)) | spl41_252),
% 11.45/2.00 inference(avatar_component_clause,[],[f6270])).
% 11.45/2.00 thf(f11337,plain,(
% 11.45/2.00 spl41_276 | ~spl41_232 | ~spl41_248 | ~spl41_251),
% 11.45/2.00 inference(avatar_split_clause,[],[f6820,f6266,f6251,f5226,f11334])).
% 11.45/2.00 thf(f11334,plain,(
% 11.45/2.00 spl41_276 <=> ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),$false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_276])])).
% 11.45/2.00 thf(f5226,plain,(
% 11.45/2.00 spl41_232 <=> ! [X0 : $tType] : ((linord1659791738miring(X0) != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_232])])).
% 11.45/2.00 thf(f6266,plain,(
% 11.45/2.00 spl41_251 <=> ($true = linord1659791738miring($o))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_251])])).
% 11.45/2.00 thf(f6820,plain,(
% 11.45/2.00 ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$false),$false)) | (~spl41_232 | ~spl41_248 | ~spl41_251)),
% 11.45/2.00 inference(forward_demodulation,[],[f6819,f6253])).
% 11.45/2.00 thf(f6819,plain,(
% 11.45/2.00 ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),zero_zero($o)),zero_zero($o))) | (~spl41_232 | ~spl41_251)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f6816])).
% 11.45/2.00 thf(f6816,plain,(
% 11.45/2.00 ($true != $true) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),zero_zero($o)),zero_zero($o))) | (~spl41_232 | ~spl41_251)),
% 11.45/2.00 inference(superposition,[],[f5227,f6267])).
% 11.45/2.00 thf(f6267,plain,(
% 11.45/2.00 ($true = linord1659791738miring($o)) | ~spl41_251),
% 11.45/2.00 inference(avatar_component_clause,[],[f6266])).
% 11.45/2.00 thf(f5227,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((linord1659791738miring(X0) != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) = $false)) ) | ~spl41_232),
% 11.45/2.00 inference(avatar_component_clause,[],[f5226])).
% 11.45/2.00 thf(f9137,plain,(
% 11.45/2.00 ~spl41_10 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9136])).
% 11.45/2.00 thf(f9136,plain,(
% 11.45/2.00 $false | (~spl41_10 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8783])).
% 11.45/2.00 thf(f8783,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_10 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2292,f8770])).
% 11.45/2.00 thf(f8770,plain,(
% 11.45/2.00 ( ! [X1 : $o] : (($false = X1)) ) | ~spl41_274),
% 11.45/2.00 inference(avatar_component_clause,[],[f8769])).
% 11.45/2.00 thf(f2292,plain,(
% 11.45/2.00 (size(nat) = $true) | ~spl41_10),
% 11.45/2.00 inference(avatar_component_clause,[],[f2290])).
% 11.45/2.00 thf(f2290,plain,(
% 11.45/2.00 spl41_10 <=> (size(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_10])])).
% 11.45/2.00 thf(f9135,plain,(
% 11.45/2.00 ~spl41_25 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9134])).
% 11.45/2.00 thf(f9134,plain,(
% 11.45/2.00 $false | (~spl41_25 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8784])).
% 11.45/2.00 thf(f8784,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_25 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2366,f8770])).
% 11.45/2.00 thf(f2366,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : (($true = size(list(X0)))) ) | ~spl41_25),
% 11.45/2.00 inference(avatar_component_clause,[],[f2365])).
% 11.45/2.00 thf(f2365,plain,(
% 11.45/2.00 spl41_25 <=> ! [X0 : $tType] : ($true = size(list(X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_25])])).
% 11.45/2.00 thf(f9133,plain,(
% 11.45/2.00 ~spl41_27 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9132])).
% 11.45/2.00 thf(f9132,plain,(
% 11.45/2.00 $false | (~spl41_27 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8785])).
% 11.45/2.00 thf(f8785,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_27 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2374,f8770])).
% 11.45/2.00 thf(f2374,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType] : (($true = size(product_prod(X0,X1)))) ) | ~spl41_27),
% 11.45/2.00 inference(avatar_component_clause,[],[f2373])).
% 11.45/2.00 thf(f2373,plain,(
% 11.45/2.00 spl41_27 <=> ! [X1 : $tType,X0 : $tType] : ($true = size(product_prod(X0,X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_27])])).
% 11.45/2.00 thf(f9131,plain,(
% 11.45/2.00 ~spl41_6 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9130])).
% 11.45/2.00 thf(f9130,plain,(
% 11.45/2.00 $false | (~spl41_6 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8786])).
% 11.45/2.00 thf(f8786,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_6 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2272,f8770])).
% 11.45/2.00 thf(f2272,plain,(
% 11.45/2.00 (zero(nat) = $true) | ~spl41_6),
% 11.45/2.00 inference(avatar_component_clause,[],[f2270])).
% 11.45/2.00 thf(f2270,plain,(
% 11.45/2.00 spl41_6 <=> (zero(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_6])])).
% 11.45/2.00 thf(f9129,plain,(
% 11.45/2.00 ~spl41_18 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9128])).
% 11.45/2.00 thf(f9128,plain,(
% 11.45/2.00 $false | (~spl41_18 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8798])).
% 11.45/2.00 thf(f8798,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_18 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2332,f8770])).
% 11.45/2.00 thf(f2332,plain,(
% 11.45/2.00 (order($o) = $true) | ~spl41_18),
% 11.45/2.00 inference(avatar_component_clause,[],[f2330])).
% 11.45/2.00 thf(f2330,plain,(
% 11.45/2.00 spl41_18 <=> (order($o) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_18])])).
% 11.45/2.00 thf(f9127,plain,(
% 11.45/2.00 ~spl41_42 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9126])).
% 11.45/2.00 thf(f9126,plain,(
% 11.45/2.00 $false | (~spl41_42 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8799])).
% 11.45/2.00 thf(f8799,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_42 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2481,f8770])).
% 11.45/2.00 thf(f2481,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : (($true = order(sTfun(X0,$o)))) ) | ~spl41_42),
% 11.45/2.00 inference(avatar_component_clause,[],[f2480])).
% 11.45/2.00 thf(f2480,plain,(
% 11.45/2.00 spl41_42 <=> ! [X0 : $tType] : ($true = order(sTfun(X0,$o)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_42])])).
% 11.45/2.00 thf(f9125,plain,(
% 11.45/2.00 ~spl41_74 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9124])).
% 11.45/2.00 thf(f9124,plain,(
% 11.45/2.00 $false | (~spl41_74 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8800])).
% 11.45/2.00 thf(f8800,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_74 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2764,f8770])).
% 11.45/2.00 thf(f2764,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,$o))))) ) | ~spl41_74),
% 11.45/2.00 inference(avatar_component_clause,[],[f2763])).
% 11.45/2.00 thf(f2763,plain,(
% 11.45/2.00 spl41_74 <=> ! [X1 : $tType,X0 : $tType] : ($true = order(sTfun(X1,sTfun(X0,$o))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_74])])).
% 11.45/2.00 thf(f9123,plain,(
% 11.45/2.00 ~spl41_108 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9122])).
% 11.45/2.00 thf(f9122,plain,(
% 11.45/2.00 $false | (~spl41_108 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8801])).
% 11.45/2.00 thf(f8801,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_108 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f3180,f8770])).
% 11.45/2.00 thf(f3180,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))) ) | ~spl41_108),
% 11.45/2.00 inference(avatar_component_clause,[],[f3179])).
% 11.45/2.00 thf(f3179,plain,(
% 11.45/2.00 spl41_108 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_108])])).
% 11.45/2.00 thf(f9121,plain,(
% 11.45/2.00 ~spl41_176 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9120])).
% 11.45/2.00 thf(f9120,plain,(
% 11.45/2.00 $false | (~spl41_176 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8802])).
% 11.45/2.00 thf(f8802,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_176 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f3993,f8770])).
% 11.45/2.00 thf(f3993,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = order(sTfun(X3,sTfun(X0,sTfun(X1,sTfun(X2,nat))))))) ) | ~spl41_176),
% 11.45/2.00 inference(avatar_component_clause,[],[f3992])).
% 11.45/2.00 thf(f3992,plain,(
% 11.45/2.00 spl41_176 <=> ! [X3 : $tType,X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X3,sTfun(X0,sTfun(X1,sTfun(X2,nat))))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_176])])).
% 11.45/2.00 thf(f9119,plain,(
% 11.45/2.00 ~spl41_177 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9118])).
% 11.45/2.00 thf(f9118,plain,(
% 11.45/2.00 $false | (~spl41_177 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8803])).
% 11.45/2.00 thf(f8803,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_177 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f4080,f8770])).
% 11.45/2.00 thf(f4080,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = order(sTfun(X3,sTfun(X0,sTfun(X1,sTfun(X2,$o))))))) ) | ~spl41_177),
% 11.45/2.00 inference(avatar_component_clause,[],[f4079])).
% 11.45/2.00 thf(f4079,plain,(
% 11.45/2.00 spl41_177 <=> ! [X3 : $tType,X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X3,sTfun(X0,sTfun(X1,sTfun(X2,$o))))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_177])])).
% 11.45/2.00 thf(f9117,plain,(
% 11.45/2.00 ~spl41_233 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9116])).
% 11.45/2.00 thf(f9116,plain,(
% 11.45/2.00 $false | (~spl41_233 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8804])).
% 11.45/2.00 thf(f8804,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_233 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f5231,f8770])).
% 11.45/2.00 thf(f5231,plain,(
% 11.45/2.00 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = order(sTfun(X4,sTfun(X0,sTfun(X1,sTfun(X2,sTfun(X3,nat)))))))) ) | ~spl41_233),
% 11.45/2.00 inference(avatar_component_clause,[],[f5230])).
% 11.45/2.00 thf(f5230,plain,(
% 11.45/2.00 spl41_233 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X4 : $tType] : ($true = order(sTfun(X4,sTfun(X0,sTfun(X1,sTfun(X2,sTfun(X3,nat)))))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_233])])).
% 11.45/2.00 thf(f9115,plain,(
% 11.45/2.00 ~spl41_101 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9114])).
% 11.45/2.00 thf(f9114,plain,(
% 11.45/2.00 $false | (~spl41_101 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8805])).
% 11.45/2.00 thf(f8805,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_101 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f3126,f8770])).
% 11.45/2.00 thf(f3126,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))) ) | ~spl41_101),
% 11.45/2.00 inference(avatar_component_clause,[],[f3125])).
% 11.45/2.00 thf(f3125,plain,(
% 11.45/2.00 spl41_101 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_101])])).
% 11.45/2.00 thf(f9113,plain,(
% 11.45/2.00 ~spl41_69 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9112])).
% 11.45/2.00 thf(f9112,plain,(
% 11.45/2.00 $false | (~spl41_69 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8806])).
% 11.45/2.00 thf(f8806,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_69 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2683,f8770])).
% 11.45/2.00 thf(f2683,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,nat))))) ) | ~spl41_69),
% 11.45/2.00 inference(avatar_component_clause,[],[f2682])).
% 11.45/2.00 thf(f2682,plain,(
% 11.45/2.00 spl41_69 <=> ! [X1 : $tType,X0 : $tType] : ($true = order(sTfun(X1,sTfun(X0,nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_69])])).
% 11.45/2.00 thf(f9111,plain,(
% 11.45/2.00 ~spl41_36 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9110])).
% 11.45/2.00 thf(f9110,plain,(
% 11.45/2.00 $false | (~spl41_36 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8807])).
% 11.45/2.00 thf(f8807,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_36 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2449,f8770])).
% 11.45/2.00 thf(f2449,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : (($true = order(sTfun(X0,nat)))) ) | ~spl41_36),
% 11.45/2.00 inference(avatar_component_clause,[],[f2448])).
% 11.45/2.00 thf(f2448,plain,(
% 11.45/2.00 spl41_36 <=> ! [X0 : $tType] : ($true = order(sTfun(X0,nat)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_36])])).
% 11.45/2.00 thf(f9109,plain,(
% 11.45/2.00 ~spl41_20 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9108])).
% 11.45/2.00 thf(f9108,plain,(
% 11.45/2.00 $false | (~spl41_20 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8808])).
% 11.45/2.00 thf(f8808,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_20 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2342,f8770])).
% 11.45/2.00 thf(f2342,plain,(
% 11.45/2.00 (order(nat) = $true) | ~spl41_20),
% 11.45/2.00 inference(avatar_component_clause,[],[f2340])).
% 11.45/2.00 thf(f2340,plain,(
% 11.45/2.00 spl41_20 <=> (order(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_20])])).
% 11.45/2.00 thf(f9107,plain,(
% 11.45/2.00 ~spl41_11 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9106])).
% 11.45/2.00 thf(f9106,plain,(
% 11.45/2.00 $false | (~spl41_11 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8809])).
% 11.45/2.00 thf(f8809,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_11 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2297,f8770])).
% 11.45/2.00 thf(f2297,plain,(
% 11.45/2.00 (mult_zero(nat) = $true) | ~spl41_11),
% 11.45/2.00 inference(avatar_component_clause,[],[f2295])).
% 11.45/2.00 thf(f2295,plain,(
% 11.45/2.00 spl41_11 <=> (mult_zero(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_11])])).
% 11.45/2.00 thf(f9105,plain,(
% 11.45/2.00 ~spl41_19 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9104])).
% 11.45/2.00 thf(f9104,plain,(
% 11.45/2.00 $false | (~spl41_19 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8812])).
% 11.45/2.00 thf(f8812,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_19 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2337,f8770])).
% 11.45/2.00 thf(f2337,plain,(
% 11.45/2.00 (linorder($o) = $true) | ~spl41_19),
% 11.45/2.00 inference(avatar_component_clause,[],[f2335])).
% 11.45/2.00 thf(f2335,plain,(
% 11.45/2.00 spl41_19 <=> (linorder($o) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_19])])).
% 11.45/2.00 thf(f9103,plain,(
% 11.45/2.00 ~spl41_21 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9102])).
% 11.45/2.00 thf(f9102,plain,(
% 11.45/2.00 $false | (~spl41_21 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8813])).
% 11.45/2.00 thf(f8813,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_21 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2347,f8770])).
% 11.45/2.00 thf(f2347,plain,(
% 11.45/2.00 (linorder(nat) = $true) | ~spl41_21),
% 11.45/2.00 inference(avatar_component_clause,[],[f2345])).
% 11.45/2.00 thf(f2345,plain,(
% 11.45/2.00 spl41_21 <=> (linorder(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_21])])).
% 11.45/2.00 thf(f9101,plain,(
% 11.45/2.00 ~spl41_9 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9100])).
% 11.45/2.00 thf(f9100,plain,(
% 11.45/2.00 $false | (~spl41_9 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8818])).
% 11.45/2.00 thf(f8818,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_9 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2287,f8770])).
% 11.45/2.00 thf(f9099,plain,(
% 11.45/2.00 ~spl41_8 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9098])).
% 11.45/2.00 thf(f9098,plain,(
% 11.45/2.00 $false | (~spl41_8 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8823])).
% 11.45/2.00 thf(f8823,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_8 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2282,f8770])).
% 11.45/2.00 thf(f2282,plain,(
% 11.45/2.00 (semiring_bits(nat) = $true) | ~spl41_8),
% 11.45/2.00 inference(avatar_component_clause,[],[f2280])).
% 11.45/2.00 thf(f2280,plain,(
% 11.45/2.00 spl41_8 <=> (semiring_bits(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_8])])).
% 11.45/2.00 thf(f9097,plain,(
% 11.45/2.00 ~spl41_17 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9096])).
% 11.45/2.00 thf(f9096,plain,(
% 11.45/2.00 $false | (~spl41_17 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8826])).
% 11.45/2.00 thf(f8826,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_17 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2327,f8770])).
% 11.45/2.00 thf(f9095,plain,(
% 11.45/2.00 ~spl41_5 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9094])).
% 11.45/2.00 thf(f9094,plain,(
% 11.45/2.00 $false | (~spl41_5 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8831])).
% 11.45/2.00 thf(f8831,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_5 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2267,f8770])).
% 11.45/2.00 thf(f9093,plain,(
% 11.45/2.00 ~spl41_16 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9092])).
% 11.45/2.00 thf(f9092,plain,(
% 11.45/2.00 $false | (~spl41_16 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8835])).
% 11.45/2.00 thf(f8835,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_16 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2322,f8770])).
% 11.45/2.00 thf(f9091,plain,(
% 11.45/2.00 ~spl41_12 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9090])).
% 11.45/2.00 thf(f9090,plain,(
% 11.45/2.00 $false | (~spl41_12 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8838])).
% 11.45/2.00 thf(f8838,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_12 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2302,f8770])).
% 11.45/2.00 thf(f9089,plain,(
% 11.45/2.00 ~spl41_22 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9088])).
% 11.45/2.00 thf(f9088,plain,(
% 11.45/2.00 $false | (~spl41_22 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8842])).
% 11.45/2.00 thf(f8842,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_22 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2352,f8770])).
% 11.45/2.00 thf(f9087,plain,(
% 11.45/2.00 ~spl41_4 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9086])).
% 11.45/2.00 thf(f9086,plain,(
% 11.45/2.00 $false | (~spl41_4 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8843])).
% 11.45/2.00 thf(f8843,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_4 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2262,f8770])).
% 11.45/2.00 thf(f9085,plain,(
% 11.45/2.00 ~spl41_13 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9084])).
% 11.45/2.00 thf(f9084,plain,(
% 11.45/2.00 $false | (~spl41_13 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8844])).
% 11.45/2.00 thf(f8844,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_13 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2307,f8770])).
% 11.45/2.00 thf(f2307,plain,(
% 11.45/2.00 (semiri1193490041visors(nat) = $true) | ~spl41_13),
% 11.45/2.00 inference(avatar_component_clause,[],[f2305])).
% 11.45/2.00 thf(f2305,plain,(
% 11.45/2.00 spl41_13 <=> (semiri1193490041visors(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_13])])).
% 11.45/2.00 thf(f9083,plain,(
% 11.45/2.00 ~spl41_24 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9082])).
% 11.45/2.00 thf(f9082,plain,(
% 11.45/2.00 $false | (~spl41_24 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8845])).
% 11.45/2.00 thf(f8845,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_24 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2362,f8770])).
% 11.45/2.00 thf(f9081,plain,(
% 11.45/2.00 ~spl41_7 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9080])).
% 11.45/2.00 thf(f9080,plain,(
% 11.45/2.00 $false | (~spl41_7 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8846])).
% 11.45/2.00 thf(f8846,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_7 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2277,f8770])).
% 11.45/2.00 thf(f2277,plain,(
% 11.45/2.00 (linord1659791738miring(nat) = $true) | ~spl41_7),
% 11.45/2.00 inference(avatar_component_clause,[],[f2275])).
% 11.45/2.00 thf(f2275,plain,(
% 11.45/2.00 spl41_7 <=> (linord1659791738miring(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_7])])).
% 11.45/2.00 thf(f9079,plain,(
% 11.45/2.00 spl41_257 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9078])).
% 11.45/2.00 thf(f9078,plain,(
% 11.45/2.00 $false | (spl41_257 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8848])).
% 11.45/2.00 thf(f8848,plain,(
% 11.45/2.00 ($false != $false) | (spl41_257 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f6600,f8770])).
% 11.45/2.00 thf(f6600,plain,(
% 11.45/2.00 ($false != linord1659791738miring($o)) | spl41_257),
% 11.45/2.00 inference(avatar_component_clause,[],[f6599])).
% 11.45/2.00 thf(f6599,plain,(
% 11.45/2.00 spl41_257 <=> ($false = linord1659791738miring($o))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_257])])).
% 11.45/2.00 thf(f9077,plain,(
% 11.45/2.00 ~spl41_251 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9076])).
% 11.45/2.00 thf(f9076,plain,(
% 11.45/2.00 $false | (~spl41_251 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8849])).
% 11.45/2.00 thf(f8849,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_251 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f6267,f8770])).
% 11.45/2.00 thf(f9075,plain,(
% 11.45/2.00 ~spl41_23 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9074])).
% 11.45/2.00 thf(f9074,plain,(
% 11.45/2.00 $false | (~spl41_23 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8850])).
% 11.45/2.00 thf(f8850,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_23 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2357,f8770])).
% 11.45/2.00 thf(f2357,plain,(
% 11.45/2.00 (canoni770627133id_add(nat) = $true) | ~spl41_23),
% 11.45/2.00 inference(avatar_component_clause,[],[f2355])).
% 11.45/2.00 thf(f2355,plain,(
% 11.45/2.00 spl41_23 <=> (canoni770627133id_add(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_23])])).
% 11.45/2.00 thf(f9073,plain,(
% 11.45/2.00 ~spl41_3 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9072])).
% 11.45/2.00 thf(f9072,plain,(
% 11.45/2.00 $false | (~spl41_3 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8852])).
% 11.45/2.00 thf(f8852,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_3 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2257,f8770])).
% 11.45/2.00 thf(f2257,plain,(
% 11.45/2.00 (linord893533164strict(nat) = $true) | ~spl41_3),
% 11.45/2.00 inference(avatar_component_clause,[],[f2255])).
% 11.45/2.00 thf(f2255,plain,(
% 11.45/2.00 spl41_3 <=> (linord893533164strict(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_3])])).
% 11.45/2.00 thf(f9071,plain,(
% 11.45/2.00 ~spl41_15 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9070])).
% 11.45/2.00 thf(f9070,plain,(
% 11.45/2.00 $false | (~spl41_15 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8853])).
% 11.45/2.00 thf(f8853,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_15 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2317,f8770])).
% 11.45/2.00 thf(f2317,plain,(
% 11.45/2.00 (semiri1923998003cancel(nat) = $true) | ~spl41_15),
% 11.45/2.00 inference(avatar_component_clause,[],[f2315])).
% 11.45/2.00 thf(f2315,plain,(
% 11.45/2.00 spl41_15 <=> (semiri1923998003cancel(nat) = $true)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_15])])).
% 11.45/2.00 thf(f9069,plain,(
% 11.45/2.00 ~spl41_14 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9068])).
% 11.45/2.00 thf(f9068,plain,(
% 11.45/2.00 $false | (~spl41_14 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8854])).
% 11.45/2.00 thf(f8854,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_14 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2312,f8770])).
% 11.45/2.00 thf(f9066,plain,(
% 11.45/2.00 ~spl41_38 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9065])).
% 11.45/2.00 thf(f9065,plain,(
% 11.45/2.00 $false | (~spl41_38 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f8991])).
% 11.45/2.00 thf(f8991,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_38 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2457,f8770])).
% 11.45/2.00 thf(f9060,plain,(
% 11.45/2.00 ~spl41_44 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9059])).
% 11.45/2.00 thf(f9059,plain,(
% 11.45/2.00 $false | (~spl41_44 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f9026])).
% 11.45/2.00 thf(f9026,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_44 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2490,f8770])).
% 11.45/2.00 thf(f9058,plain,(
% 11.45/2.00 ~spl41_259 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9057])).
% 11.45/2.00 thf(f9057,plain,(
% 11.45/2.00 $false | (~spl41_259 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f9028])).
% 11.45/2.00 thf(f9028,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_259 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f8430,f8770])).
% 11.45/2.00 thf(f9056,plain,(
% 11.45/2.00 ~spl41_48 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9055])).
% 11.45/2.00 thf(f9055,plain,(
% 11.45/2.00 $false | (~spl41_48 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f9033])).
% 11.45/2.00 thf(f9033,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_48 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2511,f8770])).
% 11.45/2.00 thf(f9054,plain,(
% 11.45/2.00 spl41_1 | ~spl41_274),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f9053])).
% 11.45/2.00 thf(f9053,plain,(
% 11.45/2.00 $false | (spl41_1 | ~spl41_274)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f9052])).
% 11.45/2.00 thf(f9052,plain,(
% 11.45/2.00 ($false != $false) | (spl41_1 | ~spl41_274)),
% 11.45/2.00 inference(superposition,[],[f2247,f8770])).
% 11.45/2.00 thf(f2247,plain,(
% 11.45/2.00 ($true != $false) | spl41_1),
% 11.45/2.00 inference(avatar_component_clause,[],[f2245])).
% 11.45/2.00 thf(f2245,plain,(
% 11.45/2.00 spl41_1 <=> ($true = $false)),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_1])])).
% 11.45/2.00 thf(f8774,plain,(
% 11.45/2.00 spl41_274 | spl41_275 | ~spl41_78),
% 11.45/2.00 inference(avatar_split_clause,[],[f2817,f2800,f8772,f8769])).
% 11.45/2.00 thf(f8772,plain,(
% 11.45/2.00 spl41_275 <=> ! [X0 : $o > nat] : ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK40($o),X0),vNOT))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_275])])).
% 11.45/2.00 thf(f2817,plain,(
% 11.45/2.00 ( ! [X0 : $o > nat,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK40($o),X0),vNOT)) | ($false = X1)) ) | ~spl41_78),
% 11.45/2.00 inference(not_proxy_clausification,[],[f2816])).
% 11.45/2.00 thf(f2816,plain,(
% 11.45/2.00 ( ! [X0 : $o > nat,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK40($o),X0),vNOT)) | ($true = vAPP($o,$o,vNOT,X1))) ) | ~spl41_78),
% 11.45/2.00 inference(not_proxy_clausification,[],[f2810])).
% 11.45/2.00 thf(f2810,plain,(
% 11.45/2.00 ( ! [X0 : $o > nat,X1 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK40($o),X0),vNOT))) | ($true = vAPP($o,$o,vNOT,X1))) ) | ~spl41_78),
% 11.45/2.00 inference(primitive_instantiation,[],[f2801])).
% 11.45/2.00 thf(f8767,plain,(
% 11.45/2.00 spl41_273 | ~spl41_72),
% 11.45/2.00 inference(avatar_split_clause,[],[f2757,f2694,f8765])).
% 11.45/2.00 thf(f8765,plain,(
% 11.45/2.00 spl41_273 <=> ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1) | (zero_zero(nat) != X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_273])])).
% 11.45/2.00 thf(f2757,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1) | (zero_zero(nat) != X0)) ) | ~spl41_72),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2756])).
% 11.45/2.00 thf(f2756,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_72),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2755])).
% 11.45/2.00 thf(f2755,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_72),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2750])).
% 11.45/2.00 thf(f2750,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK20,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_72),
% 11.45/2.00 inference(primitive_instantiation,[],[f2695])).
% 11.45/2.00 thf(f8763,plain,(
% 11.45/2.00 spl41_272 | ~spl41_71),
% 11.45/2.00 inference(avatar_split_clause,[],[f2745,f2690,f8761])).
% 11.45/2.00 thf(f8761,plain,(
% 11.45/2.00 spl41_272 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | (vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0) | (X0 = X1))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_272])])).
% 11.45/2.00 thf(f2745,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | (vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0) | (X0 = X1)) ) | ~spl41_71),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2744])).
% 11.45/2.00 thf(f2744,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | (vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_71),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2743])).
% 11.45/2.00 thf(f2743,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_71),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2738])).
% 11.45/2.00 thf(f2738,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_71),
% 11.45/2.00 inference(primitive_instantiation,[],[f2691])).
% 11.45/2.00 thf(f8759,plain,(
% 11.45/2.00 spl41_271 | ~spl41_70),
% 11.45/2.00 inference(avatar_split_clause,[],[f2733,f2686,f8757])).
% 11.45/2.00 thf(f8757,plain,(
% 11.45/2.00 spl41_271 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | (vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0) | (X0 = X1))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_271])])).
% 11.45/2.00 thf(f2733,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | (vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0) | (X0 = X1)) ) | ~spl41_70),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2732])).
% 11.45/2.00 thf(f2732,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | (vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_70),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2731])).
% 11.45/2.00 thf(f2731,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_70),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2726])).
% 11.45/2.00 thf(f2726,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_70),
% 11.45/2.00 inference(primitive_instantiation,[],[f2687])).
% 11.45/2.00 thf(f8755,plain,(
% 11.45/2.00 spl41_270 | ~spl41_68),
% 11.45/2.00 inference(avatar_split_clause,[],[f2722,f2678,f8753])).
% 11.45/2.00 thf(f8753,plain,(
% 11.45/2.00 spl41_270 <=> ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (zero_zero(nat) = X0) | (X0 != X1))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_270])])).
% 11.45/2.00 thf(f2722,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (zero_zero(nat) = X0) | (X0 != X1)) ) | ~spl41_68),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2721])).
% 11.45/2.00 thf(f2721,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (zero_zero(nat) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_68),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2720])).
% 11.45/2.00 thf(f2720,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_68),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2715])).
% 11.45/2.00 thf(f2715,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK17,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_68),
% 11.45/2.00 inference(primitive_instantiation,[],[f2679])).
% 11.45/2.00 thf(f8751,plain,(
% 11.45/2.00 spl41_269 | ~spl41_66),
% 11.45/2.00 inference(avatar_split_clause,[],[f2707,f2670,f8749])).
% 11.45/2.00 thf(f8749,plain,(
% 11.45/2.00 spl41_269 <=> ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 != X1) | (zero_zero(nat) = X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_269])])).
% 11.45/2.00 thf(f2707,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 != X1) | (zero_zero(nat) = X0)) ) | ~spl41_66),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2706])).
% 11.45/2.00 thf(f2706,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 != X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_66),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2705])).
% 11.45/2.00 thf(f2705,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_66),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2700])).
% 11.45/2.00 thf(f2700,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK6,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero(nat)))) ) | ~spl41_66),
% 11.45/2.00 inference(primitive_instantiation,[],[f2671])).
% 11.45/2.00 thf(f8747,plain,(
% 11.45/2.00 spl41_268 | ~spl41_26 | ~spl41_62),
% 11.45/2.00 inference(avatar_split_clause,[],[f2641,f2632,f2369,f8745])).
% 11.45/2.00 thf(f2632,plain,(
% 11.45/2.00 spl41_62 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK10(X0),X1)),X1)) | (linordered_field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_62])])).
% 11.45/2.00 thf(f2641,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK10(X0),X1)),X1)) | (linordered_field(X0) = $false)) ) | (~spl41_26 | ~spl41_62)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2640])).
% 11.45/2.00 thf(f2640,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK10(X0),X1)),X1)) | (linordered_field(X0) = $false)) ) | (~spl41_26 | ~spl41_62)),
% 11.45/2.00 inference(superposition,[],[f2633,f2370])).
% 11.45/2.00 thf(f2633,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((linordered_field(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK10(X0),X1)),X1))) ) | ~spl41_62),
% 11.45/2.00 inference(avatar_component_clause,[],[f2632])).
% 11.45/2.00 thf(f8743,plain,(
% 11.45/2.00 spl41_267 | ~spl41_26 | ~spl41_61),
% 11.45/2.00 inference(avatar_split_clause,[],[f2636,f2628,f2369,f8741])).
% 11.45/2.00 thf(f2628,plain,(
% 11.45/2.00 spl41_61 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK9(X0),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_61])])).
% 11.45/2.00 thf(f2636,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK9(X0),X1))) | (linordered_field(X0) = $false)) ) | (~spl41_26 | ~spl41_61)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2635])).
% 11.45/2.00 thf(f2635,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK9(X0),X1))) | (linordered_field(X0) = $false)) ) | (~spl41_26 | ~spl41_61)),
% 11.45/2.00 inference(superposition,[],[f2629,f2370])).
% 11.45/2.00 thf(f2629,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((linordered_field(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK9(X0),X1)))) ) | ~spl41_61),
% 11.45/2.00 inference(avatar_component_clause,[],[f2628])).
% 11.45/2.00 thf(f8739,plain,(
% 11.45/2.00 spl41_266),
% 11.45/2.00 inference(avatar_split_clause,[],[f2210,f8737])).
% 11.45/2.00 thf(f8737,plain,(
% 11.45/2.00 spl41_266 <=> ! [X0 : nat] : ((zero_zero(nat) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_266])])).
% 11.45/2.00 thf(f2210,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2207])).
% 11.45/2.00 thf(f2207,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1200])).
% 11.45/2.00 thf(f1200,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f298])).
% 11.45/2.00 thf(f298,plain,(
% 11.45/2.00 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))))),
% 11.45/2.00 inference(fool_elimination,[],[f297])).
% 11.45/2.00 thf(f297,plain,(
% 11.45/2.00 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))) = (zero_zero(nat) = X0))),
% 11.45/2.00 inference(rectify,[],[f11])).
% 11.45/2.00 thf(f11,axiom,(
% 11.45/2.00 ! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),vAPP(nat,nat,suc,zero_zero(nat))) = (zero_zero(nat) = X2))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_less__Suc0)).
% 11.45/2.00 thf(f8735,plain,(
% 11.45/2.00 spl41_265),
% 11.45/2.00 inference(avatar_split_clause,[],[f2122,f8733])).
% 11.45/2.00 thf(f8733,plain,(
% 11.45/2.00 spl41_265 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = X1) | (canoni770627133id_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_265])])).
% 11.45/2.00 thf(f2122,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = X1) | (canoni770627133id_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) )),
% 11.45/2.00 inference(not_proxy_clausification,[],[f2121])).
% 11.45/2.00 thf(f2121,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = X1) | (canoni770627133id_add(X0) != $true) | ($false = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2117])).
% 11.45/2.00 thf(f2117,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true) | ($false = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1266])).
% 11.45/2.00 thf(f1266,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1) = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (canoni770627133id_add(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f915])).
% 11.45/2.00 thf(f915,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1) = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (canoni770627133id_add(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f414])).
% 11.45/2.00 thf(f414,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1) = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))))),
% 11.45/2.00 inference(fool_elimination,[],[f413])).
% 11.45/2.00 thf(f413,plain,(
% 11.45/2.00 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X1 : X0] : (~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1) = (zero_zero(X0) = X1)))),
% 11.45/2.00 inference(rectify,[],[f188])).
% 11.45/2.00 thf(f188,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X2 : X0] : (~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = (zero_zero(X0) = X2)))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_not__gr__zero)).
% 11.45/2.00 thf(f8728,plain,(
% 11.45/2.00 spl41_264 | ~spl41_46 | ~spl41_248 | ~spl41_249),
% 11.45/2.00 inference(avatar_split_clause,[],[f6343,f6255,f6251,f2500,f8726])).
% 11.45/2.00 thf(f8726,plain,(
% 11.45/2.00 spl41_264 <=> ! [X0 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X0),$false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_264])])).
% 11.45/2.00 thf(f6255,plain,(
% 11.45/2.00 spl41_249 <=> ($true = canoni770627133id_add($o))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_249])])).
% 11.45/2.00 thf(f6343,plain,(
% 11.45/2.00 ( ! [X0 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X0),$false))) ) | (~spl41_46 | ~spl41_248 | ~spl41_249)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f6342])).
% 11.45/2.00 thf(f6342,plain,(
% 11.45/2.00 ( ! [X0 : $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X0),$false))) ) | (~spl41_46 | ~spl41_248 | ~spl41_249)),
% 11.45/2.00 inference(forward_demodulation,[],[f6289,f6256])).
% 11.45/2.00 thf(f6256,plain,(
% 11.45/2.00 ($true = canoni770627133id_add($o)) | ~spl41_249),
% 11.45/2.00 inference(avatar_component_clause,[],[f6255])).
% 11.45/2.00 thf(f6289,plain,(
% 11.45/2.00 ( ! [X0 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X0),$false)) | ($true != canoni770627133id_add($o))) ) | (~spl41_46 | ~spl41_248)),
% 11.45/2.00 inference(superposition,[],[f2501,f6253])).
% 11.45/2.00 thf(f8724,plain,(
% 11.45/2.00 spl41_263),
% 11.45/2.00 inference(avatar_split_clause,[],[f2120,f8722])).
% 11.45/2.00 thf(f8722,plain,(
% 11.45/2.00 spl41_263 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) != X1) | (canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_263])])).
% 11.45/2.00 thf(f2120,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) != X1) | (canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) )),
% 11.45/2.00 inference(not_proxy_clausification,[],[f2119])).
% 11.45/2.00 thf(f2119,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) != X1) | (canoni770627133id_add(X0) != $true) | ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2118])).
% 11.45/2.00 thf(f2118,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true) | ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1266])).
% 11.45/2.00 thf(f8720,plain,(
% 11.45/2.00 spl41_262),
% 11.45/2.00 inference(avatar_split_clause,[],[f2116,f8718])).
% 11.45/2.00 thf(f8718,plain,(
% 11.45/2.00 spl41_262 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = X1) | (canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_262])])).
% 11.45/2.00 thf(f2116,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = X1) | (canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2113])).
% 11.45/2.00 thf(f2113,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1267])).
% 11.45/2.00 thf(f1267,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (canoni770627133id_add(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f916])).
% 11.45/2.00 thf(f916,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (canoni770627133id_add(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f416])).
% 11.45/2.00 thf(f416,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))))),
% 11.45/2.00 inference(fool_elimination,[],[f415])).
% 11.45/2.00 thf(f415,plain,(
% 11.45/2.00 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X1 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)) = (zero_zero(X0) = X1)))),
% 11.45/2.00 inference(rectify,[],[f214])).
% 11.45/2.00 thf(f214,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) = (zero_zero(X0) = X2)))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_le__zero__eq)).
% 11.45/2.00 thf(f8716,plain,(
% 11.45/2.00 spl41_261),
% 11.45/2.00 inference(avatar_split_clause,[],[f2115,f8714])).
% 11.45/2.00 thf(f8714,plain,(
% 11.45/2.00 spl41_261 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) != X1) | (canoni770627133id_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_261])])).
% 11.45/2.00 thf(f2115,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) != X1) | (canoni770627133id_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2114])).
% 11.45/2.00 thf(f2114,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1267])).
% 11.45/2.00 thf(f8712,plain,(
% 11.45/2.00 spl41_260),
% 11.45/2.00 inference(avatar_split_clause,[],[f1718,f8710])).
% 11.45/2.00 thf(f1718,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | (zero_zero(nat) = X1) | (zero_zero(nat) = X0)) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1717])).
% 11.45/2.00 thf(f1717,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | (zero_zero(nat) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1716])).
% 11.45/2.00 thf(f1716,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1715])).
% 11.45/2.00 thf(f1715,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1714])).
% 11.45/2.00 thf(f1714,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1367])).
% 11.45/2.00 thf(f1367,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f606])).
% 11.45/2.00 thf(f606,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X1)))),
% 11.45/2.00 inference(fool_elimination,[],[f605])).
% 11.45/2.00 thf(f605,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)) = (zero_zero(nat) = X1) | (zero_zero(nat) = X0))),
% 11.45/2.00 inference(rectify,[],[f24])).
% 11.45/2.00 thf(f24,axiom,(
% 11.45/2.00 ! [X3 : nat,X2 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),X2)) = (zero_zero(nat) = X2) | (zero_zero(nat) = X3))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_mult__is__0)).
% 11.45/2.00 thf(f8431,plain,(
% 11.45/2.00 spl41_259 | ~spl41_44 | ~spl41_83),
% 11.45/2.00 inference(avatar_split_clause,[],[f2927,f2850,f2489,f8429])).
% 11.45/2.00 thf(f2850,plain,(
% 11.45/2.00 spl41_83 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_83])])).
% 11.45/2.00 thf(f2927,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))))) ) | (~spl41_44 | ~spl41_83)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2921])).
% 11.45/2.00 thf(f2921,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))))) ) | (~spl41_44 | ~spl41_83)),
% 11.45/2.00 inference(superposition,[],[f2851,f2490])).
% 11.45/2.00 thf(f2851,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1)))) ) | ~spl41_83),
% 11.45/2.00 inference(avatar_component_clause,[],[f2850])).
% 11.45/2.00 thf(f8413,plain,(
% 11.45/2.00 spl41_258 | ~spl41_26 | spl41_252),
% 11.45/2.00 inference(avatar_split_clause,[],[f6279,f6270,f2369,f8410])).
% 11.45/2.00 thf(f6279,plain,(
% 11.45/2.00 ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$true)) | (~spl41_26 | spl41_252)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f6278])).
% 11.45/2.00 thf(f6278,plain,(
% 11.45/2.00 ($true != $true) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$true)) | (~spl41_26 | spl41_252)),
% 11.45/2.00 inference(superposition,[],[f6272,f2370])).
% 11.45/2.00 thf(f6602,plain,(
% 11.45/2.00 spl41_257 | ~spl41_26 | spl41_251),
% 11.45/2.00 inference(avatar_split_clause,[],[f6275,f6266,f2369,f6599])).
% 11.45/2.00 thf(f6275,plain,(
% 11.45/2.00 ($false = linord1659791738miring($o)) | (~spl41_26 | spl41_251)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f6274])).
% 11.45/2.00 thf(f6274,plain,(
% 11.45/2.00 ($true != $true) | ($false = linord1659791738miring($o)) | (~spl41_26 | spl41_251)),
% 11.45/2.00 inference(superposition,[],[f6268,f2370])).
% 11.45/2.00 thf(f6268,plain,(
% 11.45/2.00 ($true != linord1659791738miring($o)) | spl41_251),
% 11.45/2.00 inference(avatar_component_clause,[],[f6266])).
% 11.45/2.00 thf(f6561,plain,(
% 11.45/2.00 ~spl41_48 | ~spl41_221 | ~spl41_255),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f6560])).
% 11.45/2.00 thf(f6560,plain,(
% 11.45/2.00 $false | (~spl41_48 | ~spl41_221 | ~spl41_255)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f6559])).
% 11.45/2.00 thf(f6559,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_48 | ~spl41_221 | ~spl41_255)),
% 11.45/2.00 inference(forward_demodulation,[],[f6517,f6404])).
% 11.45/2.00 thf(f6404,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0))) ) | (~spl41_221 | ~spl41_255)),
% 11.45/2.00 inference(superposition,[],[f4794,f6358])).
% 11.45/2.00 thf(f6358,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) = X0)) ) | ~spl41_255),
% 11.45/2.00 inference(avatar_component_clause,[],[f6357])).
% 11.45/2.00 thf(f6517,plain,(
% 11.45/2.00 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),zero_zero(nat))) | (~spl41_48 | ~spl41_255)),
% 11.45/2.00 inference(superposition,[],[f2511,f6358])).
% 11.45/2.00 thf(f6558,plain,(
% 11.45/2.00 ~spl41_44 | ~spl41_221 | ~spl41_255),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f6557])).
% 11.45/2.00 thf(f6557,plain,(
% 11.45/2.00 $false | (~spl41_44 | ~spl41_221 | ~spl41_255)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f6556])).
% 11.45/2.00 thf(f6556,plain,(
% 11.45/2.00 ($true = $false) | (~spl41_44 | ~spl41_221 | ~spl41_255)),
% 11.45/2.00 inference(forward_demodulation,[],[f6516,f6404])).
% 11.45/2.00 thf(f6516,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | (~spl41_44 | ~spl41_255)),
% 11.45/2.00 inference(superposition,[],[f2490,f6358])).
% 11.45/2.00 thf(f6554,plain,(
% 11.45/2.00 ~spl41_30 | ~spl41_255),
% 11.45/2.00 inference(avatar_contradiction_clause,[],[f6553])).
% 11.45/2.00 thf(f6553,plain,(
% 11.45/2.00 $false | (~spl41_30 | ~spl41_255)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f6515])).
% 11.45/2.00 thf(f6515,plain,(
% 11.45/2.00 (zero_zero(nat) != zero_zero(nat)) | (~spl41_30 | ~spl41_255)),
% 11.45/2.00 inference(superposition,[],[f2417,f6358])).
% 11.45/2.00 thf(f6381,plain,(
% 11.45/2.00 spl41_256 | spl41_255 | ~spl41_71),
% 11.45/2.00 inference(avatar_split_clause,[],[f2746,f2690,f6357,f6378])).
% 11.45/2.00 thf(f6378,plain,(
% 11.45/2.00 spl41_256 <=> (zero_zero(nat) = vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_256])])).
% 11.45/2.00 thf(f2746,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) = X0) | (zero_zero(nat) = vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))) ) | ~spl41_71),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2735])).
% 11.45/2.00 thf(f2735,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) | (zero_zero(nat) = vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))) ) | ~spl41_71),
% 11.45/2.00 inference(leibniz_equality_elimination,[],[f2691])).
% 11.45/2.00 thf(f6359,plain,(
% 11.45/2.00 spl41_254 | spl41_255 | ~spl41_70),
% 11.45/2.00 inference(avatar_split_clause,[],[f2734,f2686,f6357,f6353])).
% 11.45/2.00 thf(f6353,plain,(
% 11.45/2.00 spl41_254 <=> (zero_zero(nat) = vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_254])])).
% 11.45/2.00 thf(f2734,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) = X0) | (zero_zero(nat) = vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))) ) | ~spl41_70),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2723])).
% 11.45/2.00 thf(f2723,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) | (zero_zero(nat) = vAPP(sTfun(nat,$o),nat,sK18,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat))))) ) | ~spl41_70),
% 11.45/2.00 inference(leibniz_equality_elimination,[],[f2687])).
% 11.45/2.00 thf(f6287,plain,(
% 11.45/2.00 spl41_253 | ~spl41_26 | spl41_249),
% 11.45/2.00 inference(avatar_split_clause,[],[f6264,f6255,f2369,f6284])).
% 11.45/2.00 thf(f6284,plain,(
% 11.45/2.00 spl41_253 <=> ($false = canoni770627133id_add($o))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_253])])).
% 11.45/2.00 thf(f6264,plain,(
% 11.45/2.00 ($false = canoni770627133id_add($o)) | (~spl41_26 | spl41_249)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f6263])).
% 11.45/2.00 thf(f6263,plain,(
% 11.45/2.00 ($true != $true) | ($false = canoni770627133id_add($o)) | (~spl41_26 | spl41_249)),
% 11.45/2.00 inference(superposition,[],[f6257,f2370])).
% 11.45/2.00 thf(f6257,plain,(
% 11.45/2.00 ($true != canoni770627133id_add($o)) | spl41_249),
% 11.45/2.00 inference(avatar_component_clause,[],[f6255])).
% 11.45/2.00 thf(f6273,plain,(
% 11.45/2.00 spl41_248 | ~spl41_251 | ~spl41_252 | ~spl41_26 | ~spl41_49),
% 11.45/2.00 inference(avatar_split_clause,[],[f2569,f2524,f2369,f6270,f6266,f6251])).
% 11.45/2.00 thf(f2524,plain,(
% 11.45/2.00 spl41_49 <=> ! [X0 : $tType] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) != $true) | (linord1659791738miring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_49])])).
% 11.45/2.00 thf(f2569,plain,(
% 11.45/2.00 ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),$true)) | ($true != linord1659791738miring($o)) | ($false = zero_zero($o)) | (~spl41_26 | ~spl41_49)),
% 11.45/2.00 inference(superposition,[],[f2525,f2370])).
% 11.45/2.00 thf(f2525,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) != $true) | (linord1659791738miring(X0) != $true)) ) | ~spl41_49),
% 11.45/2.00 inference(avatar_component_clause,[],[f2524])).
% 11.45/2.00 thf(f6261,plain,(
% 11.45/2.00 spl41_248 | ~spl41_249 | spl41_250 | ~spl41_26 | ~spl41_46),
% 11.45/2.00 inference(avatar_split_clause,[],[f2513,f2500,f2369,f6259,f6255,f6251])).
% 11.45/2.00 thf(f6259,plain,(
% 11.45/2.00 spl41_250 <=> ! [X0 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X0),$true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_250])])).
% 11.45/2.00 thf(f2513,plain,(
% 11.45/2.00 ( ! [X0 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X0),$true)) | ($true != canoni770627133id_add($o)) | ($false = zero_zero($o))) ) | (~spl41_26 | ~spl41_46)),
% 11.45/2.00 inference(superposition,[],[f2501,f2370])).
% 11.45/2.00 thf(f6249,plain,(
% 11.45/2.00 spl41_247 | ~spl41_35 | ~spl41_44),
% 11.45/2.00 inference(avatar_split_clause,[],[f2494,f2489,f2444,f6247])).
% 11.45/2.00 thf(f6247,plain,(
% 11.45/2.00 spl41_247 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK5,X0)),X0)) | (zero_zero(nat) = X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_247])])).
% 11.45/2.00 thf(f2494,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK5,X0)),X0)) | (zero_zero(nat) = X0)) ) | (~spl41_35 | ~spl41_44)),
% 11.45/2.00 inference(superposition,[],[f2490,f2445])).
% 11.45/2.00 thf(f6245,plain,(
% 11.45/2.00 spl41_246 | ~spl41_34 | ~spl41_44),
% 11.45/2.00 inference(avatar_split_clause,[],[f2493,f2489,f2440,f6243])).
% 11.45/2.00 thf(f6243,plain,(
% 11.45/2.00 spl41_246 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK4,X0)),X0)) | (zero_zero(nat) = X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_246])])).
% 11.45/2.00 thf(f2493,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK4,X0)),X0)) | (zero_zero(nat) = X0)) ) | (~spl41_34 | ~spl41_44)),
% 11.45/2.00 inference(superposition,[],[f2490,f2441])).
% 11.45/2.00 thf(f6241,plain,(
% 11.45/2.00 spl41_245 | ~spl41_33 | ~spl41_44),
% 11.45/2.00 inference(avatar_split_clause,[],[f2492,f2489,f2436,f6239])).
% 11.45/2.00 thf(f6239,plain,(
% 11.45/2.00 spl41_245 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK3,X0)),X0)) | (zero_zero(nat) = X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_245])])).
% 11.45/2.00 thf(f2492,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,sK3,X0)),X0)) | (zero_zero(nat) = X0)) ) | (~spl41_33 | ~spl41_44)),
% 11.45/2.00 inference(superposition,[],[f2490,f2437])).
% 11.45/2.00 thf(f5276,plain,(
% 11.45/2.00 spl41_244 | ~spl41_31 | ~spl41_177),
% 11.45/2.00 inference(avatar_split_clause,[],[f4235,f4079,f2420,f5274])).
% 11.45/2.00 thf(f5274,plain,(
% 11.45/2.00 spl41_244 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X4 : $tType] : ($true = order(sTfun(X4,sTfun(X0,sTfun(X1,sTfun(X2,sTfun(X3,$o)))))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_244])])).
% 11.45/2.00 thf(f2420,plain,(
% 11.45/2.00 spl41_31 <=> ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X0,X1))) | ($true != order(X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_31])])).
% 11.45/2.00 thf(f4235,plain,(
% 11.45/2.00 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = order(sTfun(X4,sTfun(X0,sTfun(X1,sTfun(X2,sTfun(X3,$o)))))))) ) | (~spl41_31 | ~spl41_177)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f4234])).
% 11.45/2.00 thf(f4234,plain,(
% 11.45/2.00 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X4,sTfun(X0,sTfun(X1,sTfun(X2,sTfun(X3,$o)))))))) ) | (~spl41_31 | ~spl41_177)),
% 11.45/2.00 inference(superposition,[],[f2421,f4080])).
% 11.45/2.00 thf(f2421,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType] : (($true != order(X1)) | ($true = order(sTfun(X0,X1)))) ) | ~spl41_31),
% 11.45/2.00 inference(avatar_component_clause,[],[f2420])).
% 11.45/2.00 thf(f5272,plain,(
% 11.45/2.00 spl41_243 | ~spl41_26 | ~spl41_59),
% 11.45/2.00 inference(avatar_split_clause,[],[f2623,f2566,f2369,f5270])).
% 11.45/2.00 thf(f5270,plain,(
% 11.45/2.00 spl41_243 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_243])])).
% 11.45/2.00 thf(f2623,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)))) ) | (~spl41_26 | ~spl41_59)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2622])).
% 11.45/2.00 thf(f2622,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)))) ) | (~spl41_26 | ~spl41_59)),
% 11.45/2.00 inference(superposition,[],[f2567,f2370])).
% 11.45/2.00 thf(f5268,plain,(
% 11.45/2.00 spl41_242 | ~spl41_26 | ~spl41_58),
% 11.45/2.00 inference(avatar_split_clause,[],[f2613,f2562,f2369,f5266])).
% 11.45/2.00 thf(f5266,plain,(
% 11.45/2.00 spl41_242 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_242])])).
% 11.45/2.00 thf(f2613,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)))) ) | (~spl41_26 | ~spl41_58)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2612])).
% 11.45/2.00 thf(f2612,plain,(
% 11.45/2.00 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)))) ) | (~spl41_26 | ~spl41_58)),
% 11.45/2.00 inference(superposition,[],[f2563,f2370])).
% 11.45/2.00 thf(f5264,plain,(
% 11.45/2.00 spl41_241 | ~spl41_26 | ~spl41_57),
% 11.45/2.00 inference(avatar_split_clause,[],[f2606,f2558,f2369,f5262])).
% 11.45/2.00 thf(f5262,plain,(
% 11.45/2.00 spl41_241 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (division_ring(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_241])])).
% 11.45/2.00 thf(f2558,plain,(
% 11.45/2.00 spl41_57 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (division_ring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_57])])).
% 11.45/2.00 thf(f2606,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (division_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_57)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2605])).
% 11.45/2.00 thf(f2605,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (division_ring(X0) = $false)) ) | (~spl41_26 | ~spl41_57)),
% 11.45/2.00 inference(superposition,[],[f2559,f2370])).
% 11.45/2.00 thf(f2559,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((division_ring(X0) != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0)))) ) | ~spl41_57),
% 11.45/2.00 inference(avatar_component_clause,[],[f2558])).
% 11.45/2.00 thf(f5260,plain,(
% 11.45/2.00 spl41_240 | ~spl41_26 | ~spl41_56),
% 11.45/2.00 inference(avatar_split_clause,[],[f2603,f2554,f2369,f5258])).
% 11.45/2.00 thf(f5258,plain,(
% 11.45/2.00 spl41_240 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semidom_divide(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_240])])).
% 11.45/2.00 thf(f2554,plain,(
% 11.45/2.00 spl41_56 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semidom_divide(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_56])])).
% 11.45/2.00 thf(f2603,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semidom_divide(X0) = $false)) ) | (~spl41_26 | ~spl41_56)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2602])).
% 11.45/2.00 thf(f2602,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semidom_divide(X0) = $false)) ) | (~spl41_26 | ~spl41_56)),
% 11.45/2.00 inference(superposition,[],[f2555,f2370])).
% 11.45/2.00 thf(f2555,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((semidom_divide(X0) != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1))) ) | ~spl41_56),
% 11.45/2.00 inference(avatar_component_clause,[],[f2554])).
% 11.45/2.00 thf(f5256,plain,(
% 11.45/2.00 spl41_239 | ~spl41_26 | ~spl41_55),
% 11.45/2.00 inference(avatar_split_clause,[],[f2599,f2550,f2369,f5254])).
% 11.45/2.00 thf(f5254,plain,(
% 11.45/2.00 spl41_239 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semidom_divide(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_239])])).
% 11.45/2.00 thf(f2550,plain,(
% 11.45/2.00 spl41_55 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semidom_divide(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_55])])).
% 11.45/2.00 thf(f2599,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semidom_divide(X0) = $false)) ) | (~spl41_26 | ~spl41_55)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2598])).
% 11.45/2.00 thf(f2598,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semidom_divide(X0) = $false)) ) | (~spl41_26 | ~spl41_55)),
% 11.45/2.00 inference(superposition,[],[f2551,f2370])).
% 11.45/2.00 thf(f2551,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((semidom_divide(X0) != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0)))) ) | ~spl41_55),
% 11.45/2.00 inference(avatar_component_clause,[],[f2550])).
% 11.45/2.00 thf(f5252,plain,(
% 11.45/2.00 spl41_238 | ~spl41_26 | ~spl41_54),
% 11.45/2.00 inference(avatar_split_clause,[],[f2595,f2546,f2369,f5250])).
% 11.45/2.00 thf(f5250,plain,(
% 11.45/2.00 spl41_238 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)) | (mult_zero(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_238])])).
% 11.45/2.00 thf(f2546,plain,(
% 11.45/2.00 spl41_54 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)) | (mult_zero(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_54])])).
% 11.45/2.00 thf(f2595,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)) | (mult_zero(X0) = $false)) ) | (~spl41_26 | ~spl41_54)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2594])).
% 11.45/2.00 thf(f2594,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)) | (mult_zero(X0) = $false)) ) | (~spl41_26 | ~spl41_54)),
% 11.45/2.00 inference(superposition,[],[f2547,f2370])).
% 11.45/2.00 thf(f2547,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((mult_zero(X0) != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1))) ) | ~spl41_54),
% 11.45/2.00 inference(avatar_component_clause,[],[f2546])).
% 11.45/2.00 thf(f5248,plain,(
% 11.45/2.00 spl41_237 | ~spl41_26 | ~spl41_53),
% 11.45/2.00 inference(avatar_split_clause,[],[f2591,f2540,f2369,f5246])).
% 11.45/2.00 thf(f5246,plain,(
% 11.45/2.00 spl41_237 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),zero_zero(X0))) | (mult_zero(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_237])])).
% 11.45/2.00 thf(f2540,plain,(
% 11.45/2.00 spl41_53 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),zero_zero(X0))) | (mult_zero(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_53])])).
% 11.45/2.00 thf(f2591,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),zero_zero(X0))) | (mult_zero(X0) = $false)) ) | (~spl41_26 | ~spl41_53)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2590])).
% 11.45/2.00 thf(f2590,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),zero_zero(X0))) | (mult_zero(X0) = $false)) ) | (~spl41_26 | ~spl41_53)),
% 11.45/2.00 inference(superposition,[],[f2541,f2370])).
% 11.45/2.00 thf(f2541,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((mult_zero(X0) != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),zero_zero(X0)))) ) | ~spl41_53),
% 11.45/2.00 inference(avatar_component_clause,[],[f2540])).
% 11.45/2.00 thf(f5244,plain,(
% 11.45/2.00 spl41_236 | ~spl41_26 | ~spl41_52),
% 11.45/2.00 inference(avatar_split_clause,[],[f2582,f2536,f2369,f5242])).
% 11.45/2.00 thf(f5242,plain,(
% 11.45/2.00 spl41_236 <=> ! [X0 : $tType] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true) | (linord1659791738miring(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_236])])).
% 11.45/2.00 thf(f2536,plain,(
% 11.45/2.00 spl41_52 <=> ! [X0 : $tType] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true) | (linord1659791738miring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_52])])).
% 11.45/2.00 thf(f2582,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true) | (linord1659791738miring(X0) = $false)) ) | (~spl41_26 | ~spl41_52)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2581])).
% 11.45/2.00 thf(f2581,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : (($true != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true) | (linord1659791738miring(X0) = $false)) ) | (~spl41_26 | ~spl41_52)),
% 11.45/2.00 inference(superposition,[],[f2537,f2370])).
% 11.45/2.00 thf(f2537,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((linord1659791738miring(X0) != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true)) ) | ~spl41_52),
% 11.45/2.00 inference(avatar_component_clause,[],[f2536])).
% 11.45/2.00 thf(f5240,plain,(
% 11.45/2.00 spl41_235 | ~spl41_26 | ~spl41_51),
% 11.45/2.00 inference(avatar_split_clause,[],[f2578,f2532,f2369,f5238])).
% 11.45/2.00 thf(f5238,plain,(
% 11.45/2.00 spl41_235 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semiring_bits(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_235])])).
% 11.45/2.00 thf(f2532,plain,(
% 11.45/2.00 spl41_51 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semiring_bits(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_51])])).
% 11.45/2.00 thf(f2578,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semiring_bits(X0) = $false)) ) | (~spl41_26 | ~spl41_51)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2577])).
% 11.45/2.00 thf(f2577,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semiring_bits(X0) = $false)) ) | (~spl41_26 | ~spl41_51)),
% 11.45/2.00 inference(superposition,[],[f2533,f2370])).
% 11.45/2.00 thf(f2533,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((semiring_bits(X0) != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1))) ) | ~spl41_51),
% 11.45/2.00 inference(avatar_component_clause,[],[f2532])).
% 11.45/2.00 thf(f5236,plain,(
% 11.45/2.00 spl41_234 | ~spl41_26 | ~spl41_50),
% 11.45/2.00 inference(avatar_split_clause,[],[f2574,f2528,f2369,f5234])).
% 11.45/2.00 thf(f5234,plain,(
% 11.45/2.00 spl41_234 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semiring_bits(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_234])])).
% 11.45/2.00 thf(f2528,plain,(
% 11.45/2.00 spl41_50 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semiring_bits(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_50])])).
% 11.45/2.00 thf(f2574,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semiring_bits(X0) = $false)) ) | (~spl41_26 | ~spl41_50)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2573])).
% 11.45/2.00 thf(f2573,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semiring_bits(X0) = $false)) ) | (~spl41_26 | ~spl41_50)),
% 11.45/2.00 inference(superposition,[],[f2529,f2370])).
% 11.45/2.00 thf(f2529,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((semiring_bits(X0) != $true) | (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0)))) ) | ~spl41_50),
% 11.45/2.00 inference(avatar_component_clause,[],[f2528])).
% 11.45/2.00 thf(f5232,plain,(
% 11.45/2.00 spl41_233 | ~spl41_31 | ~spl41_176),
% 11.45/2.00 inference(avatar_split_clause,[],[f4151,f3992,f2420,f5230])).
% 11.45/2.00 thf(f4151,plain,(
% 11.45/2.00 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = order(sTfun(X4,sTfun(X0,sTfun(X1,sTfun(X2,sTfun(X3,nat)))))))) ) | (~spl41_31 | ~spl41_176)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f4150])).
% 11.45/2.00 thf(f4150,plain,(
% 11.45/2.00 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X4,sTfun(X0,sTfun(X1,sTfun(X2,sTfun(X3,nat)))))))) ) | (~spl41_31 | ~spl41_176)),
% 11.45/2.00 inference(superposition,[],[f2421,f3993])).
% 11.45/2.00 thf(f5228,plain,(
% 11.45/2.00 spl41_232 | ~spl41_26 | ~spl41_49),
% 11.45/2.00 inference(avatar_split_clause,[],[f2571,f2524,f2369,f5226])).
% 11.45/2.00 thf(f2571,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((linord1659791738miring(X0) != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) = $false)) ) | (~spl41_26 | ~spl41_49)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2570])).
% 11.45/2.00 thf(f2570,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : (($true != $true) | (linord1659791738miring(X0) != $true) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) = $false)) ) | (~spl41_26 | ~spl41_49)),
% 11.45/2.00 inference(superposition,[],[f2525,f2370])).
% 11.45/2.00 thf(f4931,plain,(
% 11.45/2.00 spl41_231 | ~spl41_44 | ~spl41_73),
% 11.45/2.00 inference(avatar_split_clause,[],[f2776,f2759,f2489,f4929])).
% 11.45/2.00 thf(f4929,plain,(
% 11.45/2.00 spl41_231 <=> ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,suc,X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_231])])).
% 11.45/2.00 thf(f2759,plain,(
% 11.45/2.00 spl41_73 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_73])])).
% 11.45/2.00 thf(f2776,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,suc,X0)))) ) | (~spl41_44 | ~spl41_73)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2770])).
% 11.45/2.00 thf(f2770,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,suc,X0)))) ) | (~spl41_44 | ~spl41_73)),
% 11.45/2.00 inference(superposition,[],[f2760,f2490])).
% 11.45/2.00 thf(f2760,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1))) ) | ~spl41_73),
% 11.45/2.00 inference(avatar_component_clause,[],[f2759])).
% 11.45/2.00 thf(f4927,plain,(
% 11.45/2.00 spl41_230 | ~spl41_48 | ~spl41_65),
% 11.45/2.00 inference(avatar_split_clause,[],[f2668,f2660,f2510,f4925])).
% 11.45/2.00 thf(f4925,plain,(
% 11.45/2.00 spl41_230 <=> ! [X0 : nat] : (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK12,vAPP(nat,nat,suc,X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_230])])).
% 11.45/2.00 thf(f2668,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK12,vAPP(nat,nat,suc,X0))))) ) | (~spl41_48 | ~spl41_65)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2663])).
% 11.45/2.00 thf(f2663,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK12,vAPP(nat,nat,suc,X0))))) ) | (~spl41_48 | ~spl41_65)),
% 11.45/2.00 inference(superposition,[],[f2661,f2511])).
% 11.45/2.00 thf(f4921,plain,(
% 11.45/2.00 spl41_229 | ~spl41_59),
% 11.45/2.00 inference(avatar_split_clause,[],[f2626,f2566,f4919])).
% 11.45/2.00 thf(f4919,plain,(
% 11.45/2.00 spl41_229 <=> ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_229])])).
% 11.45/2.00 thf(f2626,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1)) ) | ~spl41_59),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2625])).
% 11.45/2.00 thf(f2625,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_59),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2620])).
% 11.45/2.00 thf(f2620,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_59),
% 11.45/2.00 inference(primitive_instantiation,[],[f2567])).
% 11.45/2.00 thf(f4917,plain,(
% 11.45/2.00 spl41_228 | ~spl41_58),
% 11.45/2.00 inference(avatar_split_clause,[],[f2616,f2562,f4915])).
% 11.45/2.00 thf(f4915,plain,(
% 11.45/2.00 spl41_228 <=> ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_228])])).
% 11.45/2.00 thf(f2616,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1)) ) | ~spl41_58),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2615])).
% 11.45/2.00 thf(f2615,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_58),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2610])).
% 11.45/2.00 thf(f2610,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl41_58),
% 11.45/2.00 inference(primitive_instantiation,[],[f2563])).
% 11.45/2.00 thf(f4913,plain,(
% 11.45/2.00 spl41_227 | ~spl41_26 | ~spl41_47),
% 11.45/2.00 inference(avatar_split_clause,[],[f2518,f2504,f2369,f4911])).
% 11.45/2.00 thf(f4911,plain,(
% 11.45/2.00 spl41_227 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_227])])).
% 11.45/2.00 thf(f2504,plain,(
% 11.45/2.00 spl41_47 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_47])])).
% 11.45/2.00 thf(f2518,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) = $false)) ) | (~spl41_26 | ~spl41_47)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2517])).
% 11.45/2.00 thf(f2517,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) = $false)) ) | (~spl41_26 | ~spl41_47)),
% 11.45/2.00 inference(superposition,[],[f2505,f2370])).
% 11.45/2.00 thf(f2505,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((canoni770627133id_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) ) | ~spl41_47),
% 11.45/2.00 inference(avatar_component_clause,[],[f2504])).
% 11.45/2.00 thf(f4909,plain,(
% 11.45/2.00 spl41_226 | ~spl41_26 | ~spl41_46),
% 11.45/2.00 inference(avatar_split_clause,[],[f2515,f2500,f2369,f4907])).
% 11.45/2.00 thf(f4907,plain,(
% 11.45/2.00 spl41_226 <=> ! [X0 : $tType,X1 : X0] : ((canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_226])])).
% 11.45/2.00 thf(f2515,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : ((canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_46)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2514])).
% 11.45/2.00 thf(f2514,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) ) | (~spl41_26 | ~spl41_46)),
% 11.45/2.00 inference(superposition,[],[f2501,f2370])).
% 11.45/2.00 thf(f4905,plain,(
% 11.45/2.00 spl41_225),
% 11.45/2.00 inference(avatar_split_clause,[],[f2241,f4903])).
% 11.45/2.00 thf(f4903,plain,(
% 11.45/2.00 spl41_225 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (zero_zero(nat) = X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_225])])).
% 11.45/2.00 thf(f2241,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (zero_zero(nat) = X0)) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f2240])).
% 11.45/2.00 thf(f2240,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 11.45/2.00 inference(not_proxy_clausification,[],[f2236])).
% 11.45/2.00 thf(f2236,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1195])).
% 11.45/2.00 thf(f1195,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f288])).
% 11.45/2.00 thf(f288,plain,(
% 11.45/2.00 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))),
% 11.45/2.00 inference(fool_elimination,[],[f287])).
% 11.45/2.00 thf(f287,plain,(
% 11.45/2.00 ! [X0 : nat] : ((zero_zero(nat) != X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))),
% 11.45/2.00 inference(rectify,[],[f15])).
% 11.45/2.00 thf(f15,axiom,(
% 11.45/2.00 ! [X9 : nat] : ((zero_zero(nat) != X9) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X9))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_bot__nat__0_Onot__eq__extremum)).
% 11.45/2.00 thf(f4867,plain,(
% 11.45/2.00 spl41_224 | ~spl41_8 | ~spl41_51),
% 11.45/2.00 inference(avatar_split_clause,[],[f2579,f2532,f2280,f4865])).
% 11.45/2.00 thf(f4865,plain,(
% 11.45/2.00 spl41_224 <=> ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),zero_zero(nat)),X0))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_224])])).
% 11.45/2.00 thf(f2579,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),zero_zero(nat)),X0))) ) | (~spl41_8 | ~spl41_51)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2576])).
% 11.45/2.00 thf(f2576,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),zero_zero(nat)),X0))) ) | (~spl41_8 | ~spl41_51)),
% 11.45/2.00 inference(superposition,[],[f2533,f2282])).
% 11.45/2.00 thf(f4863,plain,(
% 11.45/2.00 spl41_223 | ~spl41_8 | ~spl41_50),
% 11.45/2.00 inference(avatar_split_clause,[],[f2575,f2528,f2280,f4861])).
% 11.45/2.00 thf(f4861,plain,(
% 11.45/2.00 spl41_223 <=> ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),zero_zero(nat)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_223])])).
% 11.45/2.00 thf(f2575,plain,(
% 11.45/2.00 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),zero_zero(nat)))) ) | (~spl41_8 | ~spl41_50)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2572])).
% 11.45/2.00 thf(f2572,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),zero_zero(nat)))) ) | (~spl41_8 | ~spl41_50)),
% 11.45/2.00 inference(superposition,[],[f2529,f2282])).
% 11.45/2.00 thf(f4799,plain,(
% 11.45/2.00 spl41_222 | ~spl41_31 | ~spl41_157),
% 11.45/2.00 inference(avatar_split_clause,[],[f3945,f3901,f2420,f4797])).
% 11.45/2.00 thf(f4797,plain,(
% 11.45/2.00 spl41_222 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType] : (($true = order(sTfun(X3,sTfun(X0,sTfun(X1,X2))))) | ($false = order(X2)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_222])])).
% 11.45/2.00 thf(f3901,plain,(
% 11.45/2.00 spl41_157 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,X1)))) | ($false = order(X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_157])])).
% 11.45/2.00 thf(f3945,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = order(sTfun(X3,sTfun(X0,sTfun(X1,X2))))) | ($false = order(X2))) ) | (~spl41_31 | ~spl41_157)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3944])).
% 11.45/2.00 thf(f3944,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X3,sTfun(X0,sTfun(X1,X2))))) | ($false = order(X2))) ) | (~spl41_31 | ~spl41_157)),
% 11.45/2.00 inference(superposition,[],[f2421,f3902])).
% 11.45/2.00 thf(f3902,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,X1)))) | ($false = order(X1))) ) | ~spl41_157),
% 11.45/2.00 inference(avatar_component_clause,[],[f3901])).
% 11.45/2.00 thf(f4795,plain,(
% 11.45/2.00 spl41_221 | ~spl41_26 | ~spl41_37),
% 11.45/2.00 inference(avatar_split_clause,[],[f2466,f2452,f2369,f4793])).
% 11.45/2.00 thf(f4779,plain,(
% 11.45/2.00 spl41_220),
% 11.45/2.00 inference(avatar_split_clause,[],[f1257,f4777])).
% 11.45/2.00 thf(f4777,plain,(
% 11.45/2.00 spl41_220 <=> ! [X0 : $tType] : ((ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),vAPP(sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0)))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_220])])).
% 11.45/2.00 thf(f1257,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),vAPP(sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0)))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f902])).
% 11.45/2.00 thf(f902,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),vAPP(sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0)))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f398])).
% 11.45/2.00 thf(f398,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linorder(X0) = $true) => (ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),vAPP(sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0)))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f397])).
% 11.45/2.00 thf(f397,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linorder(X0) => (ord_less(X0) = (^[X1 : X0, X2 : X0] : (! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1) => (X2 != X3))))))),
% 11.45/2.00 inference(rectify,[],[f225])).
% 11.45/2.00 thf(f225,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linorder(X0) => (ord_less(X0) = (^[X42 : X0, X56 : X0] : (! [X57 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X57),X42) => (X56 != X57))))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_greater__le__neq__conv)).
% 11.45/2.00 thf(f4775,plain,(
% 11.45/2.00 spl41_219),
% 11.45/2.00 inference(avatar_split_clause,[],[f1255,f4773])).
% 11.45/2.00 thf(f4773,plain,(
% 11.45/2.00 spl41_219 <=> ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),vAPP(sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less(X0)))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_219])])).
% 11.45/2.00 thf(f1255,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),vAPP(sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less(X0)))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f900])).
% 11.45/2.00 thf(f900,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),vAPP(sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less(X0)))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f394])).
% 11.45/2.00 thf(f394,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linorder(X0) = $true) => (ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),vAPP(sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)))),sTfun(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(X0,sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less(X0)))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f393])).
% 11.45/2.00 thf(f393,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linorder(X0) => (ord_less_eq(X0) = (^[X1 : X0, X2 : X0] : (! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1) => (X2 != X3))))))),
% 11.45/2.00 inference(rectify,[],[f223])).
% 11.45/2.00 thf(f223,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linorder(X0) => (ord_less_eq(X0) = (^[X42 : X0, X56 : X0] : (! [X57 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X57),X42) => (X56 != X57))))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_ge__less__neq__conv)).
% 11.45/2.00 thf(f4759,plain,(
% 11.45/2.00 spl41_218),
% 11.45/2.00 inference(avatar_split_clause,[],[f1256,f4757])).
% 11.45/2.00 thf(f4757,plain,(
% 11.45/2.00 spl41_218 <=> ! [X0 : $tType] : ((ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),ord_less_eq(X0))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_218])])).
% 11.45/2.00 thf(f1256,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),ord_less_eq(X0))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f901])).
% 11.45/2.00 thf(f901,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),ord_less_eq(X0))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f396])).
% 11.45/2.00 thf(f396,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linorder(X0) = $true) => (ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),ord_less_eq(X0))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f395])).
% 11.45/2.00 thf(f395,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linorder(X0) => (ord_less(X0) = (^[X1 : X0, X2 : X0] : (! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => (X1 != X3))))))),
% 11.45/2.00 inference(rectify,[],[f224])).
% 11.45/2.00 thf(f224,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linorder(X0) => (ord_less(X0) = (^[X56 : X0, X42 : X0] : (! [X57 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X42),X57) => (X56 != X57))))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_less__ge__neq__conv)).
% 11.45/2.00 thf(f4755,plain,(
% 11.45/2.00 spl41_217),
% 11.45/2.00 inference(avatar_split_clause,[],[f1254,f4753])).
% 11.45/2.00 thf(f4753,plain,(
% 11.45/2.00 spl41_217 <=> ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),ord_less(X0))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_217])])).
% 11.45/2.00 thf(f1254,plain,(
% 11.45/2.00 ( ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),ord_less(X0))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f899])).
% 11.45/2.00 thf(f899,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),ord_less(X0))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))) | (linorder(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f392])).
% 11.45/2.00 thf(f392,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linorder(X0) = $true) => (ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),ord_less(X0))))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f391])).
% 11.45/2.00 thf(f391,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linorder(X0) => (ord_less_eq(X0) = (^[X1 : X0, X2 : X0] : (! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => (X1 != X3))))))),
% 11.45/2.00 inference(rectify,[],[f226])).
% 11.45/2.00 thf(f226,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linorder(X0) => (ord_less_eq(X0) = (^[X56 : X0, X42 : X0] : (! [X57 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X42),X57) => (X56 != X57))))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_le__greater__neq__conv)).
% 11.45/2.00 thf(f4664,plain,(
% 11.45/2.00 spl41_216),
% 11.45/2.00 inference(avatar_split_clause,[],[f1448,f4662])).
% 11.45/2.00 thf(f4662,plain,(
% 11.45/2.00 spl41_216 <=> ! [X0 : $tType,X2 : nat > X0 > X0 > $o,X4 : nat,X8 : X0,X1 : nat > X0 > $o,X7 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4)),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),vAPP(nat,nat,suc,X4)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1)),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1))),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_216])])).
% 11.45/2.00 thf(f1448,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : nat > X0 > X0 > $o,X1 : nat > X0 > $o,X8 : X0,X7 : X0,X4 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4)),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),vAPP(nat,nat,suc,X4)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1)),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1))),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1161])).
% 11.45/2.00 thf(f1161,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : nat > X0 > $o,X2 : nat > X0 > X0 > $o] : (! [X4 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4)),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),vAPP(nat,nat,suc,X4)))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4)))) | (! [X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1)),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1))),X7))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1)))) | ! [X8 : X0] : ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8)))),
% 11.45/2.00 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f1158,f1160,f1159])).
% 11.45/2.00 thf(f1159,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : nat > X0 > $o,X2 : nat > X0 > X0 > $o] : (? [X3 : nat > X0] : ! [X4 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X4),vAPP(nat,X0,X3,X4)),vAPP(nat,X0,X3,vAPP(nat,nat,suc,X4)))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X4),vAPP(nat,X0,X3,X4)))) => ! [X4 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4)),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),vAPP(nat,nat,suc,X4)))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4)))))),
% 11.45/2.00 introduced(choice_axiom,[])).
% 11.45/2.00 thf(f1160,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : nat > X0 > $o,X2 : nat > X0 > X0 > $o] : (? [X5 : X0,X6 : nat] : (! [X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X6),X5),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,X6)),X7))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X6),X5))) => (! [X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1)),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1))),X7))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1)))))),
% 11.45/2.00 introduced(choice_axiom,[])).
% 11.45/2.00 thf(f1158,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : nat > X0 > $o,X2 : nat > X0 > X0 > $o] : (? [X3 : nat > X0] : ! [X4 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X4),vAPP(nat,X0,X3,X4)),vAPP(nat,X0,X3,vAPP(nat,nat,suc,X4)))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X4),vAPP(nat,X0,X3,X4)))) | ? [X5 : X0,X6 : nat] : (! [X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X6),X5),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,X6)),X7))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X6),X5))) | ! [X8 : X0] : ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8)))),
% 11.45/2.00 inference(rectify,[],[f1078])).
% 11.45/2.00 thf(f1078,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : nat > X0 > $o,X2 : nat > X0 > X0 > $o] : (? [X7 : nat > X0] : ! [X8 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X8),vAPP(nat,X0,X7,X8)),vAPP(nat,X0,X7,vAPP(nat,nat,suc,X8)))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X8),vAPP(nat,X0,X7,X8)))) | ? [X4 : X0,X5 : nat] : (! [X6 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X5),X4),X6)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,X5)),X6))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X5),X4))) | ! [X3 : X0] : ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X3)))),
% 11.45/2.00 inference(flattening,[],[f1077])).
% 11.45/2.00 thf(f1077,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : nat > X0 > $o,X2 : nat > X0 > X0 > $o] : ((? [X7 : nat > X0] : ! [X8 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X8),vAPP(nat,X0,X7,X8)),vAPP(nat,X0,X7,vAPP(nat,nat,suc,X8)))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X8),vAPP(nat,X0,X7,X8)))) | ? [X4 : X0,X5 : nat] : (! [X6 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X5),X4),X6)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,X5)),X6))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X5),X4)))) | ! [X3 : X0] : ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X3)))),
% 11.45/2.00 inference(ennf_transformation,[],[f720])).
% 11.45/2.00 thf(f720,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : nat > X0 > $o,X2 : nat > X0 > X0 > $o] : (? [X3 : X0] : ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X3)) => (! [X4 : X0,X5 : nat] : (($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X5),X4)) => ? [X6 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X5),X4),X6)) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,X5)),X6)))) => ? [X7 : nat > X0] : ! [X8 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X8),vAPP(nat,X0,X7,X8)),vAPP(nat,X0,X7,vAPP(nat,nat,suc,X8)))) & ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X8),vAPP(nat,X0,X7,X8))))))),
% 11.45/2.00 inference(fool_elimination,[],[f719])).
% 11.45/2.00 thf(f719,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : nat > X0 > $o,X2 : nat > X0 > X0 > $o] : (? [X3 : X0] : vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X3) => (! [X4 : X0,X5 : nat] : (vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X5),X4) => ? [X6 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X5),X4),X6) & vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,X5)),X6))) => ? [X7 : nat > X0] : ! [X8 : nat] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X8),vAPP(nat,X0,X7,X8)),vAPP(nat,X0,X7,vAPP(nat,nat,suc,X8))) & vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X8),vAPP(nat,X0,X7,X8)))))),
% 11.45/2.00 inference(rectify,[],[f207])).
% 11.45/2.00 thf(f207,axiom,(
% 11.45/2.00 ! [X0 : $tType,X13 : nat > X0 > $o,X48 : nat > X0 > X0 > $o] : (? [X49 : X0] : vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X13,zero_zero(nat)),X49) => (! [X14 : X0,X19 : nat] : (vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X13,X19),X14) => ? [X15 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X48,X19),X14),X15) & vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X13,vAPP(nat,nat,suc,X19)),X15))) => ? [X50 : nat > X0] : ! [X51 : nat] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X48,X51),vAPP(nat,X0,X50,X51)),vAPP(nat,X0,X50,vAPP(nat,nat,suc,X51))) & vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X13,X51),vAPP(nat,X0,X50,X51)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_dependent__nat__choice)).
% 11.45/2.00 thf(f4652,plain,(
% 11.45/2.00 spl41_215),
% 11.45/2.00 inference(avatar_split_clause,[],[f1446,f4650])).
% 11.45/2.00 thf(f4650,plain,(
% 11.45/2.00 spl41_215 <=> ! [X0 : $tType,X2 : nat > X0 > X0 > $o,X4 : nat,X8 : X0,X1 : nat > X0 > $o,X7 : X0] : (($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1)),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1))),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_215])])).
% 11.45/2.00 thf(f1446,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : nat > X0 > X0 > $o,X1 : nat > X0 > $o,X8 : X0,X7 : X0,X4 : nat] : (($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1)),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1))),X7)) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1161])).
% 11.45/2.00 thf(f4635,plain,(
% 11.45/2.00 spl41_214),
% 11.45/2.00 inference(avatar_split_clause,[],[f1447,f4633])).
% 11.45/2.00 thf(f4633,plain,(
% 11.45/2.00 spl41_214 <=> ! [X0 : $tType,X2 : nat > X0 > X0 > $o,X4 : nat,X8 : X0,X1 : nat > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4)),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),vAPP(nat,nat,suc,X4)))) | ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_214])])).
% 11.45/2.00 thf(f1447,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : nat > X0 > X0 > $o,X1 : nat > X0 > $o,X8 : X0,X4 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(nat,sTfun(X0,sTfun(X0,$o)),X2,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4)),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),vAPP(nat,nat,suc,X4)))) | ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1161])).
% 11.45/2.00 thf(f4617,plain,(
% 11.45/2.00 spl41_213),
% 11.45/2.00 inference(avatar_split_clause,[],[f1445,f4615])).
% 11.45/2.00 thf(f4615,plain,(
% 11.45/2.00 spl41_213 <=> ! [X0 : $tType,X2 : nat > X0 > X0 > $o,X4 : nat,X8 : X0,X1 : nat > X0 > $o] : (($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4))) | ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_213])])).
% 11.45/2.00 thf(f1445,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : nat > X0 > X0 > $o,X1 : nat > X0 > $o,X8 : X0,X4 : nat] : (($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,X4),vAPP(nat,X0,vAPP(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0),vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),sTfun(nat,X0)),sK29(X0),X2),X1),X4))) | ($true = vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,vAPP(sTfun(nat,sTfun(X0,$o)),nat,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),nat),sK31(X0),X2),X1)),vAPP(sTfun(nat,sTfun(X0,$o)),X0,vAPP(sTfun(nat,sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(nat,sTfun(X0,$o)),X0),sK30(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(nat,sTfun(X0,$o),X1,zero_zero(nat)),X8))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1161])).
% 11.45/2.00 thf(f4575,plain,(
% 11.45/2.00 spl41_212),
% 11.45/2.00 inference(avatar_split_clause,[],[f1444,f4573])).
% 11.45/2.00 thf(f4573,plain,(
% 11.45/2.00 spl41_212 <=> ! [X2 : nat,X0 : nat > nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK25,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_212])])).
% 11.45/2.00 thf(f1444,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat > nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK25,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),zero_zero(nat)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1157])).
% 11.45/2.00 thf(f1157,plain,(
% 11.45/2.00 ! [X0 : nat > nat > $o,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) | (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK25,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK25,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),zero_zero(nat))))),
% 11.45/2.00 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27,sK28])],[f1153,f1156,f1155,f1154])).
% 11.45/2.00 thf(f1154,plain,(
% 11.45/2.00 ! [X0 : nat > nat > $o] : (? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X4))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4))) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK25,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK25,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)))))),
% 11.45/2.00 introduced(choice_axiom,[])).
% 11.45/2.00 thf(f1155,plain,(
% 11.45/2.00 ! [X0 : nat > nat > $o] : (? [X5 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X5))) => ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)))))),
% 11.45/2.00 introduced(choice_axiom,[])).
% 11.45/2.00 thf(f1156,plain,(
% 11.45/2.00 ! [X0 : nat > nat > $o] : (? [X6 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),zero_zero(nat))) => ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),zero_zero(nat))))),
% 11.45/2.00 introduced(choice_axiom,[])).
% 11.45/2.00 thf(f1153,plain,(
% 11.45/2.00 ! [X0 : nat > nat > $o,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) | ? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X4))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4))) | ? [X5 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X5))) | ? [X6 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),zero_zero(nat))))),
% 11.45/2.00 inference(rectify,[],[f1076])).
% 11.45/2.00 thf(f1076,plain,(
% 11.45/2.00 ! [X0 : nat > nat > $o,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) | ? [X5 : nat,X6 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6))) | ? [X4 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X4))) | ? [X3 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero(nat))))),
% 11.45/2.00 inference(flattening,[],[f1075])).
% 11.45/2.00 thf(f1075,plain,(
% 11.45/2.00 ! [X0 : nat > nat > $o,X1 : nat,X2 : nat] : (((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) | ? [X5 : nat,X6 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6)))) | ? [X4 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X4)))) | ? [X3 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero(nat))))),
% 11.45/2.00 inference(ennf_transformation,[],[f718])).
% 11.45/2.00 thf(f718,plain,(
% 11.45/2.00 ! [X0 : nat > nat > $o,X1 : nat,X2 : nat] : (! [X3 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero(nat))) => (! [X4 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X4))) => (! [X5 : nat,X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)))) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)))))),
% 11.45/2.00 inference(fool_elimination,[],[f717])).
% 11.45/2.00 thf(f717,plain,(
% 11.45/2.00 ! [X0 : nat > nat > $o,X1 : nat,X2 : nat] : (! [X3 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero(nat)) => (! [X4 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X4)) => (! [X5 : nat,X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6))) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2))))),
% 11.45/2.00 inference(rectify,[],[f49])).
% 11.45/2.00 thf(f49,axiom,(
% 11.45/2.00 ! [X13 : nat > nat > $o,X3 : nat,X2 : nat] : (! [X14 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,X14),zero_zero(nat)) => (! [X25 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,zero_zero(nat)),vAPP(nat,nat,suc,X25)) => (! [X14 : nat,X25 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,X14),X25) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,vAPP(nat,nat,suc,X14)),vAPP(nat,nat,suc,X25))) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,X3),X2))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_diff__induct)).
% 11.45/2.00 thf(f4571,plain,(
% 11.45/2.00 spl41_211),
% 11.45/2.00 inference(avatar_split_clause,[],[f1253,f4569])).
% 11.45/2.00 thf(f4569,plain,(
% 11.45/2.00 spl41_211 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_211])])).
% 11.45/2.00 thf(f1253,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_semiring(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f898])).
% 11.45/2.00 thf(f898,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f897])).
% 11.45/2.00 thf(f897,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f390])).
% 11.45/2.00 thf(f390,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordered_semiring(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))))))))),
% 11.45/2.00 inference(fool_elimination,[],[f389])).
% 11.45/2.00 thf(f389,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4)))))))),
% 11.45/2.00 inference(rectify,[],[f244])).
% 11.45/2.00 thf(f244,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring(X0) => ! [X9 : X0,X11 : X0,X10 : X0,X58 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X10),X58) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X58)))))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_mult__mono_H)).
% 11.45/2.00 thf(f4567,plain,(
% 11.45/2.00 spl41_210),
% 11.45/2.00 inference(avatar_split_clause,[],[f1252,f4565])).
% 11.45/2.00 thf(f4565,plain,(
% 11.45/2.00 spl41_210 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_210])])).
% 11.45/2.00 thf(f1252,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_semiring(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f896])).
% 11.45/2.00 thf(f896,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f895])).
% 11.45/2.00 thf(f895,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f388])).
% 11.45/2.00 thf(f388,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordered_semiring(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))))))))),
% 11.45/2.00 inference(fool_elimination,[],[f387])).
% 11.45/2.00 thf(f387,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4)))))))),
% 11.45/2.00 inference(rectify,[],[f245])).
% 11.45/2.00 thf(f245,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring(X0) => ! [X9 : X0,X11 : X0,X10 : X0,X58 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X10),X58) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X58)))))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_mult__mono)).
% 11.45/2.00 thf(f4543,plain,(
% 11.45/2.00 spl41_209),
% 11.45/2.00 inference(avatar_split_clause,[],[f1340,f4541])).
% 11.45/2.00 thf(f4541,plain,(
% 11.45/2.00 spl41_209 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linordered_field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_209])])).
% 11.45/2.00 thf(f1340,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1014])).
% 11.45/2.00 thf(f1014,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f1013])).
% 11.45/2.00 thf(f1013,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f556])).
% 11.45/2.00 thf(f556,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1)))))))),
% 11.45/2.00 inference(fool_elimination,[],[f555])).
% 11.45/2.00 thf(f555,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))))))),
% 11.45/2.00 inference(rectify,[],[f182])).
% 11.45/2.00 thf(f182,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X11 : X0,X9 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X11),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X10) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X10),X11))))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_divide__strict__left__mono)).
% 11.45/2.00 thf(f4539,plain,(
% 11.45/2.00 spl41_208),
% 11.45/2.00 inference(avatar_split_clause,[],[f1338,f4537])).
% 11.45/2.00 thf(f4537,plain,(
% 11.45/2.00 spl41_208 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linordered_field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_208])])).
% 11.45/2.00 thf(f1338,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1010])).
% 11.45/2.00 thf(f1010,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f1009])).
% 11.45/2.00 thf(f1009,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f552])).
% 11.45/2.00 thf(f552,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2)))))))),
% 11.45/2.00 inference(fool_elimination,[],[f551])).
% 11.45/2.00 thf(f551,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X2))))))),
% 11.45/2.00 inference(rectify,[],[f183])).
% 11.45/2.00 thf(f183,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X10),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X10),X11))))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_divide__strict__left__mono__neg)).
% 11.45/2.00 thf(f4521,plain,(
% 11.45/2.00 spl41_207),
% 11.45/2.00 inference(avatar_split_clause,[],[f1443,f4519])).
% 11.45/2.00 thf(f4519,plain,(
% 11.45/2.00 spl41_207 <=> ! [X2 : nat,X0 : nat > nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK25,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),zero_zero(nat))))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_207])])).
% 11.45/2.00 thf(f1443,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat > nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK25,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),zero_zero(nat)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1157])).
% 11.45/2.00 thf(f4473,plain,(
% 11.45/2.00 spl41_206),
% 11.45/2.00 inference(avatar_split_clause,[],[f1265,f4471])).
% 11.45/2.00 thf(f4471,plain,(
% 11.45/2.00 spl41_206 <=> ! [X0 : $tType,X3 : nat,X2 : nat,X1 : nat > X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X2)),vAPP(nat,X0,X1,X3))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,vAPP(sTfun(nat,X0),nat,sK8(X0),X1))),vAPP(nat,X0,X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,X0),nat,sK8(X0),X1))))) | (order(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_206])])).
% 11.45/2.00 thf(f1265,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : nat > X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X2)),vAPP(nat,X0,X1,X3))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,vAPP(sTfun(nat,X0),nat,sK8(X0),X1))),vAPP(nat,X0,X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,X0),nat,sK8(X0),X1))))) | (order(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1120])).
% 11.45/2.00 thf(f1120,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : nat > X0,X2 : nat,X3 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X2)),vAPP(nat,X0,X1,X3))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,vAPP(sTfun(nat,X0),nat,sK8(X0),X1))),vAPP(nat,X0,X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,X0),nat,sK8(X0),X1)))))) | (order(X0) != $true))),
% 11.45/2.00 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f914,f1119])).
% 11.45/2.00 thf(f1119,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : nat > X0] : (? [X4 : nat] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X4)),vAPP(nat,X0,X1,vAPP(nat,nat,suc,X4)))) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,vAPP(sTfun(nat,X0),nat,sK8(X0),X1))),vAPP(nat,X0,X1,vAPP(nat,nat,suc,vAPP(sTfun(nat,X0),nat,sK8(X0),X1))))))),
% 11.45/2.00 introduced(choice_axiom,[])).
% 11.45/2.00 thf(f914,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : nat > X0,X2 : nat,X3 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X2)),vAPP(nat,X0,X1,X3))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) != $true) | ? [X4 : nat] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X4)),vAPP(nat,X0,X1,vAPP(nat,nat,suc,X4))))) | (order(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f913])).
% 11.45/2.00 thf(f913,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : nat > X0,X2 : nat,X3 : nat] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X2)),vAPP(nat,X0,X1,X3))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) != $true)) | ? [X4 : nat] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X4)),vAPP(nat,X0,X1,vAPP(nat,nat,suc,X4))))) | (order(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f412])).
% 11.45/2.00 thf(f412,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : nat > X0,X2 : nat,X3 : nat] : (! [X4 : nat] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X4)),vAPP(nat,X0,X1,vAPP(nat,nat,suc,X4)))) => ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X2)),vAPP(nat,X0,X1,X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f411])).
% 11.45/2.00 thf(f411,plain,(
% 11.45/2.00 ! [X0 : $tType] : (order(X0) => ! [X1 : nat > X0,X2 : nat,X3 : nat] : (! [X4 : nat] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X4)),vAPP(nat,X0,X1,vAPP(nat,nat,suc,X4))) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X1,X2)),vAPP(nat,X0,X1,X3)))))),
% 11.45/2.00 inference(rectify,[],[f85])).
% 11.45/2.00 thf(f85,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (order(X0) => ! [X12 : nat > X0,X2 : nat,X35 : nat] : (! [X19 : nat] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X12,X19)),vAPP(nat,X0,X12,vAPP(nat,nat,suc,X19))) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X35) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(nat,X0,X12,X2)),vAPP(nat,X0,X12,X35)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_lift__Suc__mono__less)).
% 11.45/2.00 thf(f4465,plain,(
% 11.45/2.00 spl41_205),
% 11.45/2.00 inference(avatar_split_clause,[],[f1314,f4463])).
% 11.45/2.00 thf(f4463,plain,(
% 11.45/2.00 spl41_205 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | (field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_205])])).
% 11.45/2.00 thf(f1314,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | (field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f975])).
% 11.45/2.00 thf(f975,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))) | (field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f508])).
% 11.45/2.00 thf(f508,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))))),
% 11.45/2.00 inference(fool_elimination,[],[f507])).
% 11.45/2.00 thf(f507,plain,(
% 11.45/2.00 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X4))))),
% 11.45/2.00 inference(rectify,[],[f133])).
% 11.45/2.00 thf(f133,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (field(X0) => ! [X16 : X0,X17 : X0,X40 : X0,X41 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X40),X41)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X16),X40)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X17),X41))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_times__divide__times__eq)).
% 11.45/2.00 thf(f4461,plain,(
% 11.45/2.00 spl41_204),
% 11.45/2.00 inference(avatar_split_clause,[],[f1313,f4459])).
% 11.45/2.00 thf(f4459,plain,(
% 11.45/2.00 spl41_204 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | (field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_204])])).
% 11.45/2.00 thf(f1313,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | (field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f974])).
% 11.45/2.00 thf(f974,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | (field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f506])).
% 11.45/2.00 thf(f506,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))))),
% 11.45/2.00 inference(fool_elimination,[],[f505])).
% 11.45/2.00 thf(f505,plain,(
% 11.45/2.00 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))))),
% 11.45/2.00 inference(rectify,[],[f134])).
% 11.45/2.00 thf(f134,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (field(X0) => ! [X16 : X0,X17 : X0,X40 : X0,X41 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X40),X41)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X16),X41)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X17),X40))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_divide__divide__times__eq)).
% 11.45/2.00 thf(f4448,plain,(
% 11.45/2.00 spl41_203),
% 11.45/2.00 inference(avatar_split_clause,[],[f1459,f4446])).
% 11.45/2.00 thf(f4446,plain,(
% 11.45/2.00 spl41_203 <=> ! [X2 : nat > nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1)) | ($true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X2)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_203])])).
% 11.45/2.00 thf(f1459,plain,(
% 11.45/2.00 ( ! [X2 : nat > nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1)) | ($true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X2)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1173])).
% 11.45/2.00 thf(f1173,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1)) | ($true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X2)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f1105,f1172])).
% 11.45/2.00 thf(f1172,plain,(
% 11.45/2.00 ! [X2 : nat > nat > $o] : (? [X3 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3))) => ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X2)))))),
% 11.45/2.00 introduced(choice_axiom,[])).
% 11.45/2.00 thf(f1105,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1)) | ($true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2)) | ? [X3 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(definition_folding,[],[f1082,f1104])).
% 11.45/2.00 thf(f1104,plain,(
% 11.45/2.00 ! [X2 : nat > nat > $o] : (? [X4 : nat,X5 : nat,X6 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X5))) | ~($true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2)))),
% 11.45/2.00 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 11.45/2.00 thf(f1082,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1)) | ? [X4 : nat,X5 : nat,X6 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X5))) | ? [X3 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(flattening,[],[f1081])).
% 11.45/2.00 thf(f1081,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat > nat > $o] : (((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1)) | ? [X4 : nat,X5 : nat,X6 : nat] : ((((($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X6))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X5)))) | ? [X3 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(ennf_transformation,[],[f724])).
% 11.45/2.00 thf(f724,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (! [X3 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3))) => (! [X4 : nat,X5 : nat,X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X5)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X6)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6)))))) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1)))))),
% 11.45/2.00 inference(fool_elimination,[],[f723])).
% 11.45/2.00 thf(f723,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat > nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (! [X3 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3)) => (! [X4 : nat,X5 : nat,X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X5) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X6) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6))))) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1))))),
% 11.45/2.00 inference(rectify,[],[f65])).
% 11.45/2.00 thf(f65,axiom,(
% 11.45/2.00 ! [X27 : nat,X28 : nat,X13 : nat > nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X28) => (! [X29 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,X29),vAPP(nat,nat,suc,X29)) => (! [X29 : nat,X30 : nat,X31 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X29),X30) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X30),X31) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,X29),X30) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,X30),X31) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,X29),X31))))) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X13,X27),X28))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__Suc__induct)).
% 11.45/2.00 thf(f4412,plain,(
% 11.45/2.00 spl41_202 | ~spl41_26 | ~spl41_32),
% 11.45/2.00 inference(avatar_split_clause,[],[f2434,f2430,f2369,f4410])).
% 11.45/2.00 thf(f2434,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | (~spl41_26 | ~spl41_32)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f2433])).
% 11.45/2.00 thf(f2433,plain,(
% 11.45/2.00 ( ! [X0 : nat] : (($true != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | (~spl41_26 | ~spl41_32)),
% 11.45/2.00 inference(superposition,[],[f2431,f2370])).
% 11.45/2.00 thf(f4339,plain,(
% 11.45/2.00 spl41_201),
% 11.45/2.00 inference(avatar_split_clause,[],[f1753,f4337])).
% 11.45/2.00 thf(f4337,plain,(
% 11.45/2.00 spl41_201 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | (vAPP(nat,nat,suc,X1) != vAPP(nat,nat,suc,X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_201])])).
% 11.45/2.00 thf(f1753,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | (vAPP(nat,nat,suc,X1) != vAPP(nat,nat,suc,X0))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1752])).
% 11.45/2.00 thf(f1752,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1748])).
% 11.45/2.00 thf(f1748,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1363])).
% 11.45/2.00 thf(f1363,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f598])).
% 11.45/2.00 thf(f598,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)))),
% 11.45/2.00 inference(fool_elimination,[],[f597])).
% 11.45/2.00 thf(f597,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X1) = vAPP(nat,nat,suc,X0)) = (X0 = X1))),
% 11.45/2.00 inference(rectify,[],[f14])).
% 11.45/2.00 thf(f14,axiom,(
% 11.45/2.00 ! [X7 : nat,X8 : nat] : ((vAPP(nat,nat,suc,X7) = vAPP(nat,nat,suc,X8)) = (X7 = X8))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_nat_Oinject)).
% 11.45/2.00 thf(f4309,plain,(
% 11.45/2.00 spl41_200),
% 11.45/2.00 inference(avatar_split_clause,[],[f1347,f4307])).
% 11.45/2.00 thf(f1347,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1024])).
% 11.45/2.00 thf(f1024,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f1023])).
% 11.45/2.00 thf(f1023,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f570])).
% 11.45/2.00 thf(f570,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1))))))),
% 11.45/2.00 inference(fool_elimination,[],[f569])).
% 11.45/2.00 thf(f569,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X3),X1)))))),
% 11.45/2.00 inference(rectify,[],[f181])).
% 11.45/2.00 thf(f181,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X17 : X0,X40 : X0,X16 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X17) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X40),X17)),X16) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X40),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_mult__imp__less__div__pos)).
% 11.45/2.00 thf(f4305,plain,(
% 11.45/2.00 spl41_199),
% 11.45/2.00 inference(avatar_split_clause,[],[f1346,f4303])).
% 11.45/2.00 thf(f4303,plain,(
% 11.45/2.00 spl41_199 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_199])])).
% 11.45/2.00 thf(f1346,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1022])).
% 11.45/2.00 thf(f1022,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f1021])).
% 11.45/2.00 thf(f1021,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f568])).
% 11.45/2.00 thf(f568,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1)),X3)))))),
% 11.45/2.00 inference(fool_elimination,[],[f567])).
% 11.45/2.00 thf(f567,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1)),X3))))),
% 11.45/2.00 inference(rectify,[],[f180])).
% 11.45/2.00 thf(f180,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X17 : X0,X16 : X0,X40 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X17) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X16),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X40),X17)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)),X40))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_mult__imp__div__pos__less)).
% 11.45/2.00 thf(f4301,plain,(
% 11.45/2.00 spl41_198),
% 11.45/2.00 inference(avatar_split_clause,[],[f1341,f4299])).
% 11.45/2.00 thf(f4299,plain,(
% 11.45/2.00 spl41_198 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linordered_field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_198])])).
% 11.45/2.00 thf(f1341,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1016])).
% 11.45/2.00 thf(f1016,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f1015])).
% 11.45/2.00 thf(f1015,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f558])).
% 11.45/2.00 thf(f558,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f557])).
% 11.45/2.00 thf(f557,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)))))),
% 11.45/2.00 inference(rectify,[],[f162])).
% 11.45/2.00 thf(f162,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X11),X10)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_divide__strict__right__mono)).
% 11.45/2.00 thf(f4297,plain,(
% 11.45/2.00 spl41_197),
% 11.45/2.00 inference(avatar_split_clause,[],[f1339,f4295])).
% 11.45/2.00 thf(f4295,plain,(
% 11.45/2.00 spl41_197 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linordered_field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_197])])).
% 11.45/2.00 thf(f1339,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1012])).
% 11.45/2.00 thf(f1012,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f1011])).
% 11.45/2.00 thf(f1011,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f554])).
% 11.45/2.00 thf(f554,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f553])).
% 11.45/2.00 thf(f553,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)))))),
% 11.45/2.00 inference(rectify,[],[f163])).
% 11.45/2.00 thf(f163,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X11 : X0,X9 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X11),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X10),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X11),X10)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_divide__strict__right__mono__neg)).
% 11.45/2.00 thf(f4293,plain,(
% 11.45/2.00 spl41_196),
% 11.45/2.00 inference(avatar_split_clause,[],[f1337,f4291])).
% 11.45/2.00 thf(f1337,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1008])).
% 11.45/2.00 thf(f1008,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f1007])).
% 11.45/2.00 thf(f1007,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f550])).
% 11.45/2.00 thf(f550,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(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,$o),ord_less_eq(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f549])).
% 11.45/2.00 thf(f549,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)))))),
% 11.45/2.00 inference(rectify,[],[f252])).
% 11.45/2.00 thf(f252,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X11),X10)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_divide__right__mono)).
% 11.45/2.00 thf(f4289,plain,(
% 11.45/2.00 spl41_195),
% 11.45/2.00 inference(avatar_split_clause,[],[f1336,f4287])).
% 11.45/2.00 thf(f4287,plain,(
% 11.45/2.00 spl41_195 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (linordered_field(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_195])])).
% 11.45/2.00 thf(f1336,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1006])).
% 11.45/2.00 thf(f1006,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f1005])).
% 11.45/2.00 thf(f1005,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f548])).
% 11.45/2.00 thf(f548,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(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,$o),ord_less_eq(X0),X3),zero_zero(X0))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f547])).
% 11.45/2.00 thf(f547,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X3)))))),
% 11.45/2.00 inference(rectify,[],[f246])).
% 11.45/2.00 thf(f246,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X10),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X11),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X10)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_divide__right__mono__neg)).
% 11.45/2.00 thf(f4285,plain,(
% 11.45/2.00 spl41_194),
% 11.45/2.00 inference(avatar_split_clause,[],[f1298,f4283])).
% 11.45/2.00 thf(f4283,plain,(
% 11.45/2.00 spl41_194 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord581940658strict(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_194])])).
% 11.45/2.00 thf(f1298,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord581940658strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f960])).
% 11.45/2.00 thf(f960,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord581940658strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f959])).
% 11.45/2.00 thf(f959,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord581940658strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f478])).
% 11.45/2.00 thf(f478,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord581940658strict(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))))))),
% 11.45/2.00 inference(fool_elimination,[],[f477])).
% 11.45/2.00 thf(f477,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord581940658strict(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))))),
% 11.45/2.00 inference(rectify,[],[f148])).
% 11.45/2.00 thf(f148,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord581940658strict(X0) => ! [X11 : X0,X9 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X11),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X10),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_mult__strict__left__mono__neg)).
% 11.45/2.00 thf(f4281,plain,(
% 11.45/2.00 spl41_193),
% 11.45/2.00 inference(avatar_split_clause,[],[f1751,f4279])).
% 11.45/2.00 thf(f4279,plain,(
% 11.45/2.00 spl41_193 <=> ! [X0 : nat,X1 : nat] : ((X0 != X1) | (vAPP(nat,nat,suc,X1) = vAPP(nat,nat,suc,X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_193])])).
% 11.45/2.00 thf(f1751,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | (vAPP(nat,nat,suc,X1) = vAPP(nat,nat,suc,X0))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1750])).
% 11.45/2.00 thf(f1750,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)))) )),
% 11.45/2.00 inference(equality_proxy_clausification,[],[f1749])).
% 11.45/2.00 thf(f1749,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)))) )),
% 11.45/2.00 inference(binary_proxy_clausification,[],[f1363])).
% 11.45/2.00 thf(f4277,plain,(
% 11.45/2.00 spl41_192),
% 11.45/2.00 inference(avatar_split_clause,[],[f1297,f4275])).
% 11.45/2.00 thf(f4275,plain,(
% 11.45/2.00 spl41_192 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord581940658strict(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_192])])).
% 11.45/2.00 thf(f1297,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord581940658strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f958])).
% 11.45/2.00 thf(f958,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord581940658strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f957])).
% 11.45/2.00 thf(f957,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord581940658strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f476])).
% 11.45/2.00 thf(f476,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord581940658strict(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f475])).
% 11.45/2.00 thf(f475,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord581940658strict(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)))))),
% 11.45/2.00 inference(rectify,[],[f151])).
% 11.45/2.00 thf(f151,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord581940658strict(X0) => ! [X11 : X0,X9 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X11),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X10),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_mult__strict__right__mono__neg)).
% 11.45/2.00 thf(f4273,plain,(
% 11.45/2.00 spl41_191),
% 11.45/2.00 inference(avatar_split_clause,[],[f1289,f4271])).
% 11.45/2.00 thf(f4271,plain,(
% 11.45/2.00 spl41_191 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_191])])).
% 11.45/2.00 thf(f1289,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord20386208strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f948])).
% 11.45/2.00 thf(f948,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f947])).
% 11.45/2.00 thf(f947,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f460])).
% 11.45/2.00 thf(f460,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord20386208strict(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f459])).
% 11.45/2.00 thf(f459,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)))))),
% 11.45/2.00 inference(rectify,[],[f149])).
% 11.45/2.00 thf(f149,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_mult__strict__left__mono)).
% 11.45/2.00 thf(f4269,plain,(
% 11.45/2.00 spl41_190),
% 11.45/2.00 inference(avatar_split_clause,[],[f1288,f4267])).
% 11.45/2.00 thf(f4267,plain,(
% 11.45/2.00 spl41_190 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_190])])).
% 11.45/2.00 thf(f1288,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord20386208strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f946])).
% 11.45/2.00 thf(f946,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f945])).
% 11.45/2.00 thf(f945,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f458])).
% 11.45/2.00 thf(f458,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord20386208strict(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f457])).
% 11.45/2.00 thf(f457,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)))))),
% 11.45/2.00 inference(rectify,[],[f152])).
% 11.45/2.00 thf(f152,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_mult__strict__right__mono)).
% 11.45/2.00 thf(f4265,plain,(
% 11.45/2.00 spl41_189),
% 11.45/2.00 inference(avatar_split_clause,[],[f1251,f4263])).
% 11.45/2.00 thf(f1251,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_semiring(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f894])).
% 11.45/2.00 thf(f894,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f893])).
% 11.45/2.00 thf(f893,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f386])).
% 11.45/2.00 thf(f386,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordered_semiring(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,$o),ord_less_eq(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f385])).
% 11.45/2.00 thf(f385,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)))))),
% 11.45/2.00 inference(rectify,[],[f237])).
% 11.45/2.00 thf(f237,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_mult__right__mono)).
% 11.45/2.00 thf(f4261,plain,(
% 11.45/2.00 spl41_188),
% 11.45/2.00 inference(avatar_split_clause,[],[f1250,f4259])).
% 11.45/2.00 thf(f4259,plain,(
% 11.45/2.00 spl41_188 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_188])])).
% 11.45/2.00 thf(f1250,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_semiring(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f892])).
% 11.45/2.00 thf(f892,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f891])).
% 11.45/2.00 thf(f891,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_semiring(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f384])).
% 11.45/2.00 thf(f384,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordered_semiring(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,$o),ord_less_eq(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f383])).
% 11.45/2.00 thf(f383,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)))))),
% 11.45/2.00 inference(rectify,[],[f239])).
% 11.45/2.00 thf(f239,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_mult__left__mono)).
% 11.45/2.00 thf(f4257,plain,(
% 11.45/2.00 spl41_187),
% 11.45/2.00 inference(avatar_split_clause,[],[f1241,f4255])).
% 11.45/2.00 thf(f4255,plain,(
% 11.45/2.00 spl41_187 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_187])])).
% 11.45/2.00 thf(f1241,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ring(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f882])).
% 11.45/2.00 thf(f882,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_ring(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f881])).
% 11.45/2.00 thf(f881,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_ring(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f366])).
% 11.45/2.00 thf(f366,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordered_ring(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,$o),ord_less_eq(X0),X3),zero_zero(X0))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f365])).
% 11.45/2.00 thf(f365,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_ring(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)))))),
% 11.45/2.00 inference(rectify,[],[f238])).
% 11.45/2.00 thf(f238,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_ring(X0) => ! [X11 : X0,X9 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X11),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X10),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_mult__right__mono__neg)).
% 11.45/2.00 thf(f4253,plain,(
% 11.45/2.00 spl41_186),
% 11.45/2.00 inference(avatar_split_clause,[],[f1240,f4251])).
% 11.45/2.00 thf(f4251,plain,(
% 11.45/2.00 spl41_186 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ring(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_186])])).
% 11.45/2.00 thf(f1240,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ring(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f880])).
% 11.45/2.00 thf(f880,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_ring(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f879])).
% 11.45/2.00 thf(f879,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_ring(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f364])).
% 11.45/2.00 thf(f364,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordered_ring(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,$o),ord_less_eq(X0),X3),zero_zero(X0))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))))))),
% 11.45/2.00 inference(fool_elimination,[],[f363])).
% 11.45/2.00 thf(f363,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_ring(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))))),
% 11.45/2.00 inference(rectify,[],[f241])).
% 11.45/2.00 thf(f241,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_ring(X0) => ! [X11 : X0,X9 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X11),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X10),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_mult__left__mono__neg)).
% 11.45/2.00 thf(f4249,plain,(
% 11.45/2.00 spl41_185),
% 11.45/2.00 inference(avatar_split_clause,[],[f1216,f4247])).
% 11.45/2.00 thf(f4247,plain,(
% 11.45/2.00 spl41_185 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord893533164strict(X0) != $true))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_185])])).
% 11.45/2.00 thf(f1216,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linord893533164strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f855])).
% 11.45/2.00 thf(f855,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord893533164strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f854])).
% 11.45/2.00 thf(f854,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (linord893533164strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f322])).
% 11.45/2.00 thf(f322,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord893533164strict(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f321])).
% 11.45/2.00 thf(f321,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord893533164strict(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)))))),
% 11.45/2.00 inference(rectify,[],[f154])).
% 11.45/2.00 thf(f154,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord893533164strict(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)).
% 11.45/2.00 thf(f4245,plain,(
% 11.45/2.00 spl41_184),
% 11.45/2.00 inference(avatar_split_clause,[],[f1215,f4243])).
% 11.45/2.00 thf(f1215,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere1490568538miring(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f853])).
% 11.45/2.00 thf(f853,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere1490568538miring(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f852])).
% 11.45/2.00 thf(f852,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere1490568538miring(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f320])).
% 11.45/2.00 thf(f320,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordere1490568538miring(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,$o),ord_less_eq(X0),zero_zero(X0)),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f319])).
% 11.45/2.00 thf(f319,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordere1490568538miring(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2)))))),
% 11.45/2.00 inference(rectify,[],[f229])).
% 11.45/2.00 thf(f229,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordere1490568538miring(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),X11) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X10) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_ordered__comm__semiring__class_Ocomm__mult__left__mono)).
% 11.45/2.00 thf(f4233,plain,(
% 11.45/2.00 spl41_183),
% 11.45/2.00 inference(avatar_split_clause,[],[f1423,f4231])).
% 11.45/2.00 thf(f4231,plain,(
% 11.45/2.00 spl41_183 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_183])])).
% 11.45/2.00 thf(f1423,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1070])).
% 11.45/2.00 thf(f1070,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)))),
% 11.45/2.00 inference(flattening,[],[f1069])).
% 11.45/2.00 thf(f1069,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)))),
% 11.45/2.00 inference(ennf_transformation,[],[f692])).
% 11.45/2.00 thf(f692,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)))))),
% 11.45/2.00 inference(fool_elimination,[],[f691])).
% 11.45/2.00 thf(f691,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X0) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))))),
% 11.45/2.00 inference(rectify,[],[f100])).
% 11.45/2.00 thf(f100,axiom,(
% 11.45/2.00 ! [X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),X2))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_one__less__mult)).
% 11.45/2.00 thf(f4204,plain,(
% 11.45/2.00 spl41_182),
% 11.45/2.00 inference(avatar_split_clause,[],[f1475,f4202])).
% 11.45/2.00 thf(f4202,plain,(
% 11.45/2.00 spl41_182 <=> ! [X1 : $tType,X2 : X1 > nat,X4 : X1,X0 : X1 > $o] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_182])])).
% 11.45/2.00 thf(f1475,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1177])).
% 11.45/2.00 thf(f1177,plain,(
% 11.45/2.00 ! [X0 : X1 > $o,X1 : $tType,X2 : X1 > nat] : ((! [X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))))) & ($true != vAPP(X1,$o,X0,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0)))),
% 11.45/2.00 inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f1175,f1176])).
% 11.45/2.00 thf(f1176,plain,(
% 11.45/2.00 ! [X1 : $tType,X0 : X1 > $o,X2 : X1 > nat] : (? [X3 : X1] : (! [X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,X3)))) & ($true != vAPP(X1,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,X3)))) => (! [X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))))) & ($true != vAPP(X1,$o,X0,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))))))),
% 11.45/2.00 introduced(choice_axiom,[])).
% 11.45/2.00 thf(f1175,plain,(
% 11.45/2.00 ! [X0 : X1 > $o,X1 : $tType,X2 : X1 > nat] : (? [X3 : X1] : (! [X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,X3)))) & ($true != vAPP(X1,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,X3)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0)))),
% 11.45/2.00 inference(rectify,[],[f1174])).
% 11.45/2.00 thf(f1174,plain,(
% 11.45/2.00 ! [X2 : X0 > $o,X0 : $tType,X1 : X0 > nat] : (? [X5 : X0] : (! [X6 : X0] : (($true = vAPP(X0,$o,X2,X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))) & ($true != vAPP(X0,$o,X2,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5)))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)))),
% 11.45/2.00 inference(nnf_transformation,[],[f1106])).
% 11.45/2.00 thf(f1106,plain,(
% 11.45/2.00 ! [X2 : X0 > $o,X0 : $tType,X1 : X0 > nat] : (? [X5 : X0] : (! [X6 : X0] : (($true = vAPP(X0,$o,X2,X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))) & ($true != vAPP(X0,$o,X2,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5)))) | ~($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)))),
% 11.45/2.00 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 11.45/2.00 thf(f4171,plain,(
% 11.45/2.00 spl41_181),
% 11.45/2.00 inference(avatar_split_clause,[],[f1469,f4169])).
% 11.45/2.00 thf(f1469,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1096])).
% 11.45/2.00 thf(f1096,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.00 inference(flattening,[],[f1095])).
% 11.45/2.00 thf(f1095,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.00 inference(ennf_transformation,[],[f744])).
% 11.45/2.00 thf(f744,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)))))),
% 11.45/2.00 inference(fool_elimination,[],[f743])).
% 11.45/2.00 thf(f743,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0)),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0))))),
% 11.45/2.00 inference(rectify,[],[f185])).
% 11.45/2.00 thf(f185,axiom,(
% 11.45/2.00 ! [X3 : nat,X2 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X3) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X2),X3)),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X3))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_div__less__imp__less__mult)).
% 11.45/2.00 thf(f4167,plain,(
% 11.45/2.00 spl41_180),
% 11.45/2.00 inference(avatar_split_clause,[],[f1462,f4165])).
% 11.45/2.00 thf(f1462,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1088])).
% 11.45/2.00 thf(f1088,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(flattening,[],[f1087])).
% 11.45/2.00 thf(f1087,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(ennf_transformation,[],[f730])).
% 11.45/2.00 thf(f730,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) = $true) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1)))))),
% 11.45/2.00 inference(fool_elimination,[],[f729])).
% 11.45/2.00 thf(f729,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X1))))),
% 11.45/2.00 inference(rectify,[],[f93])).
% 11.45/2.00 thf(f93,axiom,(
% 11.45/2.00 ! [X27 : nat,X28 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X28) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X27)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X28))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_mult__less__mono2)).
% 11.45/2.00 thf(f4163,plain,(
% 11.45/2.00 spl41_179),
% 11.45/2.00 inference(avatar_split_clause,[],[f1461,f4161])).
% 11.45/2.00 thf(f1461,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1086])).
% 11.45/2.00 thf(f1086,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(flattening,[],[f1085])).
% 11.45/2.00 thf(f1085,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) != $true)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.00 inference(ennf_transformation,[],[f728])).
% 11.45/2.00 thf(f728,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) = $true) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)))))),
% 11.45/2.00 inference(fool_elimination,[],[f727])).
% 11.45/2.00 thf(f727,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))))),
% 11.45/2.00 inference(rectify,[],[f94])).
% 11.45/2.00 thf(f94,axiom,(
% 11.45/2.00 ! [X27 : nat,X28 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X28) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X27),X4)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X28),X4))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mult__less__mono1)).
% 11.45/2.00 thf(f4149,plain,(
% 11.45/2.00 spl41_178),
% 11.45/2.00 inference(avatar_split_clause,[],[f1465,f4147])).
% 11.45/2.00 thf(f1465,plain,(
% 11.45/2.00 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1091])).
% 11.45/2.00 thf(f1091,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.00 inference(ennf_transformation,[],[f736])).
% 11.45/2.00 thf(f736,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))))),
% 11.45/2.00 inference(fool_elimination,[],[f735])).
% 11.45/2.00 thf(f735,plain,(
% 11.45/2.00 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))))),
% 11.45/2.00 inference(rectify,[],[f101])).
% 11.45/2.00 thf(f101,axiom,(
% 11.45/2.00 ! [X4 : nat,X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X4) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X3),X2)))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_nat__mult__div__cancel1)).
% 11.45/2.00 thf(f4081,plain,(
% 11.45/2.00 spl41_177 | ~spl41_31 | ~spl41_108),
% 11.45/2.00 inference(avatar_split_clause,[],[f3273,f3179,f2420,f4079])).
% 11.45/2.00 thf(f3273,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = order(sTfun(X3,sTfun(X0,sTfun(X1,sTfun(X2,$o))))))) ) | (~spl41_31 | ~spl41_108)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3272])).
% 11.45/2.00 thf(f3272,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X3,sTfun(X0,sTfun(X1,sTfun(X2,$o))))))) ) | (~spl41_31 | ~spl41_108)),
% 11.45/2.00 inference(superposition,[],[f2421,f3180])).
% 11.45/2.00 thf(f3994,plain,(
% 11.45/2.00 spl41_176 | ~spl41_31 | ~spl41_101),
% 11.45/2.00 inference(avatar_split_clause,[],[f3215,f3125,f2420,f3992])).
% 11.45/2.00 thf(f3215,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = order(sTfun(X3,sTfun(X0,sTfun(X1,sTfun(X2,nat))))))) ) | (~spl41_31 | ~spl41_101)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3214])).
% 11.45/2.00 thf(f3214,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X3,sTfun(X0,sTfun(X1,sTfun(X2,nat))))))) ) | (~spl41_31 | ~spl41_101)),
% 11.45/2.00 inference(superposition,[],[f2421,f3126])).
% 11.45/2.00 thf(f3977,plain,(
% 11.45/2.00 spl41_175),
% 11.45/2.00 inference(avatar_split_clause,[],[f1472,f3975])).
% 11.45/2.00 thf(f3975,plain,(
% 11.45/2.00 spl41_175 <=> ! [X1 : $tType,X0 : $tType,X3 : list(X1),X2 : list(X0)] : (vAPP(list(product_prod(X0,X1)),nat,size_size(list(product_prod(X0,X1))),vAPP(list(X1),list(product_prod(X0,X1)),vAPP(list(X0),sTfun(list(X1),list(product_prod(X0,X1))),product(X0,X1),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(list(X0),nat,size_size(list(X0)),X2)),vAPP(list(X1),nat,size_size(list(X1)),X3)))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_175])])).
% 11.45/2.00 thf(f1472,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X2 : list(X0),X3 : list(X1)] : ((vAPP(list(product_prod(X0,X1)),nat,size_size(list(product_prod(X0,X1))),vAPP(list(X1),list(product_prod(X0,X1)),vAPP(list(X0),sTfun(list(X1),list(product_prod(X0,X1))),product(X0,X1),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(list(X0),nat,size_size(list(X0)),X2)),vAPP(list(X1),nat,size_size(list(X1)),X3)))) )),
% 11.45/2.00 inference(cnf_transformation,[],[f837])).
% 11.45/2.00 thf(f837,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : $tType,X2 : list(X0),X3 : list(X1)] : (vAPP(list(product_prod(X0,X1)),nat,size_size(list(product_prod(X0,X1))),vAPP(list(X1),list(product_prod(X0,X1)),vAPP(list(X0),sTfun(list(X1),list(product_prod(X0,X1))),product(X0,X1),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(list(X0),nat,size_size(list(X0)),X2)),vAPP(list(X1),nat,size_size(list(X1)),X3)))),
% 11.45/2.00 inference(rectify,[],[f211])).
% 11.45/2.00 thf(f211,axiom,(
% 11.45/2.00 ! [X0 : $tType,X1 : $tType,X44 : list(X0),X47 : list(X1)] : (vAPP(list(product_prod(X0,X1)),nat,size_size(list(product_prod(X0,X1))),vAPP(list(X1),list(product_prod(X0,X1)),vAPP(list(X0),sTfun(list(X1),list(product_prod(X0,X1))),product(X0,X1),X44),X47)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(list(X0),nat,size_size(list(X0)),X44)),vAPP(list(X1),nat,size_size(list(X1)),X47)))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_length__product)).
% 11.45/2.00 thf(f3973,plain,(
% 11.45/2.00 spl41_174),
% 11.45/2.00 inference(avatar_split_clause,[],[f1332,f3971])).
% 11.45/2.00 thf(f1332,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1001])).
% 11.45/2.00 thf(f1001,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f1000])).
% 11.45/2.00 thf(f1000,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f540])).
% 11.45/2.00 thf(f540,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f539])).
% 11.45/2.00 thf(f539,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)))))),
% 11.45/2.00 inference(rectify,[],[f158])).
% 11.45/2.00 thf(f158,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X16 : X0,X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X16) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X17) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_divide__pos__pos)).
% 11.45/2.00 thf(f3969,plain,(
% 11.45/2.00 spl41_173),
% 11.45/2.00 inference(avatar_split_clause,[],[f1329,f3967])).
% 11.45/2.00 thf(f1329,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f1126])).
% 11.45/2.00 thf(f1126,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f999,f1125])).
% 11.45/2.00 thf(f1125,plain,(
% 11.45/2.00 ! [X0 : $tType,X1 : X0,X2 : X0] : (? [X3 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) = $true) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3))) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)))))),
% 11.45/2.00 introduced(choice_axiom,[])).
% 11.45/2.00 thf(f999,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (? [X3 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) = $true) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f998])).
% 11.45/2.00 thf(f998,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((? [X3 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) = $true) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f538])).
% 11.45/2.00 thf(f538,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) => ? [X3 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) = $true) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3))))))),
% 11.45/2.00 inference(fool_elimination,[],[f537])).
% 11.45/2.00 thf(f537,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) => ? [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X3)))))),
% 11.45/2.00 inference(rectify,[],[f209])).
% 11.45/2.00 thf(f209,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X52 : X0,X53 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X52) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X53) => ? [X54 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X54),X53) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X54),X52) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X54)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_field__lbound__gt__zero)).
% 11.45/2.00 thf(f3965,plain,(
% 11.45/2.00 spl41_172),
% 11.45/2.00 inference(avatar_split_clause,[],[f1328,f3963])).
% 11.45/2.00 thf(f1328,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f997])).
% 11.45/2.00 thf(f997,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f996])).
% 11.45/2.00 thf(f996,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f536])).
% 11.45/2.00 thf(f536,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f535])).
% 11.45/2.00 thf(f535,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0)))))),
% 11.45/2.00 inference(rectify,[],[f157])).
% 11.45/2.00 thf(f157,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X16 : X0,X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X16) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X17),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)),zero_zero(X0)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_divide__pos__neg)).
% 11.45/2.00 thf(f3961,plain,(
% 11.45/2.00 spl41_171),
% 11.45/2.00 inference(avatar_split_clause,[],[f1327,f3959])).
% 11.45/2.00 thf(f1327,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f995])).
% 11.45/2.00 thf(f995,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f994])).
% 11.45/2.00 thf(f994,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f534])).
% 11.45/2.00 thf(f534,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f533])).
% 11.45/2.00 thf(f533,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)))))),
% 11.45/2.00 inference(rectify,[],[f250])).
% 11.45/2.00 thf(f250,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X16 : X0,X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X16) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X17) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_divide__nonneg__nonneg)).
% 11.45/2.00 thf(f3957,plain,(
% 11.45/2.00 spl41_170),
% 11.45/2.00 inference(avatar_split_clause,[],[f1326,f3955])).
% 11.45/2.00 thf(f1326,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f993])).
% 11.45/2.00 thf(f993,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f992])).
% 11.45/2.00 thf(f992,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f532])).
% 11.45/2.00 thf(f532,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f531])).
% 11.45/2.00 thf(f531,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0)))))),
% 11.45/2.00 inference(rectify,[],[f249])).
% 11.45/2.00 thf(f249,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X16 : X0,X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X16) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X17),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)),zero_zero(X0)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_divide__nonneg__nonpos)).
% 11.45/2.00 thf(f3953,plain,(
% 11.45/2.00 spl41_169),
% 11.45/2.00 inference(avatar_split_clause,[],[f1325,f3951])).
% 11.45/2.00 thf(f1325,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f991])).
% 11.45/2.00 thf(f991,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f990])).
% 11.45/2.00 thf(f990,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f530])).
% 11.45/2.00 thf(f530,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f529])).
% 11.45/2.00 thf(f529,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0)))))),
% 11.45/2.00 inference(rectify,[],[f156])).
% 11.45/2.00 thf(f156,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X16 : X0,X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X16),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X17) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)),zero_zero(X0)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_divide__neg__pos)).
% 11.45/2.00 thf(f3949,plain,(
% 11.45/2.00 spl41_168),
% 11.45/2.00 inference(avatar_split_clause,[],[f1324,f3947])).
% 11.45/2.00 thf(f1324,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f989])).
% 11.45/2.00 thf(f989,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f988])).
% 11.45/2.00 thf(f988,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f528])).
% 11.45/2.00 thf(f528,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f527])).
% 11.45/2.00 thf(f527,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)))))),
% 11.45/2.00 inference(rectify,[],[f155])).
% 11.45/2.00 thf(f155,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X16 : X0,X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X16),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X17),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_divide__neg__neg)).
% 11.45/2.00 thf(f3943,plain,(
% 11.45/2.00 spl41_167),
% 11.45/2.00 inference(avatar_split_clause,[],[f1323,f3941])).
% 11.45/2.00 thf(f1323,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f987])).
% 11.45/2.00 thf(f987,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f986])).
% 11.45/2.00 thf(f986,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f526])).
% 11.45/2.00 thf(f526,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f525])).
% 11.45/2.00 thf(f525,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),zero_zero(X0)))))),
% 11.45/2.00 inference(rectify,[],[f248])).
% 11.45/2.00 thf(f248,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X16 : X0,X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X16),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X17) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)),zero_zero(X0)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_divide__nonpos__nonneg)).
% 11.45/2.00 thf(f3939,plain,(
% 11.45/2.00 spl41_166),
% 11.45/2.00 inference(avatar_split_clause,[],[f1322,f3937])).
% 11.45/2.00 thf(f1322,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (linordered_field(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f985])).
% 11.45/2.00 thf(f985,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f984])).
% 11.45/2.00 thf(f984,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) | (linordered_field(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f524])).
% 11.45/2.00 thf(f524,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f523])).
% 11.45/2.00 thf(f523,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)))))),
% 11.45/2.00 inference(rectify,[],[f247])).
% 11.45/2.00 thf(f247,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linordered_field(X0) => ! [X16 : X0,X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X16),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X17),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X16),X17)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_divide__nonpos__nonpos)).
% 11.45/2.00 thf(f3935,plain,(
% 11.45/2.00 spl41_165),
% 11.45/2.00 inference(avatar_split_clause,[],[f1294,f3933])).
% 11.45/2.00 thf(f1294,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (linord581940658strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f954])).
% 11.45/2.00 thf(f954,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) | (linord581940658strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f953])).
% 11.45/2.00 thf(f953,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) | (linord581940658strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f470])).
% 11.45/2.00 thf(f470,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord581940658strict(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f469])).
% 11.45/2.00 thf(f469,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord581940658strict(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))))),
% 11.45/2.00 inference(rectify,[],[f136])).
% 11.45/2.00 thf(f136,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord581940658strict(X0) => ! [X9 : X0,X11 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X9),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X11),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_mult__neg__neg)).
% 11.45/2.00 thf(f3931,plain,(
% 11.45/2.00 spl41_164),
% 11.45/2.00 inference(avatar_split_clause,[],[f1279,f3929])).
% 11.45/2.00 thf(f1279,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord20386208strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f934])).
% 11.45/2.00 thf(f934,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f933])).
% 11.45/2.00 thf(f933,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f440])).
% 11.45/2.00 thf(f440,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord20386208strict(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true))))),
% 11.45/2.00 inference(fool_elimination,[],[f439])).
% 11.45/2.00 thf(f439,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2))))),
% 11.45/2.00 inference(rectify,[],[f144])).
% 11.45/2.00 thf(f144,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X9 : X0,X11 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X9) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X11))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_zero__less__mult__pos)).
% 11.45/2.00 thf(f3927,plain,(
% 11.45/2.00 spl41_163),
% 11.45/2.00 inference(avatar_split_clause,[],[f1278,f3925])).
% 11.45/2.00 thf(f1278,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (linord20386208strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f932])).
% 11.45/2.00 thf(f932,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f931])).
% 11.45/2.00 thf(f931,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f438])).
% 11.45/2.00 thf(f438,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord20386208strict(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)))))),
% 11.45/2.00 inference(fool_elimination,[],[f437])).
% 11.45/2.00 thf(f437,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))))),
% 11.45/2.00 inference(rectify,[],[f145])).
% 11.45/2.00 thf(f145,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X11 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X9)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X9) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X11))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_zero__less__mult__pos2)).
% 11.45/2.00 thf(f3923,plain,(
% 11.45/2.00 spl41_162),
% 11.45/2.00 inference(avatar_split_clause,[],[f1277,f3921])).
% 11.45/2.00 thf(f1277,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linord20386208strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f930])).
% 11.45/2.00 thf(f930,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f929])).
% 11.45/2.00 thf(f929,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f436])).
% 11.45/2.00 thf(f436,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord20386208strict(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f435])).
% 11.45/2.00 thf(f435,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))))),
% 11.45/2.00 inference(rectify,[],[f141])).
% 11.45/2.00 thf(f141,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X9 : X0,X11 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X11) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_mult__pos__pos)).
% 11.45/2.00 thf(f3919,plain,(
% 11.45/2.00 spl41_161),
% 11.45/2.00 inference(avatar_split_clause,[],[f1275,f3917])).
% 11.45/2.00 thf(f1275,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linord20386208strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f926])).
% 11.45/2.00 thf(f926,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f925])).
% 11.45/2.00 thf(f925,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f432])).
% 11.45/2.00 thf(f432,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord20386208strict(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f431])).
% 11.45/2.00 thf(f431,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0)))))),
% 11.45/2.00 inference(rectify,[],[f140])).
% 11.45/2.00 thf(f140,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X9 : X0,X11 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X11),zero_zero(X0)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)),zero_zero(X0)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_mult__pos__neg)).
% 11.45/2.00 thf(f3915,plain,(
% 11.45/2.00 spl41_160),
% 11.45/2.00 inference(avatar_split_clause,[],[f1274,f3913])).
% 11.45/2.00 thf(f1274,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (linord20386208strict(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f924])).
% 11.45/2.00 thf(f924,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f923])).
% 11.45/2.00 thf(f923,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))) | (linord20386208strict(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f430])).
% 11.45/2.00 thf(f430,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((linord20386208strict(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) = $true) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))))))),
% 11.45/2.00 inference(fool_elimination,[],[f429])).
% 11.45/2.00 thf(f429,plain,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0)))))),
% 11.45/2.00 inference(rectify,[],[f139])).
% 11.45/2.00 thf(f139,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (linord20386208strict(X0) => ! [X9 : X0,X11 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X9),zero_zero(X0)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X11) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)),zero_zero(X0)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_mult__neg__pos)).
% 11.45/2.00 thf(f3911,plain,(
% 11.45/2.00 spl41_159),
% 11.45/2.00 inference(avatar_split_clause,[],[f1263,f3909])).
% 11.45/2.00 thf(f1263,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (ordered_semiring_0(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f911])).
% 11.45/2.00 thf(f911,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) | (ordered_semiring_0(X0) != $true))),
% 11.45/2.00 inference(flattening,[],[f910])).
% 11.45/2.00 thf(f910,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) | (ordered_semiring_0(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f408])).
% 11.45/2.00 thf(f408,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordered_semiring_0(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))))))),
% 11.45/2.00 inference(fool_elimination,[],[f407])).
% 11.45/2.00 thf(f407,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring_0(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))))),
% 11.45/2.00 inference(rectify,[],[f234])).
% 11.45/2.00 thf(f234,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring_0(X0) => ! [X9 : X0,X11 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X9) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X11) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_mult__nonneg__nonneg)).
% 11.45/2.00 thf(f3907,plain,(
% 11.45/2.00 spl41_158),
% 11.45/2.00 inference(avatar_split_clause,[],[f1259,f3905])).
% 11.45/2.00 thf(f1259,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (ordered_semiring_0(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f903])).
% 11.45/2.00 thf(f903,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | ((($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) & ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))))) | (ordered_semiring_0(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f400])).
% 11.45/2.00 thf(f400,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordered_semiring_0(X0) = $true) => ! [X1 : X0,X2 : X0] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) | ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) = $true) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0)))))),
% 11.45/2.00 inference(fool_elimination,[],[f399])).
% 11.45/2.00 thf(f399,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring_0(X0) => ! [X1 : X0,X2 : X0] : (((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))))),
% 11.45/2.00 inference(rectify,[],[f235])).
% 11.45/2.00 thf(f235,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_semiring_0(X0) => ! [X9 : X0,X11 : X0] : (((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X11) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X11),zero_zero(X0)) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X9))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)),zero_zero(X0))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_split__mult__neg__le)).
% 11.45/2.00 thf(f3903,plain,(
% 11.45/2.00 spl41_157 | ~spl41_31 | ~spl41_90),
% 11.45/2.00 inference(avatar_split_clause,[],[f3017,f2970,f2420,f3901])).
% 11.45/2.00 thf(f2970,plain,(
% 11.45/2.00 spl41_90 <=> ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,X0))) | (order(X0) = $false))),
% 11.45/2.00 introduced(avatar_definition,[new_symbols(naming,[spl41_90])])).
% 11.45/2.00 thf(f3017,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,X1)))) | ($false = order(X1))) ) | (~spl41_31 | ~spl41_90)),
% 11.45/2.00 inference(trivial_inequality_removal,[],[f3016])).
% 11.45/2.00 thf(f3016,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X2,sTfun(X0,X1)))) | ($false = order(X1))) ) | (~spl41_31 | ~spl41_90)),
% 11.45/2.00 inference(superposition,[],[f2421,f2971])).
% 11.45/2.00 thf(f2971,plain,(
% 11.45/2.00 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,X0))) | (order(X0) = $false)) ) | ~spl41_90),
% 11.45/2.00 inference(avatar_component_clause,[],[f2970])).
% 11.45/2.00 thf(f3899,plain,(
% 11.45/2.00 spl41_156),
% 11.45/2.00 inference(avatar_split_clause,[],[f1258,f3897])).
% 11.45/2.00 thf(f1258,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (ordered_semiring_0(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f903])).
% 11.45/2.00 thf(f3895,plain,(
% 11.45/2.00 spl41_155),
% 11.45/2.00 inference(avatar_split_clause,[],[f1232,f3893])).
% 11.45/2.00 thf(f1232,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (ordered_ring(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f871])).
% 11.45/2.00 thf(f871,plain,(
% 11.45/2.00 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | (((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) & (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))))) | (ordered_ring(X0) != $true))),
% 11.45/2.00 inference(ennf_transformation,[],[f350])).
% 11.45/2.00 thf(f350,plain,(
% 11.45/2.00 ! [X0 : $tType] : ((ordered_ring(X0) = $true) => ! [X1 : X0,X2 : X0] : ((((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) = $true) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0)))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)))))),
% 11.45/2.00 inference(fool_elimination,[],[f349])).
% 11.45/2.00 thf(f349,plain,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_ring(X0) => ! [X1 : X0,X2 : X0] : (((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),zero_zero(X0)) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))))),
% 11.45/2.00 inference(rectify,[],[f242])).
% 11.45/2.00 thf(f242,axiom,(
% 11.45/2.00 ! [X0 : $tType] : (ordered_ring(X0) => ! [X9 : X0,X11 : X0] : (((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X11),zero_zero(X0)) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),zero_zero(X0))) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X11) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X9))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11))))),
% 11.45/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_split__mult__pos__le)).
% 11.45/2.00 thf(f3891,plain,(
% 11.45/2.00 spl41_154),
% 11.45/2.00 inference(avatar_split_clause,[],[f1231,f3889])).
% 11.45/2.00 thf(f1231,plain,(
% 11.45/2.00 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (ordered_ring(X0) != $true)) )),
% 11.45/2.00 inference(cnf_transformation,[],[f871])).
% 11.45/2.00 thf(f3857,plain,(
% 11.45/2.00 spl41_153),
% 11.45/2.00 inference(avatar_split_clause,[],[f1417,f3855])).
% 11.45/2.00 thf(f1417,plain,(
% 11.45/2.00 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1063])).
% 11.45/2.01 thf(f1063,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.01 inference(flattening,[],[f1062])).
% 11.45/2.01 thf(f1062,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.01 inference(ennf_transformation,[],[f682])).
% 11.45/2.01 thf(f682,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)))))),
% 11.45/2.01 inference(fool_elimination,[],[f681])).
% 11.45/2.01 thf(f681,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0))))),
% 11.45/2.01 inference(rectify,[],[f99])).
% 11.45/2.01 thf(f99,axiom,(
% 11.45/2.01 ! [X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),X2))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_n__less__m__mult__n)).
% 11.45/2.01 thf(f3853,plain,(
% 11.45/2.01 spl41_152),
% 11.45/2.01 inference(avatar_split_clause,[],[f1416,f3851])).
% 11.45/2.01 thf(f1416,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1061])).
% 11.45/2.01 thf(f1061,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.01 inference(flattening,[],[f1060])).
% 11.45/2.01 thf(f1060,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.01 inference(ennf_transformation,[],[f680])).
% 11.45/2.01 thf(f680,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)))))),
% 11.45/2.01 inference(fool_elimination,[],[f679])).
% 11.45/2.01 thf(f679,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1))))),
% 11.45/2.01 inference(rectify,[],[f98])).
% 11.45/2.01 thf(f98,axiom,(
% 11.45/2.01 ! [X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,zero_zero(nat))),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X3))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_n__less__n__mult__m)).
% 11.45/2.01 thf(f3849,plain,(
% 11.45/2.01 spl41_151),
% 11.45/2.01 inference(avatar_split_clause,[],[f1331,f3847])).
% 11.45/2.01 thf(f1331,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X2)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1126])).
% 11.45/2.01 thf(f3844,plain,(
% 11.45/2.01 spl41_150),
% 11.45/2.01 inference(avatar_split_clause,[],[f1330,f3842])).
% 11.45/2.01 thf(f1330,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK11(X0),X2),X1)),X1)) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X2) != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1126])).
% 11.45/2.01 thf(f3730,plain,(
% 11.45/2.01 spl41_149),
% 11.45/2.01 inference(avatar_split_clause,[],[f1391,f3728])).
% 11.45/2.01 thf(f1391,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2)))) | ($true != wellorder(X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1136])).
% 11.45/2.01 thf(f1136,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2))))))) | ($true != wellorder(X0)))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f1036,f1135])).
% 11.45/2.01 thf(f1135,plain,(
% 11.45/2.01 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o] : (? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))))) => (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2)))))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1036,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)))))) | ($true != wellorder(X0)))),
% 11.45/2.01 inference(ennf_transformation,[],[f644])).
% 11.45/2.01 thf(f644,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (($true = wellorder(X0)) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))) => ($true = vAPP(X1,$o,X3,X6))) => ($true = vAPP(X1,$o,X3,X5))) => ($true = vAPP(X1,$o,X3,X4))))),
% 11.45/2.01 inference(fool_elimination,[],[f643])).
% 11.45/2.01 thf(f643,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (wellorder(X0) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)) => vAPP(X1,$o,X3,X6)) => vAPP(X1,$o,X3,X5)) => vAPP(X1,$o,X3,X4)))),
% 11.45/2.01 inference(rectify,[],[f29])).
% 11.45/2.01 thf(f29,axiom,(
% 11.45/2.01 ! [X1 : $tType,X0 : $tType] : (wellorder(X1) => ! [X12 : X0 > X1,X13 : X0 > $o,X9 : X0] : (! [X14 : X0] : (! [X15 : X0] : (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X12,X15)),vAPP(X0,X1,X12,X14)) => vAPP(X0,$o,X13,X15)) => vAPP(X0,$o,X13,X14)) => vAPP(X0,$o,X13,X9)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_measure__induct)).
% 11.45/2.01 thf(f3726,plain,(
% 11.45/2.01 spl41_148),
% 11.45/2.01 inference(avatar_split_clause,[],[f1389,f3724])).
% 11.45/2.01 thf(f1389,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2)))) | ($true != wellorder(X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1134])).
% 11.45/2.01 thf(f1134,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2))))))) | ($true != wellorder(X0)))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f1035,f1133])).
% 11.45/2.01 thf(f1133,plain,(
% 11.45/2.01 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o] : (? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))))) => (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2)))))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1035,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)))))) | ($true != wellorder(X0)))),
% 11.45/2.01 inference(ennf_transformation,[],[f642])).
% 11.45/2.01 thf(f642,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (($true = wellorder(X0)) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))) => ($true = vAPP(X1,$o,X3,X6))) => ($true = vAPP(X1,$o,X3,X5))) => ($true = vAPP(X1,$o,X3,X4))))),
% 11.45/2.01 inference(fool_elimination,[],[f641])).
% 11.45/2.01 thf(f641,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (wellorder(X0) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)) => vAPP(X1,$o,X3,X6)) => vAPP(X1,$o,X3,X5)) => vAPP(X1,$o,X3,X4)))),
% 11.45/2.01 inference(rectify,[],[f28])).
% 11.45/2.01 thf(f28,axiom,(
% 11.45/2.01 ! [X1 : $tType,X0 : $tType] : (wellorder(X1) => ! [X12 : X0 > X1,X13 : X0 > $o,X9 : X0] : (! [X14 : X0] : (! [X15 : X0] : (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X12,X15)),vAPP(X0,X1,X12,X14)) => vAPP(X0,$o,X13,X15)) => vAPP(X0,$o,X13,X14)) => vAPP(X0,$o,X13,X9)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_measure__induct__rule)).
% 11.45/2.01 thf(f3700,plain,(
% 11.45/2.01 spl41_147),
% 11.45/2.01 inference(avatar_split_clause,[],[f1453,f3698])).
% 11.45/2.01 thf(f1453,plain,(
% 11.45/2.01 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,X0)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | ($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1167])).
% 11.45/2.01 thf(f1167,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,X2,X0)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | (($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1))) & (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1)) = X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f1103,f1166])).
% 11.45/2.01 thf(f1166,plain,(
% 11.45/2.01 ! [X1 : nat,X2 : nat > $o] : (? [X3 : nat] : (($true != vAPP(nat,$o,X2,X3)) & (vAPP(nat,nat,suc,X3) = X1)) => (($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1))) & (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1)) = X1)))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1103,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,X2,X0)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | ? [X3 : nat] : (($true != vAPP(nat,$o,X2,X3)) & (vAPP(nat,nat,suc,X3) = X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(definition_folding,[],[f1080,f1102])).
% 11.45/2.01 thf(f1102,plain,(
% 11.45/2.01 ! [X2 : nat > $o,X1 : nat] : (? [X4 : nat] : (($true != vAPP(nat,$o,X2,X4)) & ($true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X1))) | ~($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)))),
% 11.45/2.01 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 11.45/2.01 thf(f1080,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,X2,X0)) | ? [X4 : nat] : (($true != vAPP(nat,$o,X2,X4)) & ($true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X1))) | ? [X3 : nat] : (($true != vAPP(nat,$o,X2,X3)) & (vAPP(nat,nat,suc,X3) = X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(flattening,[],[f1079])).
% 11.45/2.01 thf(f1079,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (((($true = vAPP(nat,$o,X2,X0)) | ? [X4 : nat] : ((($true != vAPP(nat,$o,X2,X4)) & ($true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X1)))) | ? [X3 : nat] : (($true != vAPP(nat,$o,X2,X3)) & (vAPP(nat,nat,suc,X3) = X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f722])).
% 11.45/2.01 thf(f722,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (! [X3 : nat] : ((vAPP(nat,nat,suc,X3) = X1) => ($true = vAPP(nat,$o,X2,X3))) => (! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X1)) => (($true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4))) => ($true = vAPP(nat,$o,X2,X4)))) => ($true = vAPP(nat,$o,X2,X0)))))),
% 11.45/2.01 inference(fool_elimination,[],[f721])).
% 11.45/2.01 thf(f721,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (! [X3 : nat] : ((vAPP(nat,nat,suc,X3) = X1) => vAPP(nat,$o,X2,X3)) => (! [X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X1) => (vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4)) => vAPP(nat,$o,X2,X4))) => vAPP(nat,$o,X2,X0))))),
% 11.45/2.01 inference(rectify,[],[f64])).
% 11.45/2.01 thf(f64,axiom,(
% 11.45/2.01 ! [X27 : nat,X28 : nat,X13 : nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X28) => (! [X29 : nat] : ((vAPP(nat,nat,suc,X29) = X28) => vAPP(nat,$o,X13,X29)) => (! [X29 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X29),X28) => (vAPP(nat,$o,X13,vAPP(nat,nat,suc,X29)) => vAPP(nat,$o,X13,X29))) => vAPP(nat,$o,X13,X27))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_strict__inc__induct)).
% 11.45/2.01 thf(f3696,plain,(
% 11.45/2.01 spl41_146),
% 11.45/2.01 inference(avatar_split_clause,[],[f1452,f3694])).
% 11.45/2.01 thf(f1452,plain,(
% 11.45/2.01 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,X0)) | ($true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)) | (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK33,X2),X1)) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1167])).
% 11.45/2.01 thf(f3687,plain,(
% 11.45/2.01 spl41_145),
% 11.45/2.01 inference(avatar_split_clause,[],[f1473,f3685])).
% 11.45/2.01 thf(f1473,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1177])).
% 11.45/2.01 thf(f3659,plain,(
% 11.45/2.01 spl41_144),
% 11.45/2.01 inference(avatar_split_clause,[],[f1418,f3657])).
% 11.45/2.01 thf(f1418,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1064])).
% 11.45/2.01 thf(f1064,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.01 inference(ennf_transformation,[],[f684])).
% 11.45/2.01 thf(f684,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))),X0))))),
% 11.45/2.01 inference(fool_elimination,[],[f683])).
% 11.45/2.01 thf(f683,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X0))),X0)))),
% 11.45/2.01 inference(rectify,[],[f109])).
% 11.45/2.01 thf(f109,axiom,(
% 11.45/2.01 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X2),X3))),X3)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_less__div__Suc__mult)).
% 11.45/2.01 thf(f3655,plain,(
% 11.45/2.01 spl41_143),
% 11.45/2.01 inference(avatar_split_clause,[],[f1311,f3653])).
% 11.45/2.01 thf(f1311,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (zero_zero(X0) = X1) | (field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f972])).
% 11.45/2.01 thf(f972,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (zero_zero(X0) = X1)) | (field(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f502])).
% 11.45/2.01 thf(f502,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))))),
% 11.45/2.01 inference(fool_elimination,[],[f501])).
% 11.45/2.01 thf(f501,plain,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))))),
% 11.45/2.01 inference(rectify,[],[f105])).
% 11.45/2.01 thf(f105,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X10 : X0,X9 : X0,X11 : X0] : ((zero_zero(X0) != X10) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X11) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_nonzero__mult__divide__mult__cancel__left2)).
% 11.45/2.01 thf(f3650,plain,(
% 11.45/2.01 spl41_142),
% 11.45/2.01 inference(avatar_split_clause,[],[f1310,f3648])).
% 11.45/2.01 thf(f1310,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (zero_zero(X0) = X1) | (field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f971])).
% 11.45/2.01 thf(f971,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (zero_zero(X0) = X1)) | (field(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f500])).
% 11.45/2.01 thf(f500,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))))),
% 11.45/2.01 inference(fool_elimination,[],[f499])).
% 11.45/2.01 thf(f499,plain,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))))),
% 11.45/2.01 inference(rectify,[],[f104])).
% 11.45/2.01 thf(f104,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X10 : X0,X9 : X0,X11 : X0] : ((zero_zero(X0) != X10) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X11) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_nonzero__mult__divide__mult__cancel__right)).
% 11.45/2.01 thf(f3646,plain,(
% 11.45/2.01 spl41_141),
% 11.45/2.01 inference(avatar_split_clause,[],[f1309,f3644])).
% 11.45/2.01 thf(f1309,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (zero_zero(X0) = X1) | (field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f970])).
% 11.45/2.01 thf(f970,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (zero_zero(X0) = X1)) | (field(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f498])).
% 11.45/2.01 thf(f498,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)))))),
% 11.45/2.01 inference(fool_elimination,[],[f497])).
% 11.45/2.01 thf(f497,plain,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)))))),
% 11.45/2.01 inference(rectify,[],[f102])).
% 11.45/2.01 thf(f102,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X10 : X0,X9 : X0,X11 : X0] : ((zero_zero(X0) != X10) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X11) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_nonzero__mult__divide__mult__cancel__right2)).
% 11.45/2.01 thf(f3642,plain,(
% 11.45/2.01 spl41_140),
% 11.45/2.01 inference(avatar_split_clause,[],[f1308,f3640])).
% 11.45/2.01 thf(f1308,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (zero_zero(X0) = X1) | (field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f969])).
% 11.45/2.01 thf(f969,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (zero_zero(X0) = X1)) & ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (zero_zero(X0) != X1))) | (field(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f496])).
% 11.45/2.01 thf(f496,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) & ((zero_zero(X0) = X1) => (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))))),
% 11.45/2.01 inference(fool_elimination,[],[f495])).
% 11.45/2.01 thf(f495,plain,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) & ((zero_zero(X0) = X1) => (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))))),
% 11.45/2.01 inference(rectify,[],[f108])).
% 11.45/2.01 thf(f108,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X10 : X0,X9 : X0,X11 : X0] : (((zero_zero(X0) != X10) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X11))) & ((zero_zero(X0) = X10) => (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11))))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_mult__divide__mult__cancel__left__if)).
% 11.45/2.01 thf(f3638,plain,(
% 11.45/2.01 spl41_139),
% 11.45/2.01 inference(avatar_split_clause,[],[f1238,f3636])).
% 11.45/2.01 thf(f1238,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (zero_zero(X0) = X1) | (euclid191655569cancel(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f877])).
% 11.45/2.01 thf(f877,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1))) | (zero_zero(X0) = X1)) | (euclid191655569cancel(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f360])).
% 11.45/2.01 thf(f360,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((euclid191655569cancel(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))))),
% 11.45/2.01 inference(fool_elimination,[],[f359])).
% 11.45/2.01 thf(f359,plain,(
% 11.45/2.01 ! [X0 : $tType] : (euclid191655569cancel(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)))))),
% 11.45/2.01 inference(rectify,[],[f26])).
% 11.45/2.01 thf(f26,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (euclid191655569cancel(X0) => ! [X10 : X0,X9 : X0,X11 : X0] : ((zero_zero(X0) != X10) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X11) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_div__mult__mult2)).
% 11.45/2.01 thf(f3634,plain,(
% 11.45/2.01 spl41_138),
% 11.45/2.01 inference(avatar_split_clause,[],[f1237,f3632])).
% 11.45/2.01 thf(f1237,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (zero_zero(X0) = X1) | (euclid191655569cancel(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f876])).
% 11.45/2.01 thf(f876,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) | (zero_zero(X0) = X1)) & ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (zero_zero(X0) != X1))) | (euclid191655569cancel(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f358])).
% 11.45/2.01 thf(f358,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((euclid191655569cancel(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) & ((zero_zero(X0) = X1) => (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))))),
% 11.45/2.01 inference(fool_elimination,[],[f357])).
% 11.45/2.01 thf(f357,plain,(
% 11.45/2.01 ! [X0 : $tType] : (euclid191655569cancel(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3))) & ((zero_zero(X0) = X1) => (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))))),
% 11.45/2.01 inference(rectify,[],[f25])).
% 11.45/2.01 thf(f25,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (euclid191655569cancel(X0) => ! [X10 : X0,X9 : X0,X11 : X0] : (((zero_zero(X0) != X10) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X11))) & ((zero_zero(X0) = X10) => (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11))))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_div__mult__mult1__if)).
% 11.45/2.01 thf(f3600,plain,(
% 11.45/2.01 spl41_137),
% 11.45/2.01 inference(avatar_split_clause,[],[f1479,f3598])).
% 11.45/2.01 thf(f1479,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1))))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1181])).
% 11.45/2.01 thf(f1181,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1))))) & ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1)))))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f1101,f1180])).
% 11.45/2.01 thf(f1180,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat] : (? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4)))) & ($true != vAPP(X0,$o,X1,X4))) => (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1))))) & ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1101,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | ? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4)))) & ($true != vAPP(X0,$o,X1,X4))))),
% 11.45/2.01 inference(ennf_transformation,[],[f839])).
% 11.45/2.01 thf(f839,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) => ? [X5 : X0] : (($true != vAPP(X0,$o,X1,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4))))) => ($true = vAPP(X0,$o,X1,X3)))),
% 11.45/2.01 inference(flattening,[],[f752])).
% 11.45/2.01 thf(f752,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (! [X4 : X0] : (~($true = vAPP(X0,$o,X1,X4)) => ? [X5 : X0] : (~($true = vAPP(X0,$o,X1,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4))))) => ($true = vAPP(X0,$o,X1,X3)))),
% 11.45/2.01 inference(fool_elimination,[],[f751])).
% 11.45/2.01 thf(f751,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (! [X4 : X0] : (~vAPP(X0,$o,X1,X4) => ? [X5 : X0] : (~vAPP(X0,$o,X1,X5) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4)))) => vAPP(X0,$o,X1,X3))),
% 11.45/2.01 inference(rectify,[],[f32])).
% 11.45/2.01 thf(f32,axiom,(
% 11.45/2.01 ! [X0 : $tType,X13 : X0 > $o,X18 : X0 > nat,X16 : X0] : (! [X14 : X0] : (~vAPP(X0,$o,X13,X14) => ? [X15 : X0] : (~vAPP(X0,$o,X13,X15) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X18,X15)),vAPP(X0,nat,X18,X14)))) => vAPP(X0,$o,X13,X16))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_infinite__descent__measure)).
% 11.45/2.01 thf(f3596,plain,(
% 11.45/2.01 spl41_136),
% 11.45/2.01 inference(avatar_split_clause,[],[f1441,f3594])).
% 11.45/2.01 thf(f1441,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0) > $o,X4 : list(X0)] : (($true = vAPP(list(X0),$o,X1,X2)) | ($true = vAPP(list(X0),$o,X1,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X4)),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1))))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1152])).
% 11.45/2.01 thf(f1152,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : list(X0) > $o,X2 : list(X0)] : (($true = vAPP(list(X0),$o,X1,X2)) | (($true != vAPP(list(X0),$o,X1,vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1))) & ! [X4 : list(X0)] : (($true = vAPP(list(X0),$o,X1,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X4)),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1)))))))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f1074,f1151])).
% 11.45/2.01 thf(f1151,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : list(X0) > $o] : (? [X3 : list(X0)] : (($true != vAPP(list(X0),$o,X1,X3)) & ! [X4 : list(X0)] : (($true = vAPP(list(X0),$o,X1,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X4)),vAPP(list(X0),nat,size_size(list(X0)),X3))))) => (($true != vAPP(list(X0),$o,X1,vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1))) & ! [X4 : list(X0)] : (($true = vAPP(list(X0),$o,X1,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X4)),vAPP(list(X0),nat,size_size(list(X0)),vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1)))))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1074,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : list(X0) > $o,X2 : list(X0)] : (($true = vAPP(list(X0),$o,X1,X2)) | ? [X3 : list(X0)] : (($true != vAPP(list(X0),$o,X1,X3)) & ! [X4 : list(X0)] : (($true = vAPP(list(X0),$o,X1,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X4)),vAPP(list(X0),nat,size_size(list(X0)),X3))))))),
% 11.45/2.01 inference(ennf_transformation,[],[f716])).
% 11.45/2.01 thf(f716,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : list(X0) > $o,X2 : list(X0)] : (! [X3 : list(X0)] : (! [X4 : list(X0)] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X4)),vAPP(list(X0),nat,size_size(list(X0)),X3))) => ($true = vAPP(list(X0),$o,X1,X4))) => ($true = vAPP(list(X0),$o,X1,X3))) => ($true = vAPP(list(X0),$o,X1,X2)))),
% 11.45/2.01 inference(fool_elimination,[],[f715])).
% 11.45/2.01 thf(f715,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : list(X0) > $o,X2 : list(X0)] : (! [X3 : list(X0)] : (! [X4 : list(X0)] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X4)),vAPP(list(X0),nat,size_size(list(X0)),X3)) => vAPP(list(X0),$o,X1,X4)) => vAPP(list(X0),$o,X1,X3)) => vAPP(list(X0),$o,X1,X2))),
% 11.45/2.01 inference(rectify,[],[f203])).
% 11.45/2.01 thf(f203,axiom,(
% 11.45/2.01 ! [X0 : $tType,X13 : list(X0) > $o,X44 : list(X0)] : (! [X45 : list(X0)] : (! [X46 : list(X0)] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(X0),nat,size_size(list(X0)),X46)),vAPP(list(X0),nat,size_size(list(X0)),X45)) => vAPP(list(X0),$o,X13,X46)) => vAPP(list(X0),$o,X13,X45)) => vAPP(list(X0),$o,X13,X44))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_length__induct)).
% 11.45/2.01 thf(f3430,plain,(
% 11.45/2.01 spl41_135 | ~spl41_28 | ~spl41_35),
% 11.45/2.01 inference(avatar_split_clause,[],[f2464,f2444,f2405,f3428])).
% 11.45/2.01 thf(f3428,plain,(
% 11.45/2.01 spl41_135 <=> ! [X0 : nat] : ((vAPP(nat,nat,sK5,X0) != X0) | (zero_zero(nat) = X0))),
% 11.45/2.01 introduced(avatar_definition,[new_symbols(naming,[spl41_135])])).
% 11.45/2.01 thf(f2464,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((vAPP(nat,nat,sK5,X0) != X0) | (zero_zero(nat) = X0)) ) | (~spl41_28 | ~spl41_35)),
% 11.45/2.01 inference(superposition,[],[f2406,f2445])).
% 11.45/2.01 thf(f3426,plain,(
% 11.45/2.01 spl41_134),
% 11.45/2.01 inference(avatar_split_clause,[],[f1476,f3424])).
% 11.45/2.01 thf(f1476,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)) | (zero_zero(nat) = vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1179])).
% 11.45/2.01 thf(f1179,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1))) & (zero_zero(nat) = vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1)))))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f1107,f1178])).
% 11.45/2.01 thf(f1178,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o] : (? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & (zero_zero(nat) = vAPP(X0,nat,X1,X4))) => (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1))) & (zero_zero(nat) = vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1107,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & (zero_zero(nat) = vAPP(X0,nat,X1,X4))))),
% 11.45/2.01 inference(definition_folding,[],[f1100,f1106])).
% 11.45/2.01 thf(f1100,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ? [X5 : X0] : (! [X6 : X0] : (($true = vAPP(X0,$o,X2,X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))) & ($true != vAPP(X0,$o,X2,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5)))) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & (zero_zero(nat) = vAPP(X0,nat,X1,X4))))),
% 11.45/2.01 inference(flattening,[],[f1099])).
% 11.45/2.01 thf(f1099,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : ((($true = vAPP(X0,$o,X2,X3)) | ? [X5 : X0] : ((! [X6 : X0] : (($true = vAPP(X0,$o,X2,X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))) & ($true != vAPP(X0,$o,X2,X5))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5))))) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & (zero_zero(nat) = vAPP(X0,nat,X1,X4))))),
% 11.45/2.01 inference(ennf_transformation,[],[f838])).
% 11.45/2.01 thf(f838,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (! [X4 : X0] : ((zero_zero(nat) = vAPP(X0,nat,X1,X4)) => ($true = vAPP(X0,$o,X2,X4))) => (! [X5 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5))) => (($true != vAPP(X0,$o,X2,X5)) => ? [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))))) => ($true = vAPP(X0,$o,X2,X3))))),
% 11.45/2.01 inference(flattening,[],[f750])).
% 11.45/2.01 thf(f750,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (! [X4 : X0] : ((zero_zero(nat) = vAPP(X0,nat,X1,X4)) => ($true = vAPP(X0,$o,X2,X4))) => (! [X5 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5))) => (~($true = vAPP(X0,$o,X2,X5)) => ? [X6 : X0] : (~($true = vAPP(X0,$o,X2,X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))))) => ($true = vAPP(X0,$o,X2,X3))))),
% 11.45/2.01 inference(fool_elimination,[],[f749])).
% 11.45/2.01 thf(f749,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (! [X4 : X0] : ((zero_zero(nat) = vAPP(X0,nat,X1,X4)) => vAPP(X0,$o,X2,X4)) => (! [X5 : X0] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5)) => (~vAPP(X0,$o,X2,X5) => ? [X6 : X0] : (~vAPP(X0,$o,X2,X6) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5))))) => vAPP(X0,$o,X2,X3)))),
% 11.45/2.01 inference(rectify,[],[f55])).
% 11.45/2.01 thf(f55,axiom,(
% 11.45/2.01 ! [X0 : $tType,X18 : X0 > nat,X13 : X0 > $o,X16 : X0] : (! [X14 : X0] : ((zero_zero(nat) = vAPP(X0,nat,X18,X14)) => vAPP(X0,$o,X13,X14)) => (! [X14 : X0] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X18,X14)) => (~vAPP(X0,$o,X13,X14) => ? [X15 : X0] : (~vAPP(X0,$o,X13,X15) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X18,X15)),vAPP(X0,nat,X18,X14))))) => vAPP(X0,$o,X13,X16)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_infinite__descent0__measure)).
% 11.45/2.01 thf(f3367,plain,(
% 11.45/2.01 spl41_133 | ~spl41_28 | ~spl41_34),
% 11.45/2.01 inference(avatar_split_clause,[],[f2462,f2440,f2405,f3365])).
% 11.45/2.01 thf(f3365,plain,(
% 11.45/2.01 spl41_133 <=> ! [X0 : nat] : ((vAPP(nat,nat,sK4,X0) != X0) | (zero_zero(nat) = X0))),
% 11.45/2.01 introduced(avatar_definition,[new_symbols(naming,[spl41_133])])).
% 11.45/2.01 thf(f2462,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((vAPP(nat,nat,sK4,X0) != X0) | (zero_zero(nat) = X0)) ) | (~spl41_28 | ~spl41_34)),
% 11.45/2.01 inference(superposition,[],[f2406,f2441])).
% 11.45/2.01 thf(f3359,plain,(
% 11.45/2.01 spl41_132),
% 11.45/2.01 inference(avatar_split_clause,[],[f1477,f3357])).
% 11.45/2.01 thf(f1477,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP2(X0),X1),X2)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK39(X0),X2),X1)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1179])).
% 11.45/2.01 thf(f3355,plain,(
% 11.45/2.01 spl41_131),
% 11.45/2.01 inference(avatar_split_clause,[],[f1439,f3353])).
% 11.45/2.01 thf(f3353,plain,(
% 11.45/2.01 spl41_131 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | (zero_zero(nat) = X0))),
% 11.45/2.01 introduced(avatar_definition,[new_symbols(naming,[spl41_131])])).
% 11.45/2.01 thf(f1439,plain,(
% 11.45/2.01 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | (zero_zero(nat) = X0)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1072])).
% 11.45/2.01 thf(f1072,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | (zero_zero(nat) = X0)) & ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | (zero_zero(nat) != X0)))),
% 11.45/2.01 inference(ennf_transformation,[],[f835])).
% 11.45/2.01 thf(f835,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : (((zero_zero(nat) != X0) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)))) & ((zero_zero(nat) = X0) => (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)))))),
% 11.45/2.01 inference(rectify,[],[f3])).
% 11.45/2.01 thf(f3,axiom,(
% 11.45/2.01 ! [X4 : nat,X3 : nat,X2 : nat] : (((zero_zero(nat) != X4) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X3),X2))) & ((zero_zero(nat) = X4) => (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X2)))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_nat__mult__div__cancel__disj)).
% 11.45/2.01 thf(f3351,plain,(
% 11.45/2.01 spl41_130),
% 11.45/2.01 inference(avatar_split_clause,[],[f1304,f3349])).
% 11.45/2.01 thf(f1304,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3)) | (field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f966])).
% 11.45/2.01 thf(f966,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3)) | (field(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f490])).
% 11.45/2.01 thf(f490,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3)))),
% 11.45/2.01 inference(fool_elimination,[],[f489])).
% 11.45/2.01 thf(f489,plain,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3)))),
% 11.45/2.01 inference(rectify,[],[f124])).
% 11.45/2.01 thf(f124,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X11 : X0,X10 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X11),X10)),X9) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X9)),X10)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_times__divide__eq__left)).
% 11.45/2.01 thf(f3347,plain,(
% 11.45/2.01 spl41_129),
% 11.45/2.01 inference(avatar_split_clause,[],[f1303,f3345])).
% 11.45/2.01 thf(f1303,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | (field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f965])).
% 11.45/2.01 thf(f965,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))) | (field(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f488])).
% 11.45/2.01 thf(f488,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))))),
% 11.45/2.01 inference(fool_elimination,[],[f487])).
% 11.45/2.01 thf(f487,plain,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3))))),
% 11.45/2.01 inference(rectify,[],[f112])).
% 11.45/2.01 thf(f112,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X11)),X10) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_divide__divide__eq__left)).
% 11.45/2.01 thf(f3343,plain,(
% 11.45/2.01 spl41_128),
% 11.45/2.01 inference(avatar_split_clause,[],[f1302,f3341])).
% 11.45/2.01 thf(f1302,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2)) | (field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f964])).
% 11.45/2.01 thf(f964,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2)) | (field(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f486])).
% 11.45/2.01 thf(f486,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((field(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2)))),
% 11.45/2.01 inference(fool_elimination,[],[f485])).
% 11.45/2.01 thf(f485,plain,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3)),X2)))),
% 11.45/2.01 inference(rectify,[],[f111])).
% 11.45/2.01 thf(f111,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (field(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X11),X10)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)),X11)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_divide__divide__eq__right)).
% 11.45/2.01 thf(f3339,plain,(
% 11.45/2.01 spl41_127),
% 11.45/2.01 inference(avatar_split_clause,[],[f1281,f3337])).
% 11.45/2.01 thf(f1281,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | (division_ring(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f936])).
% 11.45/2.01 thf(f936,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))) | (division_ring(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f444])).
% 11.45/2.01 thf(f444,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((division_ring(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))))),
% 11.45/2.01 inference(fool_elimination,[],[f443])).
% 11.45/2.01 thf(f443,plain,(
% 11.45/2.01 ! [X0 : $tType] : (division_ring(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X2))))),
% 11.45/2.01 inference(rectify,[],[f135])).
% 11.45/2.01 thf(f135,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (division_ring(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),X11)),X10) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X10),X11))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_divide__divide__eq__left_H)).
% 11.45/2.01 thf(f3335,plain,(
% 11.45/2.01 spl41_126),
% 11.45/2.01 inference(avatar_split_clause,[],[f1280,f3333])).
% 11.45/2.01 thf(f1280,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (division_ring(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f935])).
% 11.45/2.01 thf(f935,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (division_ring(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f442])).
% 11.45/2.01 thf(f442,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((division_ring(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 11.45/2.01 inference(fool_elimination,[],[f441])).
% 11.45/2.01 thf(f441,plain,(
% 11.45/2.01 ! [X0 : $tType] : (division_ring(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 11.45/2.01 inference(rectify,[],[f110])).
% 11.45/2.01 thf(f110,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (division_ring(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X11),X10)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)),X10)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_times__divide__eq__right)).
% 11.45/2.01 thf(f3331,plain,(
% 11.45/2.01 spl41_125),
% 11.45/2.01 inference(avatar_split_clause,[],[f1235,f3329])).
% 11.45/2.01 thf(f1235,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (ab_semigroup_mult(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f875])).
% 11.45/2.01 thf(f875,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (ab_semigroup_mult(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f356])).
% 11.45/2.01 thf(f356,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((ab_semigroup_mult(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 11.45/2.01 inference(fool_elimination,[],[f355])).
% 11.45/2.01 thf(f355,plain,(
% 11.45/2.01 ! [X0 : $tType] : (ab_semigroup_mult(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 11.45/2.01 inference(rectify,[],[f194])).
% 11.45/2.01 thf(f194,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (ab_semigroup_mult(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)),X10)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_ab__semigroup__mult__class_Omult__ac_I1_J)).
% 11.45/2.01 thf(f3327,plain,(
% 11.45/2.01 spl41_124),
% 11.45/2.01 inference(avatar_split_clause,[],[f1234,f3325])).
% 11.45/2.01 thf(f1234,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (ab_semigroup_mult(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f874])).
% 11.45/2.01 thf(f874,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (ab_semigroup_mult(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f354])).
% 11.45/2.01 thf(f354,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((ab_semigroup_mult(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))),
% 11.45/2.01 inference(fool_elimination,[],[f353])).
% 11.45/2.01 thf(f353,plain,(
% 11.45/2.01 ! [X0 : $tType] : (ab_semigroup_mult(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))),
% 11.45/2.01 inference(rectify,[],[f191])).
% 11.45/2.01 thf(f191,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (ab_semigroup_mult(X0) => ! [X11 : X0,X9 : X0,X10 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_mult_Oleft__commute)).
% 11.45/2.01 thf(f3323,plain,(
% 11.45/2.01 spl41_123 | ~spl41_28 | ~spl41_33),
% 11.45/2.01 inference(avatar_split_clause,[],[f2460,f2436,f2405,f3321])).
% 11.45/2.01 thf(f3321,plain,(
% 11.45/2.01 spl41_123 <=> ! [X0 : nat] : ((vAPP(nat,nat,sK3,X0) != X0) | (zero_zero(nat) = X0))),
% 11.45/2.01 introduced(avatar_definition,[new_symbols(naming,[spl41_123])])).
% 11.45/2.01 thf(f2460,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((vAPP(nat,nat,sK3,X0) != X0) | (zero_zero(nat) = X0)) ) | (~spl41_28 | ~spl41_33)),
% 11.45/2.01 inference(superposition,[],[f2406,f2437])).
% 11.45/2.01 thf(f3319,plain,(
% 11.45/2.01 spl41_122),
% 11.45/2.01 inference(avatar_split_clause,[],[f1214,f3317])).
% 11.45/2.01 thf(f1214,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (semigroup_mult(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f851])).
% 11.45/2.01 thf(f851,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (semigroup_mult(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f318])).
% 11.45/2.01 thf(f318,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((semigroup_mult(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 11.45/2.01 inference(fool_elimination,[],[f317])).
% 11.45/2.01 thf(f317,plain,(
% 11.45/2.01 ! [X0 : $tType] : (semigroup_mult(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 11.45/2.01 inference(rectify,[],[f193])).
% 11.45/2.01 thf(f193,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (semigroup_mult(X0) => ! [X9 : X0,X11 : X0,X10 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X11),X10)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)),X10)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_mult_Oassoc)).
% 11.45/2.01 thf(f3311,plain,(
% 11.45/2.01 spl41_121),
% 11.45/2.01 inference(avatar_split_clause,[],[f1470,f3309])).
% 11.45/2.01 thf(f1470,plain,(
% 11.45/2.01 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1097])).
% 11.45/2.01 thf(f1097,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))))),
% 11.45/2.01 inference(ennf_transformation,[],[f746])).
% 11.45/2.01 thf(f746,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2))) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X2)),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f745])).
% 11.45/2.01 thf(f745,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X2)),X1))),
% 11.45/2.01 inference(rectify,[],[f97])).
% 11.45/2.01 thf(f97,axiom,(
% 11.45/2.01 ! [X3 : nat,X27 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X27),X2)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X3),X2)),X27))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Euclidean__Division_Oless__mult__imp__div__less)).
% 11.45/2.01 thf(f3300,plain,(
% 11.45/2.01 spl41_120),
% 11.45/2.01 inference(avatar_split_clause,[],[f1427,f3298])).
% 11.45/2.01 thf(f1427,plain,(
% 11.45/2.01 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)),X2))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f833])).
% 11.45/2.01 thf(f833,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)),X2))),
% 11.45/2.01 inference(rectify,[],[f83])).
% 11.45/2.01 thf(f83,axiom,(
% 11.45/2.01 ! [X3 : nat,X2 : nat,X34 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X34)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X3),X2)),X34))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_div__mult2__eq)).
% 11.45/2.01 thf(f3289,plain,(
% 11.45/2.01 spl41_119),
% 11.45/2.01 inference(avatar_split_clause,[],[f1460,f3287])).
% 11.45/2.01 thf(f1460,plain,(
% 11.45/2.01 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1084])).
% 11.45/2.01 thf(f1084,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(flattening,[],[f1083])).
% 11.45/2.01 thf(f1083,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f726])).
% 11.45/2.01 thf(f726,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X2))))),
% 11.45/2.01 inference(fool_elimination,[],[f725])).
% 11.45/2.01 thf(f725,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X2)))),
% 11.45/2.01 inference(rectify,[],[f66])).
% 11.45/2.01 thf(f66,axiom,(
% 11.45/2.01 ! [X27 : nat,X28 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X28) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X28),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X27)),X4)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__trans__Suc)).
% 11.45/2.01 thf(f3277,plain,(
% 11.45/2.01 spl41_118),
% 11.45/2.01 inference(avatar_split_clause,[],[f1449,f3275])).
% 11.45/2.01 thf(f1449,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)),X1)) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1165])).
% 11.45/2.01 thf(f1165,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : ((($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0))) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)),X1))) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f1163,f1164])).
% 11.45/2.01 thf(f1164,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X1))) => (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0))) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)),X1))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1163,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X1))) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0)))),
% 11.45/2.01 inference(rectify,[],[f1162])).
% 11.45/2.01 thf(f1162,plain,(
% 11.45/2.01 ! [X2 : nat > $o,X1 : nat] : (? [X4 : nat] : (($true != vAPP(nat,$o,X2,X4)) & ($true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X1))) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2)))),
% 11.45/2.01 inference(nnf_transformation,[],[f1102])).
% 11.45/2.01 thf(f3271,plain,(
% 11.45/2.01 spl41_117),
% 11.45/2.01 inference(avatar_split_clause,[],[f1407,f3269])).
% 11.45/2.01 thf(f1407,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0))) | (vAPP(nat,nat,suc,X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1146])).
% 11.45/2.01 thf(f1146,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)))) | (vAPP(nat,nat,suc,X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f1051,f1145])).
% 11.45/2.01 thf(f1145,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (? [X2 : nat] : ((vAPP(nat,nat,suc,X2) = X1) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2))) => ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1051,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (? [X2 : nat] : ((vAPP(nat,nat,suc,X2) = X1) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2))) | (vAPP(nat,nat,suc,X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(flattening,[],[f1050])).
% 11.45/2.01 thf(f1050,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : ((? [X2 : nat] : ((vAPP(nat,nat,suc,X2) = X1) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2))) | (vAPP(nat,nat,suc,X0) = X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f664])).
% 11.45/2.01 thf(f664,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ((vAPP(nat,nat,suc,X0) != X1) => ~! [X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) => (vAPP(nat,nat,suc,X2) != X1))))),
% 11.45/2.01 inference(fool_elimination,[],[f663])).
% 11.45/2.01 thf(f663,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => ((vAPP(nat,nat,suc,X0) != X1) => ~! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2) => (vAPP(nat,nat,suc,X2) != X1))))),
% 11.45/2.01 inference(rectify,[],[f79])).
% 11.45/2.01 thf(f79,axiom,(
% 11.45/2.01 ! [X27 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X4) => ((vAPP(nat,nat,suc,X27) != X4) => ~! [X30 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X30) => (vAPP(nat,nat,suc,X30) != X4))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Nat_OlessE)).
% 11.45/2.01 thf(f3248,plain,(
% 11.45/2.01 spl41_116),
% 11.45/2.01 inference(avatar_split_clause,[],[f1474,f3246])).
% 11.45/2.01 thf(f1474,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true != vAPP(X1,$o,X0,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK38(X1),X2),X0))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP2(X1),X2),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1177])).
% 11.45/2.01 thf(f3237,plain,(
% 11.45/2.01 spl41_115),
% 11.45/2.01 inference(avatar_split_clause,[],[f1509,f3235])).
% 11.45/2.01 thf(f1509,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X3))) | (field(X0) != $true)) )),
% 11.45/2.01 inference(equality_resolution,[],[f1307])).
% 11.45/2.01 thf(f1307,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (zero_zero(X0) != X1) | (field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f969])).
% 11.45/2.01 thf(f3233,plain,(
% 11.45/2.01 spl41_114),
% 11.45/2.01 inference(avatar_split_clause,[],[f1505,f3231])).
% 11.45/2.01 thf(f1505,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X3))) | (euclid191655569cancel(X0) != $true)) )),
% 11.45/2.01 inference(equality_resolution,[],[f1236])).
% 11.45/2.01 thf(f1236,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (zero_zero(X0) != X1) | (euclid191655569cancel(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f876])).
% 11.45/2.01 thf(f3213,plain,(
% 11.45/2.01 spl41_113),
% 11.45/2.01 inference(avatar_split_clause,[],[f1450,f3211])).
% 11.45/2.01 thf(f1450,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0)))) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1165])).
% 11.45/2.01 thf(f3209,plain,(
% 11.45/2.01 spl41_112),
% 11.45/2.01 inference(avatar_split_clause,[],[f1420,f3207])).
% 11.45/2.01 thf(f1420,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1148])).
% 11.45/2.01 thf(f1148,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X1) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f1067,f1147])).
% 11.45/2.01 thf(f1147,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (? [X2 : nat] : ((vAPP(nat,nat,suc,X2) = X1) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2))) => ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X1) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1067,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (? [X2 : nat] : ((vAPP(nat,nat,suc,X2) = X1) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f688])).
% 11.45/2.01 thf(f688,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) => ~! [X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) => (vAPP(nat,nat,suc,X2) != X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f687])).
% 11.45/2.01 thf(f687,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1) => ~! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2) => (vAPP(nat,nat,suc,X2) != X1)))),
% 11.45/2.01 inference(rectify,[],[f77])).
% 11.45/2.01 thf(f77,axiom,(
% 11.45/2.01 ! [X27 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X27)),X4) => ~! [X30 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X30) => (vAPP(nat,nat,suc,X30) != X4)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Suc__lessE)).
% 11.45/2.01 thf(f3205,plain,(
% 11.45/2.01 spl41_111),
% 11.45/2.01 inference(avatar_split_clause,[],[f1402,f3203])).
% 11.45/2.01 thf(f1402,plain,(
% 11.45/2.01 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1144])).
% 11.45/2.01 thf(f1144,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK20,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK20,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,X0)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f1045,f1143])).
% 11.45/2.01 thf(f1143,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) != $true)) & ($true != vAPP(nat,$o,X0,X2)) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) = $true)) => (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK20,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK20,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,X0)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1045,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) != $true)) & ($true != vAPP(nat,$o,X0,X2)) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) = $true)) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(flattening,[],[f1044])).
% 11.45/2.01 thf(f1044,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : ((($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : ((! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) != $true)) & ($true != vAPP(nat,$o,X0,X2))) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) = $true))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(ennf_transformation,[],[f830])).
% 11.45/2.01 thf(f830,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) => (! [X2 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) = $true) => (($true != vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (($true != vAPP(nat,$o,X0,X3)) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) = $true)))) => ($true = vAPP(nat,$o,X0,X1))))),
% 11.45/2.01 inference(flattening,[],[f654])).
% 11.45/2.01 thf(f654,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) => (! [X2 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) = $true) => (~($true = vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (~($true = vAPP(nat,$o,X0,X3)) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) = $true)))) => ($true = vAPP(nat,$o,X0,X1))))),
% 11.45/2.01 inference(fool_elimination,[],[f653])).
% 11.45/2.01 thf(f653,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (vAPP(nat,$o,X0,zero_zero(nat)) => (! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) => (~vAPP(nat,$o,X0,X2) => ? [X3 : nat] : (~vAPP(nat,$o,X0,X3) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))) => vAPP(nat,$o,X0,X1)))),
% 11.45/2.01 inference(rectify,[],[f57])).
% 11.45/2.01 thf(f57,axiom,(
% 11.45/2.01 ! [X13 : nat > $o,X2 : nat] : (vAPP(nat,$o,X13,zero_zero(nat)) => (! [X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X19) => (~vAPP(nat,$o,X13,X19) => ? [X20 : nat] : (~vAPP(nat,$o,X13,X20) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X20),X19)))) => vAPP(nat,$o,X13,X2)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_infinite__descent0)).
% 11.45/2.01 thf(f3197,plain,(
% 11.45/2.01 spl41_110),
% 11.45/2.01 inference(avatar_split_clause,[],[f1455,f3195])).
% 11.45/2.01 thf(f1455,plain,(
% 11.45/2.01 ( ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1171])).
% 11.45/2.01 thf(f1171,plain,(
% 11.45/2.01 ! [X0 : nat > nat > $o] : ((($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36])],[f1169,f1170])).
% 11.45/2.01 thf(f1170,plain,(
% 11.45/2.01 ! [X0 : nat > nat > $o] : (? [X1 : nat,X2 : nat,X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X2),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) = $true) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1169,plain,(
% 11.45/2.01 ! [X0 : nat > nat > $o] : (? [X1 : nat,X2 : nat,X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X2),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) = $true) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0)))),
% 11.45/2.01 inference(rectify,[],[f1168])).
% 11.45/2.01 thf(f1168,plain,(
% 11.45/2.01 ! [X2 : nat > nat > $o] : (? [X4 : nat,X5 : nat,X6 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X5))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2)))),
% 11.45/2.01 inference(nnf_transformation,[],[f1104])).
% 11.45/2.01 thf(f3193,plain,(
% 11.45/2.01 spl41_109),
% 11.45/2.01 inference(avatar_split_clause,[],[f1454,f3191])).
% 11.45/2.01 thf(f1454,plain,(
% 11.45/2.01 ( ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1171])).
% 11.45/2.01 thf(f3181,plain,(
% 11.45/2.01 spl41_108 | ~spl41_31 | ~spl41_74),
% 11.45/2.01 inference(avatar_split_clause,[],[f2929,f2763,f2420,f3179])).
% 11.45/2.01 thf(f2929,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))) ) | (~spl41_31 | ~spl41_74)),
% 11.45/2.01 inference(trivial_inequality_removal,[],[f2928])).
% 11.45/2.01 thf(f2928,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))) ) | (~spl41_31 | ~spl41_74)),
% 11.45/2.01 inference(superposition,[],[f2421,f2764])).
% 11.45/2.01 thf(f3165,plain,(
% 11.45/2.01 spl41_107),
% 11.45/2.01 inference(avatar_split_clause,[],[f1458,f3163])).
% 11.45/2.01 thf(f1458,plain,(
% 11.45/2.01 ( ! [X0 : nat > nat > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1171])).
% 11.45/2.01 thf(f3161,plain,(
% 11.45/2.01 spl41_106),
% 11.45/2.01 inference(avatar_split_clause,[],[f1457,f3159])).
% 11.45/2.01 thf(f1457,plain,(
% 11.45/2.01 ( ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1171])).
% 11.45/2.01 thf(f3157,plain,(
% 11.45/2.01 spl41_105),
% 11.45/2.01 inference(avatar_split_clause,[],[f1456,f3155])).
% 11.45/2.01 thf(f1456,plain,(
% 11.45/2.01 ( ! [X0 : nat > nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0))) | ($true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1171])).
% 11.45/2.01 thf(f3153,plain,(
% 11.45/2.01 spl41_104),
% 11.45/2.01 inference(avatar_split_clause,[],[f1414,f3151])).
% 11.45/2.01 thf(f1414,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1058])).
% 11.45/2.01 thf(f1058,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.01 inference(ennf_transformation,[],[f676])).
% 11.45/2.01 thf(f676,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1))),
% 11.45/2.01 inference(fool_elimination,[],[f675])).
% 11.45/2.01 thf(f675,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),X0) = X1))),
% 11.45/2.01 inference(rectify,[],[f2])).
% 11.45/2.01 thf(f2,axiom,(
% 11.45/2.01 ! [X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X2),X3)),X2) = X3))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_div__mult__self1__is__m)).
% 11.45/2.01 thf(f3149,plain,(
% 11.45/2.01 spl41_103),
% 11.45/2.01 inference(avatar_split_clause,[],[f1413,f3147])).
% 11.45/2.01 thf(f1413,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1057])).
% 11.45/2.01 thf(f1057,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.01 inference(ennf_transformation,[],[f674])).
% 11.45/2.01 thf(f674,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1))),
% 11.45/2.01 inference(fool_elimination,[],[f673])).
% 11.45/2.01 thf(f673,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X0)),X0) = X1))),
% 11.45/2.01 inference(rectify,[],[f1])).
% 11.45/2.01 thf(f1,axiom,(
% 11.45/2.01 ! [X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),X2)),X2) = X3))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_div__mult__self__is__m)).
% 11.45/2.01 thf(f3139,plain,(
% 11.45/2.01 spl41_102),
% 11.45/2.01 inference(avatar_split_clause,[],[f1409,f3137])).
% 11.45/2.01 thf(f1409,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1053])).
% 11.45/2.01 thf(f1053,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(flattening,[],[f1052])).
% 11.45/2.01 thf(f1052,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) | (vAPP(nat,nat,suc,X0) = X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f666])).
% 11.45/2.01 thf(f666,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ((vAPP(nat,nat,suc,X0) != X1) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))))),
% 11.45/2.01 inference(fool_elimination,[],[f665])).
% 11.45/2.01 thf(f665,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => ((vAPP(nat,nat,suc,X0) != X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.45/2.01 inference(rectify,[],[f76])).
% 11.45/2.01 thf(f76,axiom,(
% 11.45/2.01 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => ((vAPP(nat,nat,suc,X3) != X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X3)),X2)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Suc__lessI)).
% 11.45/2.01 thf(f3127,plain,(
% 11.45/2.01 spl41_101 | ~spl41_31 | ~spl41_69),
% 11.45/2.01 inference(avatar_split_clause,[],[f2836,f2682,f2420,f3125])).
% 11.45/2.01 thf(f2836,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))) ) | (~spl41_31 | ~spl41_69)),
% 11.45/2.01 inference(trivial_inequality_removal,[],[f2835])).
% 11.45/2.01 thf(f2835,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))) ) | (~spl41_31 | ~spl41_69)),
% 11.45/2.01 inference(superposition,[],[f2421,f2683])).
% 11.45/2.01 thf(f3117,plain,(
% 11.45/2.01 spl41_100),
% 11.45/2.01 inference(avatar_split_clause,[],[f1451,f3115])).
% 11.45/2.01 thf(f1451,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK32,X1),X0))) | ($true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1165])).
% 11.45/2.01 thf(f3113,plain,(
% 11.45/2.01 spl41_99),
% 11.45/2.01 inference(avatar_split_clause,[],[f1408,f3111])).
% 11.45/2.01 thf(f1408,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1) | (vAPP(nat,nat,suc,X0) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1146])).
% 11.45/2.01 thf(f3025,plain,(
% 11.45/2.01 spl41_98),
% 11.45/2.01 inference(avatar_split_clause,[],[f1424,f3023])).
% 11.45/2.01 thf(f1424,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1071])).
% 11.45/2.01 thf(f1071,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))))),
% 11.45/2.01 inference(ennf_transformation,[],[f694])).
% 11.45/2.01 thf(f694,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f693])).
% 11.45/2.01 thf(f693,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))),
% 11.45/2.01 inference(rectify,[],[f67])).
% 11.45/2.01 thf(f67,axiom,(
% 11.45/2.01 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X2)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Suc__less__SucD)).
% 11.45/2.01 thf(f3021,plain,(
% 11.45/2.01 spl41_97),
% 11.45/2.01 inference(avatar_split_clause,[],[f1412,f3019])).
% 11.45/2.01 thf(f1412,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1056])).
% 11.45/2.01 thf(f1056,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f672])).
% 11.45/2.01 thf(f672,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))))),
% 11.45/2.01 inference(fool_elimination,[],[f671])).
% 11.45/2.01 thf(f671,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))),
% 11.45/2.01 inference(rectify,[],[f19])).
% 11.45/2.01 thf(f19,axiom,(
% 11.45/2.01 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X2)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Suc__mono)).
% 11.45/2.01 thf(f3015,plain,(
% 11.45/2.01 spl41_96),
% 11.45/2.01 inference(avatar_split_clause,[],[f1400,f3013])).
% 11.45/2.01 thf(f1400,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1144])).
% 11.45/2.01 thf(f3011,plain,(
% 11.45/2.01 spl41_95),
% 11.45/2.01 inference(avatar_split_clause,[],[f1392,f3009])).
% 11.45/2.01 thf(f1392,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK16(X0,X1),X3),X2))) | ($true != wellorder(X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1136])).
% 11.45/2.01 thf(f3007,plain,(
% 11.45/2.01 spl41_94),
% 11.45/2.01 inference(avatar_split_clause,[],[f1390,f3005])).
% 11.45/2.01 thf(f1390,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK15(X0,X1),X3),X2))) | ($true != wellorder(X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1134])).
% 11.45/2.01 thf(f2986,plain,(
% 11.45/2.01 spl41_93),
% 11.45/2.01 inference(avatar_split_clause,[],[f1421,f2984])).
% 11.45/2.01 thf(f1421,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1148])).
% 11.45/2.01 thf(f2982,plain,(
% 11.45/2.01 spl41_92),
% 11.45/2.01 inference(avatar_split_clause,[],[f1384,f2980])).
% 11.45/2.01 thf(f1384,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1032])).
% 11.45/2.01 thf(f1032,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(flattening,[],[f1031])).
% 11.45/2.01 thf(f1031,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f828])).
% 11.45/2.01 thf(f828,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) => (X0 = X1)))),
% 11.45/2.01 inference(flattening,[],[f636])).
% 11.45/2.01 thf(f636,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) => (X0 = X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f635])).
% 11.45/2.01 thf(f635,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1)) => (X0 = X1)))),
% 11.45/2.01 inference(rectify,[],[f68])).
% 11.45/2.01 thf(f68,axiom,(
% 11.45/2.01 ! [X2 : nat,X3 : nat] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),vAPP(nat,nat,suc,X3)) => (X2 = X3)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__antisym)).
% 11.45/2.01 thf(f2978,plain,(
% 11.45/2.01 spl41_91),
% 11.45/2.01 inference(avatar_split_clause,[],[f1213,f2976])).
% 11.45/2.01 thf(f1213,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | (linordered_idom(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f850])).
% 11.45/2.01 thf(f850,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2)) | (linordered_idom(X0) != $true))),
% 11.45/2.01 inference(flattening,[],[f849])).
% 11.45/2.01 thf(f849,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (X1 = X2)) | (linordered_idom(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f813])).
% 11.45/2.01 thf(f813,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : X0,X2 : X0] : ((X1 != X2) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))))),
% 11.45/2.01 inference(flattening,[],[f316])).
% 11.45/2.01 thf(f316,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : X0,X2 : X0] : ((X1 != X2) => (~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))))),
% 11.45/2.01 inference(fool_elimination,[],[f315])).
% 11.45/2.01 thf(f315,plain,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : X0,X2 : X0] : ((X1 != X2) => (~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))))),
% 11.45/2.01 inference(rectify,[],[f127])).
% 11.45/2.01 thf(f127,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_idom(X0) => ! [X16 : X0,X17 : X0] : ((X16 != X17) => (~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X16),X17) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X17),X16))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_linorder__neqE__linordered__idom)).
% 11.45/2.01 thf(f2972,plain,(
% 11.45/2.01 spl41_90 | ~spl41_26 | ~spl41_31),
% 11.45/2.01 inference(avatar_split_clause,[],[f2426,f2420,f2369,f2970])).
% 11.45/2.01 thf(f2426,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,X0))) | (order(X0) = $false)) ) | (~spl41_26 | ~spl41_31)),
% 11.45/2.01 inference(trivial_inequality_removal,[],[f2425])).
% 11.45/2.01 thf(f2425,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,X0))) | (order(X0) = $false)) ) | (~spl41_26 | ~spl41_31)),
% 11.45/2.01 inference(superposition,[],[f2421,f2370])).
% 11.45/2.01 thf(f2966,plain,(
% 11.45/2.01 spl41_89),
% 11.45/2.01 inference(avatar_split_clause,[],[f1387,f2964])).
% 11.45/2.01 thf(f1387,plain,(
% 11.45/2.01 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK14,X0)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1132])).
% 11.45/2.01 thf(f1132,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0))) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK14,X0))))))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f1034,f1131])).
% 11.45/2.01 thf(f1131,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) != $true))) => (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0))) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK14,X0))))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1034,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) != $true))))),
% 11.45/2.01 inference(ennf_transformation,[],[f640])).
% 11.45/2.01 thf(f640,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (! [X3 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) = $true) => ($true = vAPP(nat,$o,X0,X3))) => ($true = vAPP(nat,$o,X0,X2))) => ($true = vAPP(nat,$o,X0,X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f639])).
% 11.45/2.01 thf(f639,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (! [X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => vAPP(nat,$o,X0,X3)) => vAPP(nat,$o,X0,X2)) => vAPP(nat,$o,X0,X1))),
% 11.45/2.01 inference(rectify,[],[f35])).
% 11.45/2.01 thf(f35,axiom,(
% 11.45/2.01 ! [X13 : nat > $o,X2 : nat] : (! [X19 : nat] : (! [X20 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X20),X19) => vAPP(nat,$o,X13,X20)) => vAPP(nat,$o,X13,X19)) => vAPP(nat,$o,X13,X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_nat__less__induct)).
% 11.45/2.01 thf(f2962,plain,(
% 11.45/2.01 spl41_88),
% 11.45/2.01 inference(avatar_split_clause,[],[f1386,f2960])).
% 11.45/2.01 thf(f1386,plain,(
% 11.45/2.01 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK13,X0)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1130])).
% 11.45/2.01 thf(f1130,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK13,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)))))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f1033,f1129])).
% 11.45/2.01 thf(f1129,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) != $true)) & ($true != vAPP(nat,$o,X0,X2))) => (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK13,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1033,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) != $true)) & ($true != vAPP(nat,$o,X0,X2))))),
% 11.45/2.01 inference(ennf_transformation,[],[f829])).
% 11.45/2.01 thf(f829,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (($true != vAPP(nat,$o,X0,X3)) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) = $true))) => ($true = vAPP(nat,$o,X0,X1)))),
% 11.45/2.01 inference(flattening,[],[f638])).
% 11.45/2.01 thf(f638,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (~($true = vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (~($true = vAPP(nat,$o,X0,X3)) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) = $true))) => ($true = vAPP(nat,$o,X0,X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f637])).
% 11.45/2.01 thf(f637,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (~vAPP(nat,$o,X0,X2) => ? [X3 : nat] : (~vAPP(nat,$o,X0,X3) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) => vAPP(nat,$o,X0,X1))),
% 11.45/2.01 inference(rectify,[],[f34])).
% 11.45/2.01 thf(f34,axiom,(
% 11.45/2.01 ! [X13 : nat > $o,X2 : nat] : (! [X19 : nat] : (~vAPP(nat,$o,X13,X19) => ? [X20 : nat] : (~vAPP(nat,$o,X13,X20) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X20),X19))) => vAPP(nat,$o,X13,X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_infinite__descent)).
% 11.45/2.01 thf(f2948,plain,(
% 11.45/2.01 spl41_87),
% 11.45/2.01 inference(avatar_split_clause,[],[f1507,f2946])).
% 11.45/2.01 thf(f1507,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1)),X1) = X3) | (zero_zero(X0) = X1) | (division_ring(X0) != $true)) )),
% 11.45/2.01 inference(equality_resolution,[],[f1286])).
% 11.45/2.01 thf(f1286,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1) = X3) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1) != X2) | (zero_zero(X0) = X1) | (division_ring(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f942])).
% 11.45/2.01 thf(f942,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1) = X3) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1) != X2) | (zero_zero(X0) = X1)) | (division_ring(X0) != $true))),
% 11.45/2.01 inference(flattening,[],[f941])).
% 11.45/2.01 thf(f941,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1) = X3) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1) != X2)) | (zero_zero(X0) = X1)) | (division_ring(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f454])).
% 11.45/2.01 thf(f454,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((division_ring(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1) = X2) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1) = X3))))),
% 11.45/2.01 inference(fool_elimination,[],[f453])).
% 11.45/2.01 thf(f453,plain,(
% 11.45/2.01 ! [X0 : $tType] : (division_ring(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((zero_zero(X0) != X1) => ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X3),X1) = X2) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X2),X1) = X3))))),
% 11.45/2.01 inference(rectify,[],[f167])).
% 11.45/2.01 thf(f167,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (division_ring(X0) => ! [X10 : X0,X11 : X0,X9 : X0] : ((zero_zero(X0) != X10) => ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X10) = X11) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X11),X10) = X9))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_divide__eq__imp)).
% 11.45/2.01 thf(f2944,plain,(
% 11.45/2.01 spl41_86),
% 11.45/2.01 inference(avatar_split_clause,[],[f1245,f2942])).
% 11.45/2.01 thf(f1245,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2) | (zero_zero(X0) = X1) | (semidom_divide(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f886])).
% 11.45/2.01 thf(f886,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2) | (zero_zero(X0) = X1)) | (semidom_divide(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f374])).
% 11.45/2.01 thf(f374,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((semidom_divide(X0) = $true) => ! [X1 : X0,X2 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2)))),
% 11.45/2.01 inference(fool_elimination,[],[f373])).
% 11.45/2.01 thf(f373,plain,(
% 11.45/2.01 ! [X0 : $tType] : (semidom_divide(X0) => ! [X1 : X0,X2 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)),X1) = X2)))),
% 11.45/2.01 inference(rectify,[],[f103])).
% 11.45/2.01 thf(f103,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (semidom_divide(X0) => ! [X11 : X0,X9 : X0] : ((zero_zero(X0) != X11) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)),X11) = X9)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_nonzero__mult__div__cancel__right)).
% 11.45/2.01 thf(f2940,plain,(
% 11.45/2.01 spl41_85),
% 11.45/2.01 inference(avatar_split_clause,[],[f1244,f2938])).
% 11.45/2.01 thf(f1244,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X1) = X2) | (zero_zero(X0) = X1) | (semidom_divide(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f885])).
% 11.45/2.01 thf(f885,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X1) = X2) | (zero_zero(X0) = X1)) | (semidom_divide(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f372])).
% 11.45/2.01 thf(f372,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((semidom_divide(X0) = $true) => ! [X1 : X0,X2 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X1) = X2)))),
% 11.45/2.01 inference(fool_elimination,[],[f371])).
% 11.45/2.01 thf(f371,plain,(
% 11.45/2.01 ! [X0 : $tType] : (semidom_divide(X0) => ! [X1 : X0,X2 : X0] : ((zero_zero(X0) != X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X1) = X2)))),
% 11.45/2.01 inference(rectify,[],[f106])).
% 11.45/2.01 thf(f106,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (semidom_divide(X0) => ! [X9 : X0,X11 : X0] : ((zero_zero(X0) != X9) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X11)),X9) = X11)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_nonzero__mult__div__cancel__left)).
% 11.45/2.01 thf(f2856,plain,(
% 11.45/2.01 spl41_84),
% 11.45/2.01 inference(avatar_split_clause,[],[f1422,f2854])).
% 11.45/2.01 thf(f1422,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1068])).
% 11.45/2.01 thf(f1068,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f690])).
% 11.45/2.01 thf(f690,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f689])).
% 11.45/2.01 thf(f689,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X0)),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))),
% 11.45/2.01 inference(rectify,[],[f78])).
% 11.45/2.01 thf(f78,axiom,(
% 11.45/2.01 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,suc,X3)),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Suc__lessD)).
% 11.45/2.01 thf(f2852,plain,(
% 11.45/2.01 spl41_83),
% 11.45/2.01 inference(avatar_split_clause,[],[f1411,f2850])).
% 11.45/2.01 thf(f1411,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1055])).
% 11.45/2.01 thf(f1055,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f670])).
% 11.45/2.01 thf(f670,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1))))),
% 11.45/2.01 inference(fool_elimination,[],[f669])).
% 11.45/2.01 thf(f669,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X1)))),
% 11.45/2.01 inference(rectify,[],[f74])).
% 11.45/2.01 thf(f74,axiom,(
% 11.45/2.01 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,suc,X2)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__SucI)).
% 11.45/2.01 thf(f2848,plain,(
% 11.45/2.01 spl41_82),
% 11.45/2.01 inference(avatar_split_clause,[],[f1399,f2846])).
% 11.45/2.01 thf(f1399,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1142])).
% 11.45/2.01 thf(f1142,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0)))) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f1043,f1141])).
% 11.45/2.01 thf(f1141,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (? [X2 : nat] : (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true = vAPP(nat,$o,X0,X2))) => (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0)))) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1043,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true = vAPP(nat,$o,X0,X2))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(flattening,[],[f1042])).
% 11.45/2.01 thf(f1042,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : ((($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true = vAPP(nat,$o,X0,X2)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(ennf_transformation,[],[f652])).
% 11.45/2.01 thf(f652,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) => (! [X2 : nat] : (($true = vAPP(nat,$o,X0,X2)) => ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)))) => ($true = vAPP(nat,$o,X0,X1))))),
% 11.45/2.01 inference(fool_elimination,[],[f651])).
% 11.45/2.01 thf(f651,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (vAPP(nat,$o,X0,zero_zero(nat)) => (! [X2 : nat] : (vAPP(nat,$o,X0,X2) => vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) => vAPP(nat,$o,X0,X1)))),
% 11.45/2.01 inference(rectify,[],[f43])).
% 11.45/2.01 thf(f43,axiom,(
% 11.45/2.01 ! [X13 : nat > $o,X5 : nat] : (vAPP(nat,$o,X13,zero_zero(nat)) => (! [X24 : nat] : (vAPP(nat,$o,X13,X24) => vAPP(nat,$o,X13,vAPP(nat,nat,suc,X24))) => vAPP(nat,$o,X13,X5)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_old_Onat_Oinducts)).
% 11.45/2.01 thf(f2844,plain,(
% 11.45/2.01 spl41_81),
% 11.45/2.01 inference(avatar_split_clause,[],[f1397,f2842])).
% 11.45/2.01 thf(f1397,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,X0)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1140])).
% 11.45/2.01 thf(f1140,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,X0)))) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK18,X0)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f1041,f1139])).
% 11.45/2.01 thf(f1139,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (? [X2 : nat] : (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true = vAPP(nat,$o,X0,X2))) => (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK18,X0)))) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK18,X0)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1041,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true = vAPP(nat,$o,X0,X2))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(flattening,[],[f1040])).
% 11.45/2.01 thf(f1040,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : ((($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (($true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true = vAPP(nat,$o,X0,X2)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(ennf_transformation,[],[f650])).
% 11.45/2.01 thf(f650,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) => (! [X2 : nat] : (($true = vAPP(nat,$o,X0,X2)) => ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)))) => ($true = vAPP(nat,$o,X0,X1))))),
% 11.45/2.01 inference(fool_elimination,[],[f649])).
% 11.45/2.01 thf(f649,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (vAPP(nat,$o,X0,zero_zero(nat)) => (! [X2 : nat] : (vAPP(nat,$o,X0,X2) => vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) => vAPP(nat,$o,X0,X1)))),
% 11.45/2.01 inference(rectify,[],[f50])).
% 11.45/2.01 thf(f50,axiom,(
% 11.45/2.01 ! [X13 : nat > $o,X2 : nat] : (vAPP(nat,$o,X13,zero_zero(nat)) => (! [X19 : nat] : (vAPP(nat,$o,X13,X19) => vAPP(nat,$o,X13,vAPP(nat,nat,suc,X19))) => vAPP(nat,$o,X13,X2)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__induct)).
% 11.45/2.01 thf(f2840,plain,(
% 11.45/2.01 spl41_80),
% 11.45/2.01 inference(avatar_split_clause,[],[f1394,f2838])).
% 11.45/2.01 thf(f1394,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,X0)))) | ($true != vAPP(nat,$o,X0,X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1138])).
% 11.45/2.01 thf(f1138,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) | (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK17,X0))) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,X0))))) | ($true != vAPP(nat,$o,X0,X1)))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f1039,f1137])).
% 11.45/2.01 thf(f1137,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)))) => (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK17,X0))) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK17,X0))))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1039,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) | ? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)))) | ($true != vAPP(nat,$o,X0,X1)))),
% 11.45/2.01 inference(flattening,[],[f1038])).
% 11.45/2.01 thf(f1038,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : ((($true = vAPP(nat,$o,X0,zero_zero(nat))) | ? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))))) | ($true != vAPP(nat,$o,X0,X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f648])).
% 11.45/2.01 thf(f648,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) => (! [X2 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) => ($true = vAPP(nat,$o,X0,X2))) => ($true = vAPP(nat,$o,X0,zero_zero(nat)))))),
% 11.45/2.01 inference(fool_elimination,[],[f647])).
% 11.45/2.01 thf(f647,plain,(
% 11.45/2.01 ! [X0 : nat > $o,X1 : nat] : (vAPP(nat,$o,X0,X1) => (! [X2 : nat] : (vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) => vAPP(nat,$o,X0,X2)) => vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(rectify,[],[f48])).
% 11.45/2.01 thf(f48,axiom,(
% 11.45/2.01 ! [X13 : nat > $o,X4 : nat] : (vAPP(nat,$o,X13,X4) => (! [X19 : nat] : (vAPP(nat,$o,X13,vAPP(nat,nat,suc,X19)) => vAPP(nat,$o,X13,X19)) => vAPP(nat,$o,X13,zero_zero(nat))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zero__induct)).
% 11.45/2.01 thf(f2834,plain,(
% 11.45/2.01 spl41_79),
% 11.45/2.01 inference(avatar_split_clause,[],[f1209,f2832])).
% 11.45/2.01 thf(f1209,plain,(
% 11.45/2.01 ( ! [X2 : nat,X0 : nat > $o] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,X0)))) | ($true != vAPP(nat,$o,X0,X2)) | ($true = vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1116])).
% 11.45/2.01 thf(f1116,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : ((($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0)))) | ! [X2 : nat] : ($true != vAPP(nat,$o,X0,X2)) | ($true = vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f1114,f1115])).
% 11.45/2.01 thf(f1115,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (? [X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X1))) & ($true != vAPP(nat,$o,X0,X1))) => (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK6,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0)))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1114,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (? [X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X1))) & ($true != vAPP(nat,$o,X0,X1))) | ! [X2 : nat] : ($true != vAPP(nat,$o,X0,X2)) | ($true = vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(rectify,[],[f845])).
% 11.45/2.01 thf(f845,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (? [X2 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true != vAPP(nat,$o,X0,X2))) | ! [X1 : nat] : ($true != vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(flattening,[],[f844])).
% 11.45/2.01 thf(f844,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : ((? [X2 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true != vAPP(nat,$o,X0,X2))) | ! [X1 : nat] : ($true != vAPP(nat,$o,X0,X1))) | ($true = vAPP(nat,$o,X0,zero_zero(nat))))),
% 11.45/2.01 inference(ennf_transformation,[],[f811])).
% 11.45/2.01 thf(f811,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (($true != vAPP(nat,$o,X0,zero_zero(nat))) => (? [X1 : nat] : ($true = vAPP(nat,$o,X0,X1)) => ? [X2 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ($true != vAPP(nat,$o,X0,X2)))))),
% 11.45/2.01 inference(flattening,[],[f308])).
% 11.45/2.01 thf(f308,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (~($true = vAPP(nat,$o,X0,zero_zero(nat))) => (? [X1 : nat] : ($true = vAPP(nat,$o,X0,X1)) => ? [X2 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))) & ~($true = vAPP(nat,$o,X0,X2)))))),
% 11.45/2.01 inference(fool_elimination,[],[f307])).
% 11.45/2.01 thf(f307,plain,(
% 11.45/2.01 ! [X0 : nat > $o] : (~vAPP(nat,$o,X0,zero_zero(nat)) => (? [X1 : nat] : vAPP(nat,$o,X0,X1) => ? [X2 : nat] : (vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) & ~vAPP(nat,$o,X0,X2))))),
% 11.45/2.01 inference(rectify,[],[f208])).
% 11.45/2.01 thf(f208,axiom,(
% 11.45/2.01 ! [X13 : nat > $o] : (~vAPP(nat,$o,X13,zero_zero(nat)) => (? [X49 : nat] : vAPP(nat,$o,X13,X49) => ? [X19 : nat] : (vAPP(nat,$o,X13,vAPP(nat,nat,suc,X19)) & ~vAPP(nat,$o,X13,X19))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_exists__least__lemma)).
% 11.45/2.01 thf(f2802,plain,(
% 11.45/2.01 spl41_78),
% 11.45/2.01 inference(avatar_split_clause,[],[f1478,f2800])).
% 11.45/2.01 thf(f1478,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK40(X0),X2),X1)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1181])).
% 11.45/2.01 thf(f2790,plain,(
% 11.45/2.01 spl41_77),
% 11.45/2.01 inference(avatar_split_clause,[],[f1212,f2788])).
% 11.45/2.01 thf(f1212,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1))) | (linordered_ring(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f848])).
% 11.45/2.01 thf(f848,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1))) | (linordered_ring(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f314])).
% 11.45/2.01 thf(f314,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linordered_ring(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1))))),
% 11.45/2.01 inference(fool_elimination,[],[f313])).
% 11.45/2.01 thf(f313,plain,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_ring(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)))),
% 11.45/2.01 inference(rectify,[],[f243])).
% 11.45/2.01 thf(f243,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_ring(X0) => ! [X9 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X9)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_zero__le__square)).
% 11.45/2.01 thf(f2786,plain,(
% 11.45/2.01 spl41_76),
% 11.45/2.01 inference(avatar_split_clause,[],[f1211,f2784])).
% 11.45/2.01 thf(f1211,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0))) | (linordered_ring(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f847])).
% 11.45/2.01 thf(f847,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0))) | (linordered_ring(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f812])).
% 11.45/2.01 thf(f812,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linordered_ring(X0) = $true) => ! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0))))),
% 11.45/2.01 inference(flattening,[],[f312])).
% 11.45/2.01 thf(f312,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linordered_ring(X0) = $true) => ! [X1 : X0] : ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0))))),
% 11.45/2.01 inference(fool_elimination,[],[f311])).
% 11.45/2.01 thf(f311,plain,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_ring(X0) => ! [X1 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X1)),zero_zero(X0)))),
% 11.45/2.01 inference(rectify,[],[f137])).
% 11.45/2.01 thf(f137,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_ring(X0) => ! [X9 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),X9)),zero_zero(X0)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_not__square__less__zero)).
% 11.45/2.01 thf(f2769,plain,(
% 11.45/2.01 spl41_75),
% 11.45/2.01 inference(avatar_split_clause,[],[f1410,f2767])).
% 11.45/2.01 thf(f1410,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1054])).
% 11.45/2.01 thf(f1054,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f668])).
% 11.45/2.01 thf(f668,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f667])).
% 11.45/2.01 thf(f667,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1))),
% 11.45/2.01 inference(rectify,[],[f199])).
% 11.45/2.01 thf(f199,axiom,(
% 11.45/2.01 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_gr__implies__gr0)).
% 11.45/2.01 thf(f2765,plain,(
% 11.45/2.01 spl41_74 | ~spl41_31 | ~spl41_42),
% 11.45/2.01 inference(avatar_split_clause,[],[f2544,f2480,f2420,f2763])).
% 11.45/2.01 thf(f2544,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,$o))))) ) | (~spl41_31 | ~spl41_42)),
% 11.45/2.01 inference(trivial_inequality_removal,[],[f2543])).
% 11.45/2.01 thf(f2543,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,sTfun(X0,$o))))) ) | (~spl41_31 | ~spl41_42)),
% 11.45/2.01 inference(superposition,[],[f2421,f2481])).
% 11.45/2.01 thf(f2761,plain,(
% 11.45/2.01 spl41_73),
% 11.45/2.01 inference(avatar_split_clause,[],[f1406,f2759])).
% 11.45/2.01 thf(f1406,plain,(
% 11.45/2.01 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1049])).
% 11.45/2.01 thf(f1049,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f662])).
% 11.45/2.01 thf(f662,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f661])).
% 11.45/2.01 thf(f661,plain,(
% 11.45/2.01 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),X1)))),
% 11.45/2.01 inference(rectify,[],[f4])).
% 11.45/2.01 thf(f4,axiom,(
% 11.45/2.01 ! [X3 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X3),X2)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_div__less)).
% 11.45/2.01 thf(f2696,plain,(
% 11.45/2.01 spl41_72),
% 11.45/2.01 inference(avatar_split_clause,[],[f1401,f2694])).
% 11.45/2.01 thf(f1401,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK20,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1144])).
% 11.45/2.01 thf(f2692,plain,(
% 11.45/2.01 spl41_71),
% 11.45/2.01 inference(avatar_split_clause,[],[f1398,f2690])).
% 11.45/2.01 thf(f1398,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1142])).
% 11.45/2.01 thf(f2688,plain,(
% 11.45/2.01 spl41_70),
% 11.45/2.01 inference(avatar_split_clause,[],[f1396,f2686])).
% 11.45/2.01 thf(f1396,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK18,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1140])).
% 11.45/2.01 thf(f2684,plain,(
% 11.45/2.01 spl41_69 | ~spl41_31 | ~spl41_36),
% 11.45/2.01 inference(avatar_split_clause,[],[f2508,f2448,f2420,f2682])).
% 11.45/2.01 thf(f2508,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,nat))))) ) | (~spl41_31 | ~spl41_36)),
% 11.45/2.01 inference(trivial_inequality_removal,[],[f2507])).
% 11.45/2.01 thf(f2507,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,sTfun(X0,nat))))) ) | (~spl41_31 | ~spl41_36)),
% 11.45/2.01 inference(superposition,[],[f2421,f2449])).
% 11.45/2.01 thf(f2680,plain,(
% 11.45/2.01 spl41_68),
% 11.45/2.01 inference(avatar_split_clause,[],[f1395,f2678])).
% 11.45/2.01 thf(f1395,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK17,X0))) | ($true != vAPP(nat,$o,X0,X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1138])).
% 11.45/2.01 thf(f2676,plain,(
% 11.45/2.01 spl41_67),
% 11.45/2.01 inference(avatar_split_clause,[],[f1222,f2674])).
% 11.45/2.01 thf(f1222,plain,(
% 11.45/2.01 ( ! [X0 : $tType] : ((times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))) | (ab_semigroup_mult(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f861])).
% 11.45/2.01 thf(f861,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))) | (ab_semigroup_mult(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f334])).
% 11.45/2.01 thf(f334,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((ab_semigroup_mult(X0) = $true) => (times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))))),
% 11.45/2.01 inference(fool_elimination,[],[f333])).
% 11.45/2.01 thf(f333,plain,(
% 11.45/2.01 ! [X0 : $tType] : (ab_semigroup_mult(X0) => (times_times(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)))))),
% 11.45/2.01 inference(rectify,[],[f192])).
% 11.45/2.01 thf(f192,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (ab_semigroup_mult(X0) => (times_times(X0) = (^[X42 : X0, X43 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X43),X42)))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_mult_Ocommute)).
% 11.45/2.01 thf(f2672,plain,(
% 11.45/2.01 spl41_66),
% 11.45/2.01 inference(avatar_split_clause,[],[f1208,f2670])).
% 11.45/2.01 thf(f1208,plain,(
% 11.45/2.01 ( ! [X2 : nat,X0 : nat > $o] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0))) | ($true != vAPP(nat,$o,X0,X2)) | ($true = vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1116])).
% 11.45/2.01 thf(f2662,plain,(
% 11.45/2.01 spl41_65),
% 11.45/2.01 inference(avatar_split_clause,[],[f1348,f2660])).
% 11.45/2.01 thf(f1348,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK12,X0)) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1128])).
% 11.45/2.01 thf(f1128,plain,(
% 11.45/2.01 ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK12,X0)) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f1025,f1127])).
% 11.45/2.01 thf(f1127,plain,(
% 11.45/2.01 ! [X0 : nat] : (? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0) => (vAPP(nat,nat,suc,vAPP(nat,nat,sK12,X0)) = X0))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f1025,plain,(
% 11.45/2.01 ! [X0 : nat] : (? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 11.45/2.01 inference(ennf_transformation,[],[f572])).
% 11.45/2.01 thf(f572,plain,(
% 11.45/2.01 ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => ? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0))),
% 11.45/2.01 inference(fool_elimination,[],[f571])).
% 11.45/2.01 thf(f571,plain,(
% 11.45/2.01 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => ? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0))),
% 11.45/2.01 inference(rectify,[],[f87])).
% 11.45/2.01 thf(f87,axiom,(
% 11.45/2.01 ! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) => ? [X23 : nat] : (vAPP(nat,nat,suc,X23) = X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_gr0__implies__Suc)).
% 11.45/2.01 thf(f2650,plain,(
% 11.45/2.01 spl41_64),
% 11.45/2.01 inference(avatar_split_clause,[],[f1442,f2648])).
% 11.45/2.01 thf(f1442,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0) > $o] : (($true = vAPP(list(X0),$o,X1,X2)) | ($true != vAPP(list(X0),$o,X1,vAPP(sTfun(list(X0),$o),list(X0),sK24(X0),X1)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1152])).
% 11.45/2.01 thf(f2646,plain,(
% 11.45/2.01 spl41_63),
% 11.45/2.01 inference(avatar_split_clause,[],[f1184,f2643])).
% 11.45/2.01 thf(f1184,plain,(
% 11.45/2.01 (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),k) = vAPP(nat,nat,suc,n))),
% 11.45/2.01 inference(cnf_transformation,[],[f279])).
% 11.45/2.01 thf(f279,axiom,(
% 11.45/2.01 (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(list(a),nat,size_size(list(a)),xs)),k) = vAPP(nat,nat,suc,n))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 11.45/2.01 thf(f2634,plain,(
% 11.45/2.01 spl41_62),
% 11.45/2.01 inference(avatar_split_clause,[],[f1317,f2632])).
% 11.45/2.01 thf(f1317,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK10(X0),X1)),X1)) | (linordered_field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1124])).
% 11.45/2.01 thf(f1124,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK10(X0),X1)),X1)) | (linordered_field(X0) != $true))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f979,f1123])).
% 11.45/2.01 thf(f1123,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK10(X0),X1)),X1)))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f979,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (linordered_field(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f514])).
% 11.45/2.01 thf(f514,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f513])).
% 11.45/2.01 thf(f513,plain,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0] : ? [X2 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))),
% 11.45/2.01 inference(rectify,[],[f125])).
% 11.45/2.01 thf(f125,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_field(X0) => ! [X38 : X0] : ? [X25 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X25),X38))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_linordered__field__no__lb)).
% 11.45/2.01 thf(f2630,plain,(
% 11.45/2.01 spl41_61),
% 11.45/2.01 inference(avatar_split_clause,[],[f1316,f2628])).
% 11.45/2.01 thf(f1316,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK9(X0),X1))) | (linordered_field(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1122])).
% 11.45/2.01 thf(f1122,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK9(X0),X1))) | (linordered_field(X0) != $true))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f978,f1121])).
% 11.45/2.01 thf(f1121,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK9(X0),X1))))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f978,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (linordered_field(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f512])).
% 11.45/2.01 thf(f512,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linordered_field(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 11.45/2.01 inference(fool_elimination,[],[f511])).
% 11.45/2.01 thf(f511,plain,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_field(X0) => ! [X1 : X0] : ? [X2 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))),
% 11.45/2.01 inference(rectify,[],[f126])).
% 11.45/2.01 thf(f126,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (linordered_field(X0) => ! [X38 : X0] : ? [X39 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X38),X39))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_linordered__field__no__ub)).
% 11.45/2.01 thf(f2588,plain,(
% 11.45/2.01 spl41_60 | ~spl41_26 | spl41_29),
% 11.45/2.01 inference(avatar_split_clause,[],[f2414,f2409,f2369,f2585])).
% 11.45/2.01 thf(f2409,plain,(
% 11.45/2.01 spl41_29 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs)) = $true)),
% 11.45/2.01 introduced(avatar_definition,[new_symbols(naming,[spl41_29])])).
% 11.45/2.01 thf(f2414,plain,(
% 11.45/2.01 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs)) = $false) | (~spl41_26 | spl41_29)),
% 11.45/2.01 inference(trivial_inequality_removal,[],[f2413])).
% 11.45/2.01 thf(f2413,plain,(
% 11.45/2.01 ($true != $true) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs)) = $false) | (~spl41_26 | spl41_29)),
% 11.45/2.01 inference(superposition,[],[f2411,f2370])).
% 11.45/2.01 thf(f2411,plain,(
% 11.45/2.01 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs)) != $true) | spl41_29),
% 11.45/2.01 inference(avatar_component_clause,[],[f2409])).
% 11.45/2.01 thf(f2568,plain,(
% 11.45/2.01 spl41_59),
% 11.45/2.01 inference(avatar_split_clause,[],[f1388,f2566])).
% 11.45/2.01 thf(f1388,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1132])).
% 11.45/2.01 thf(f2564,plain,(
% 11.45/2.01 spl41_58),
% 11.45/2.01 inference(avatar_split_clause,[],[f1385,f2562])).
% 11.45/2.01 thf(f1385,plain,(
% 11.45/2.01 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1130])).
% 11.45/2.01 thf(f2560,plain,(
% 11.45/2.01 spl41_57),
% 11.45/2.01 inference(avatar_split_clause,[],[f1273,f2558])).
% 11.45/2.01 thf(f1273,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (division_ring(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f922])).
% 11.45/2.01 thf(f922,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (division_ring(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f428])).
% 11.45/2.01 thf(f428,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((division_ring(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(fool_elimination,[],[f427])).
% 11.45/2.01 thf(f427,plain,(
% 11.45/2.01 ! [X0 : $tType] : (division_ring(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(rectify,[],[f123])).
% 11.45/2.01 thf(f123,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (division_ring(X0) => ! [X9 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),zero_zero(X0))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_division__ring__divide__zero)).
% 11.45/2.01 thf(f2556,plain,(
% 11.45/2.01 spl41_56),
% 11.45/2.01 inference(avatar_split_clause,[],[f1243,f2554])).
% 11.45/2.01 thf(f1243,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semidom_divide(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f884])).
% 11.45/2.01 thf(f884,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semidom_divide(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f370])).
% 11.45/2.01 thf(f370,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((semidom_divide(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f369])).
% 11.45/2.01 thf(f369,plain,(
% 11.45/2.01 ! [X0 : $tType] : (semidom_divide(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)))),
% 11.45/2.01 inference(rectify,[],[f118])).
% 11.45/2.01 thf(f118,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (semidom_divide(X0) => ! [X9 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X9)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_div__0)).
% 11.45/2.01 thf(f2552,plain,(
% 11.45/2.01 spl41_55),
% 11.45/2.01 inference(avatar_split_clause,[],[f1242,f2550])).
% 11.45/2.01 thf(f1242,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semidom_divide(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f883])).
% 11.45/2.01 thf(f883,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semidom_divide(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f368])).
% 11.45/2.01 thf(f368,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((semidom_divide(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(fool_elimination,[],[f367])).
% 11.45/2.01 thf(f367,plain,(
% 11.45/2.01 ! [X0 : $tType] : (semidom_divide(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(rectify,[],[f120])).
% 11.45/2.01 thf(f120,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (semidom_divide(X0) => ! [X9 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),zero_zero(X0))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_div__by__0)).
% 11.45/2.01 thf(f2548,plain,(
% 11.45/2.01 spl41_54),
% 11.45/2.01 inference(avatar_split_clause,[],[f1224,f2546])).
% 11.45/2.01 thf(f1224,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)) | (mult_zero(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f863])).
% 11.45/2.01 thf(f863,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)) | (mult_zero(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f338])).
% 11.45/2.01 thf(f338,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((mult_zero(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f337])).
% 11.45/2.01 thf(f337,plain,(
% 11.45/2.01 ! [X0 : $tType] : (mult_zero(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X1)))),
% 11.45/2.01 inference(rectify,[],[f113])).
% 11.45/2.01 thf(f113,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (mult_zero(X0) => ! [X9 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),zero_zero(X0)),X9)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_mult__zero__left)).
% 11.45/2.01 thf(f2542,plain,(
% 11.45/2.01 spl41_53),
% 11.45/2.01 inference(avatar_split_clause,[],[f1223,f2540])).
% 11.45/2.01 thf(f1223,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),zero_zero(X0))) | (mult_zero(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f862])).
% 11.45/2.01 thf(f862,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),zero_zero(X0))) | (mult_zero(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f336])).
% 11.45/2.01 thf(f336,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((mult_zero(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(fool_elimination,[],[f335])).
% 11.45/2.01 thf(f335,plain,(
% 11.45/2.01 ! [X0 : $tType] : (mult_zero(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(rectify,[],[f114])).
% 11.45/2.01 thf(f114,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (mult_zero(X0) => ! [X9 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X9),zero_zero(X0))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_mult__zero__right)).
% 11.45/2.01 thf(f2538,plain,(
% 11.45/2.01 spl41_52),
% 11.45/2.01 inference(avatar_split_clause,[],[f1221,f2536])).
% 11.45/2.01 thf(f1221,plain,(
% 11.45/2.01 ( ! [X0 : $tType] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true) | (linord1659791738miring(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f860])).
% 11.45/2.01 thf(f860,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true) | (linord1659791738miring(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f332])).
% 11.45/2.01 thf(f332,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linord1659791738miring(X0) = $true) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true))),
% 11.45/2.01 inference(fool_elimination,[],[f331])).
% 11.45/2.01 thf(f331,plain,(
% 11.45/2.01 ! [X0 : $tType] : (linord1659791738miring(X0) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)))),
% 11.45/2.01 inference(rectify,[],[f221])).
% 11.45/2.01 thf(f221,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (linord1659791738miring(X0) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_le__numeral__extra_I3_J)).
% 11.45/2.01 thf(f2534,plain,(
% 11.45/2.01 spl41_51),
% 11.45/2.01 inference(avatar_split_clause,[],[f1220,f2532])).
% 11.45/2.01 thf(f1220,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semiring_bits(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f859])).
% 11.45/2.01 thf(f859,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)) | (semiring_bits(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f330])).
% 11.45/2.01 thf(f330,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((semiring_bits(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f329])).
% 11.45/2.01 thf(f329,plain,(
% 11.45/2.01 ! [X0 : $tType] : (semiring_bits(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X1)))),
% 11.45/2.01 inference(rectify,[],[f186])).
% 11.45/2.01 thf(f186,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (semiring_bits(X0) => ! [X9 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),zero_zero(X0)),X9)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_bits__div__0)).
% 11.45/2.01 thf(f2530,plain,(
% 11.45/2.01 spl41_50),
% 11.45/2.01 inference(avatar_split_clause,[],[f1219,f2528])).
% 11.45/2.01 thf(f1219,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semiring_bits(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f858])).
% 11.45/2.01 thf(f858,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))) | (semiring_bits(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f328])).
% 11.45/2.01 thf(f328,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((semiring_bits(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(fool_elimination,[],[f327])).
% 11.45/2.01 thf(f327,plain,(
% 11.45/2.01 ! [X0 : $tType] : (semiring_bits(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(rectify,[],[f187])).
% 11.45/2.01 thf(f187,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (semiring_bits(X0) => ! [X9 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),divide_divide(X0),X9),zero_zero(X0))))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_bits__div__by__0)).
% 11.45/2.01 thf(f2526,plain,(
% 11.45/2.01 spl41_49),
% 11.45/2.01 inference(avatar_split_clause,[],[f1218,f2524])).
% 11.45/2.01 thf(f1218,plain,(
% 11.45/2.01 ( ! [X0 : $tType] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) != $true) | (linord1659791738miring(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f857])).
% 11.45/2.01 thf(f857,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) != $true) | (linord1659791738miring(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f814])).
% 11.45/2.01 thf(f814,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linord1659791738miring(X0) = $true) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) != $true))),
% 11.45/2.01 inference(flattening,[],[f326])).
% 11.45/2.01 thf(f326,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((linord1659791738miring(X0) = $true) => ~(vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)) = $true))),
% 11.45/2.01 inference(fool_elimination,[],[f325])).
% 11.45/2.01 thf(f325,plain,(
% 11.45/2.01 ! [X0 : $tType] : (linord1659791738miring(X0) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)))),
% 11.45/2.01 inference(rectify,[],[f210])).
% 11.45/2.01 thf(f210,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (linord1659791738miring(X0) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),zero_zero(X0)),zero_zero(X0)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_less__numeral__extra_I3_J)).
% 11.45/2.01 thf(f2512,plain,(
% 11.45/2.01 spl41_48),
% 11.45/2.01 inference(avatar_split_clause,[],[f1359,f2510])).
% 11.45/2.01 thf(f1359,plain,(
% 11.45/2.01 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,suc,X0)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f594])).
% 11.45/2.01 thf(f594,plain,(
% 11.45/2.01 ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,suc,X0)))),
% 11.45/2.01 inference(fool_elimination,[],[f593])).
% 11.45/2.01 thf(f593,plain,(
% 11.45/2.01 ! [X0 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,suc,X0))),
% 11.45/2.01 inference(rectify,[],[f12])).
% 11.45/2.01 thf(f12,axiom,(
% 11.45/2.01 ! [X2 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,suc,X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__less__Suc)).
% 11.45/2.01 thf(f2506,plain,(
% 11.45/2.01 spl41_47),
% 11.45/2.01 inference(avatar_split_clause,[],[f1271,f2504])).
% 11.45/2.01 thf(f1271,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f920])).
% 11.45/2.01 thf(f920,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f424])).
% 11.45/2.01 thf(f424,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f423])).
% 11.45/2.01 thf(f423,plain,(
% 11.45/2.01 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))),
% 11.45/2.01 inference(rectify,[],[f222])).
% 11.45/2.01 thf(f222,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X16 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X16))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_zero__le)).
% 11.45/2.01 thf(f2502,plain,(
% 11.45/2.01 spl41_46),
% 11.45/2.01 inference(avatar_split_clause,[],[f1270,f2500])).
% 11.45/2.01 thf(f1270,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (canoni770627133id_add(X0) != $true)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f919])).
% 11.45/2.01 thf(f919,plain,(
% 11.45/2.01 ! [X0 : $tType] : (! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (canoni770627133id_add(X0) != $true))),
% 11.45/2.01 inference(ennf_transformation,[],[f815])).
% 11.45/2.01 thf(f815,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(flattening,[],[f422])).
% 11.45/2.01 thf(f422,plain,(
% 11.45/2.01 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0] : ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))))),
% 11.45/2.01 inference(fool_elimination,[],[f421])).
% 11.45/2.01 thf(f421,plain,(
% 11.45/2.01 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X1 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))),
% 11.45/2.01 inference(rectify,[],[f197])).
% 11.45/2.01 thf(f197,axiom,(
% 11.45/2.01 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X2 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),zero_zero(X0)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_not__less__zero)).
% 11.45/2.01 thf(f2498,plain,(
% 11.45/2.01 spl41_45),
% 11.45/2.01 inference(avatar_split_clause,[],[f1194,f2496])).
% 11.45/2.01 thf(f1194,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))) = X0)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f807])).
% 11.45/2.01 thf(f807,plain,(
% 11.45/2.01 ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(nat,nat,suc,zero_zero(nat))) = X0)),
% 11.45/2.01 inference(rectify,[],[f5])).
% 11.45/2.01 thf(f5,axiom,(
% 11.45/2.01 ! [X3 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X3),vAPP(nat,nat,suc,zero_zero(nat))) = X3)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_div__by__Suc__0)).
% 11.45/2.01 thf(f2491,plain,(
% 11.45/2.01 spl41_44),
% 11.45/2.01 inference(avatar_split_clause,[],[f1358,f2489])).
% 11.45/2.01 thf(f1358,plain,(
% 11.45/2.01 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X0)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f592])).
% 11.45/2.01 thf(f592,plain,(
% 11.45/2.01 ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X0)))),
% 11.45/2.01 inference(fool_elimination,[],[f591])).
% 11.45/2.01 thf(f591,plain,(
% 11.45/2.01 ! [X0 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,X0))),
% 11.45/2.01 inference(rectify,[],[f20])).
% 11.45/2.01 thf(f20,axiom,(
% 11.45/2.01 ! [X2 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),vAPP(nat,nat,suc,X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_lessI)).
% 11.45/2.01 thf(f2487,plain,(
% 11.45/2.01 spl41_43),
% 11.45/2.01 inference(avatar_split_clause,[],[f2243,f2484])).
% 11.45/2.01 thf(f2484,plain,(
% 11.45/2.01 spl41_43 <=> (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),zero_zero(nat)),zero_zero(nat)))),
% 11.45/2.01 introduced(avatar_definition,[new_symbols(naming,[spl41_43])])).
% 11.45/2.01 thf(f2243,plain,(
% 11.45/2.01 (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),zero_zero(nat)),zero_zero(nat)))),
% 11.45/2.01 inference(forward_demodulation,[],[f2242,f1193])).
% 11.45/2.01 thf(f1193,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f806])).
% 11.45/2.01 thf(f806,plain,(
% 11.45/2.01 ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X0))),
% 11.45/2.01 inference(rectify,[],[f81])).
% 11.45/2.01 thf(f81,axiom,(
% 11.45/2.01 ! [X2 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_mult__0)).
% 11.45/2.01 thf(f2242,plain,(
% 11.45/2.01 ( ! [X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X1)),zero_zero(nat)))) )),
% 11.45/2.01 inference(forward_demodulation,[],[f1514,f1193])).
% 11.45/2.01 thf(f1514,plain,(
% 11.45/2.01 ( ! [X2 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X2)))) )),
% 11.45/2.01 inference(equality_resolution,[],[f1438])).
% 11.45/2.01 thf(f1438,plain,(
% 11.45/2.01 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2))) | (zero_zero(nat) != X0)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1072])).
% 11.45/2.01 thf(f2482,plain,(
% 11.45/2.01 spl41_42 | ~spl41_18 | ~spl41_31),
% 11.45/2.01 inference(avatar_split_clause,[],[f2428,f2420,f2330,f2480])).
% 11.45/2.01 thf(f2428,plain,(
% 11.45/2.01 ( ! [X0 : $tType] : (($true = order(sTfun(X0,$o)))) ) | (~spl41_18 | ~spl41_31)),
% 11.45/2.01 inference(trivial_inequality_removal,[],[f2423])).
% 11.45/2.01 thf(f2423,plain,(
% 11.45/2.01 ( ! [X0 : $tType] : (($true != $true) | ($true = order(sTfun(X0,$o)))) ) | (~spl41_18 | ~spl41_31)),
% 11.45/2.01 inference(superposition,[],[f2421,f2332])).
% 11.45/2.01 thf(f2478,plain,(
% 11.45/2.01 spl41_41),
% 11.45/2.01 inference(avatar_split_clause,[],[f1425,f2476])).
% 11.45/2.01 thf(f1425,plain,(
% 11.45/2.01 ( ! [X0 : $tType,X1 : nat] : ((vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK23(X0),X1)) = X1)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1150])).
% 11.45/2.01 thf(f1150,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : nat] : (vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK23(X0),X1)) = X1)),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f832,f1149])).
% 11.45/2.01 thf(f1149,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : nat] : (? [X2 : list(X0)] : (vAPP(list(X0),nat,size_size(list(X0)),X2) = X1) => (vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK23(X0),X1)) = X1))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f832,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : nat] : ? [X2 : list(X0)] : (vAPP(list(X0),nat,size_size(list(X0)),X2) = X1)),
% 11.45/2.01 inference(rectify,[],[f204])).
% 11.45/2.01 thf(f204,axiom,(
% 11.45/2.01 ! [X0 : $tType,X2 : nat] : ? [X45 : list(X0)] : (vAPP(list(X0),nat,size_size(list(X0)),X45) = X2)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_Ex__list__of__length)).
% 11.45/2.01 thf(f2474,plain,(
% 11.45/2.01 spl41_40),
% 11.45/2.01 inference(avatar_split_clause,[],[f1193,f2472])).
% 11.45/2.01 thf(f2472,plain,(
% 11.45/2.01 spl41_40 <=> ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X0))),
% 11.45/2.01 introduced(avatar_definition,[new_symbols(naming,[spl41_40])])).
% 11.45/2.01 thf(f2470,plain,(
% 11.45/2.01 spl41_39),
% 11.45/2.01 inference(avatar_split_clause,[],[f1192,f2468])).
% 11.45/2.01 thf(f2468,plain,(
% 11.45/2.01 spl41_39 <=> ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),zero_zero(nat)))),
% 11.45/2.01 introduced(avatar_definition,[new_symbols(naming,[spl41_39])])).
% 11.45/2.01 thf(f1192,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f805])).
% 11.45/2.01 thf(f805,plain,(
% 11.45/2.01 ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),zero_zero(nat)))),
% 11.45/2.01 inference(rectify,[],[f23])).
% 11.45/2.01 thf(f23,axiom,(
% 11.45/2.01 ! [X3 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),zero_zero(nat)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_mult__0__right)).
% 11.45/2.01 thf(f2458,plain,(
% 11.45/2.01 spl41_38),
% 11.45/2.01 inference(avatar_split_clause,[],[f1356,f2456])).
% 11.45/2.01 thf(f1356,plain,(
% 11.45/2.01 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f588])).
% 11.45/2.01 thf(f588,plain,(
% 11.45/2.01 ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0))),
% 11.45/2.01 inference(fool_elimination,[],[f587])).
% 11.45/2.01 thf(f587,plain,(
% 11.45/2.01 ! [X0 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0)),
% 11.45/2.01 inference(rectify,[],[f216])).
% 11.45/2.01 thf(f216,axiom,(
% 11.45/2.01 ! [X2 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X2)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_le0)).
% 11.45/2.01 thf(f2454,plain,(
% 11.45/2.01 spl41_37),
% 11.45/2.01 inference(avatar_split_clause,[],[f1351,f2452])).
% 11.45/2.01 thf(f1351,plain,(
% 11.45/2.01 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f818])).
% 11.45/2.01 thf(f818,plain,(
% 11.45/2.01 ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))),
% 11.45/2.01 inference(flattening,[],[f578])).
% 11.45/2.01 thf(f578,plain,(
% 11.45/2.01 ! [X0 : nat] : ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))),
% 11.45/2.01 inference(fool_elimination,[],[f577])).
% 11.45/2.01 thf(f577,plain,(
% 11.45/2.01 ! [X0 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat))),
% 11.45/2.01 inference(rectify,[],[f59])).
% 11.45/2.01 thf(f59,axiom,(
% 11.45/2.01 ! [X2 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),zero_zero(nat))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__zeroE)).
% 11.45/2.01 thf(f2450,plain,(
% 11.45/2.01 spl41_36 | ~spl41_20 | ~spl41_31),
% 11.45/2.01 inference(avatar_split_clause,[],[f2427,f2420,f2340,f2448])).
% 11.45/2.01 thf(f2427,plain,(
% 11.45/2.01 ( ! [X0 : $tType] : (($true = order(sTfun(X0,nat)))) ) | (~spl41_20 | ~spl41_31)),
% 11.45/2.01 inference(trivial_inequality_removal,[],[f2424])).
% 11.45/2.01 thf(f2424,plain,(
% 11.45/2.01 ( ! [X0 : $tType] : (($true != $true) | ($true = order(sTfun(X0,nat)))) ) | (~spl41_20 | ~spl41_31)),
% 11.45/2.01 inference(superposition,[],[f2421,f2342])).
% 11.45/2.01 thf(f2446,plain,(
% 11.45/2.01 spl41_35),
% 11.45/2.01 inference(avatar_split_clause,[],[f1206,f2444])).
% 11.45/2.01 thf(f1206,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0) | (zero_zero(nat) = X0)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1113])).
% 11.45/2.01 thf(f1113,plain,(
% 11.45/2.01 ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0) | (zero_zero(nat) = X0))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f842,f1112])).
% 11.45/2.01 thf(f1112,plain,(
% 11.45/2.01 ! [X0 : nat] : (? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0) => (vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f842,plain,(
% 11.45/2.01 ! [X0 : nat] : (? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0) | (zero_zero(nat) = X0))),
% 11.45/2.01 inference(ennf_transformation,[],[f810])).
% 11.45/2.01 thf(f810,plain,(
% 11.45/2.01 ! [X0 : nat] : ((zero_zero(nat) != X0) => ? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0))),
% 11.45/2.01 inference(rectify,[],[f42])).
% 11.45/2.01 thf(f42,axiom,(
% 11.45/2.01 ! [X2 : nat] : ((zero_zero(nat) != X2) => ? [X23 : nat] : (vAPP(nat,nat,suc,X23) = X2))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_not0__implies__Suc)).
% 11.45/2.01 thf(f2442,plain,(
% 11.45/2.01 spl41_34),
% 11.45/2.01 inference(avatar_split_clause,[],[f1205,f2440])).
% 11.45/2.01 thf(f1205,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0) | (zero_zero(nat) = X0)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1111])).
% 11.45/2.01 thf(f1111,plain,(
% 11.45/2.01 ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0) | (zero_zero(nat) = X0))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f841,f1110])).
% 11.45/2.01 thf(f1110,plain,(
% 11.45/2.01 ! [X0 : nat] : (? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0) => (vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f841,plain,(
% 11.45/2.01 ! [X0 : nat] : (? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0) | (zero_zero(nat) = X0))),
% 11.45/2.01 inference(ennf_transformation,[],[f809])).
% 11.45/2.01 thf(f809,plain,(
% 11.45/2.01 ! [X0 : nat] : ((zero_zero(nat) != X0) => ~! [X1 : nat] : (vAPP(nat,nat,suc,X1) != X0))),
% 11.45/2.01 inference(rectify,[],[f206])).
% 11.45/2.01 thf(f206,axiom,(
% 11.45/2.01 ! [X16 : nat] : ((zero_zero(nat) != X16) => ~! [X19 : nat] : (vAPP(nat,nat,suc,X19) != X16))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_list__decode_Ocases)).
% 11.45/2.01 thf(f2438,plain,(
% 11.45/2.01 spl41_33),
% 11.45/2.01 inference(avatar_split_clause,[],[f1204,f2436])).
% 11.45/2.01 thf(f1204,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0) | (zero_zero(nat) = X0)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1109])).
% 11.45/2.01 thf(f1109,plain,(
% 11.45/2.01 ! [X0 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0) | (zero_zero(nat) = X0))),
% 11.45/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f840,f1108])).
% 11.45/2.01 thf(f1108,plain,(
% 11.45/2.01 ! [X0 : nat] : (? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0) => (vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0))),
% 11.45/2.01 introduced(choice_axiom,[])).
% 11.45/2.01 thf(f840,plain,(
% 11.45/2.01 ! [X0 : nat] : (? [X1 : nat] : (vAPP(nat,nat,suc,X1) = X0) | (zero_zero(nat) = X0))),
% 11.45/2.01 inference(ennf_transformation,[],[f808])).
% 11.45/2.01 thf(f808,plain,(
% 11.45/2.01 ! [X0 : nat] : ((zero_zero(nat) != X0) => ~! [X1 : nat] : (vAPP(nat,nat,suc,X1) != X0))),
% 11.45/2.01 inference(rectify,[],[f44])).
% 11.45/2.01 thf(f44,axiom,(
% 11.45/2.01 ! [X17 : nat] : ((zero_zero(nat) != X17) => ~! [X24 : nat] : (vAPP(nat,nat,suc,X24) != X17))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_old_Onat_Oexhaust)).
% 11.45/2.01 thf(f2432,plain,(
% 11.45/2.01 spl41_32),
% 11.45/2.01 inference(avatar_split_clause,[],[f1349,f2430])).
% 11.45/2.01 thf(f1349,plain,(
% 11.45/2.01 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f816])).
% 11.45/2.01 thf(f816,plain,(
% 11.45/2.01 ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 11.45/2.01 inference(flattening,[],[f574])).
% 11.45/2.01 thf(f574,plain,(
% 11.45/2.01 ! [X0 : nat] : ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 11.45/2.01 inference(fool_elimination,[],[f573])).
% 11.45/2.01 thf(f573,plain,(
% 11.45/2.01 ! [X0 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0)),
% 11.45/2.01 inference(rectify,[],[f39])).
% 11.45/2.01 thf(f39,axiom,(
% 11.45/2.01 ! [X2 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X2)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__not__refl)).
% 11.45/2.01 thf(f2422,plain,(
% 11.45/2.01 spl41_31),
% 11.45/2.01 inference(avatar_split_clause,[],[f1393,f2420])).
% 11.45/2.01 thf(f1393,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X0,X1))) | ($true != order(X1))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f1037])).
% 11.45/2.01 thf(f1037,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (($true = order(sTfun(X0,X1))) | ($true != order(X1)))),
% 11.45/2.01 inference(ennf_transformation,[],[f646])).
% 11.45/2.01 thf(f646,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (($true = order(X1)) => ($true = order(sTfun(X0,X1))))),
% 11.45/2.01 inference(fool_elimination,[],[f645])).
% 11.45/2.01 thf(f645,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : (order(X1) => order(sTfun(X0,X1)))),
% 11.45/2.01 inference(rectify,[],[f254])).
% 11.45/2.01 thf(f254,axiom,(
% 11.45/2.01 ! [X59 : $tType,X60 : $tType] : (order(X60) => order(sTfun(X59,X60)))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder)).
% 11.45/2.01 thf(f2418,plain,(
% 11.45/2.01 spl41_30),
% 11.45/2.01 inference(avatar_split_clause,[],[f1186,f2416])).
% 11.45/2.01 thf(f1186,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((zero_zero(nat) != vAPP(nat,nat,suc,X0))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f799])).
% 11.45/2.01 thf(f799,plain,(
% 11.45/2.01 ! [X0 : nat] : (zero_zero(nat) != vAPP(nat,nat,suc,X0))),
% 11.45/2.01 inference(rectify,[],[f54])).
% 11.45/2.01 thf(f54,axiom,(
% 11.45/2.01 ! [X7 : nat] : (zero_zero(nat) != vAPP(nat,nat,suc,X7))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_nat_Odistinct_I1_J)).
% 11.45/2.01 thf(f2412,plain,(
% 11.45/2.01 ~spl41_29),
% 11.45/2.01 inference(avatar_split_clause,[],[f1182,f2409])).
% 11.45/2.01 thf(f1182,plain,(
% 11.45/2.01 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs)) != $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f797])).
% 11.45/2.01 thf(f797,plain,(
% 11.45/2.01 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs)) != $true)),
% 11.45/2.01 inference(flattening,[],[f286])).
% 11.45/2.01 thf(f286,plain,(
% 11.45/2.01 ~(vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs)) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f285])).
% 11.45/2.01 thf(f285,plain,(
% 11.45/2.01 ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs))),
% 11.45/2.01 inference(rectify,[],[f282])).
% 11.45/2.01 thf(f282,negated_conjecture,(
% 11.45/2.01 ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs))),
% 11.45/2.01 inference(negated_conjecture,[],[f281])).
% 11.45/2.01 thf(f281,conjecture,(
% 11.45/2.01 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),n),k)),vAPP(list(a),nat,size_size(list(a)),xs))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 11.45/2.01 thf(f2407,plain,(
% 11.45/2.01 spl41_28),
% 11.45/2.01 inference(avatar_split_clause,[],[f1185,f2405])).
% 11.45/2.01 thf(f1185,plain,(
% 11.45/2.01 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,X0) != X0)) )),
% 11.45/2.01 inference(cnf_transformation,[],[f798])).
% 11.45/2.01 thf(f798,plain,(
% 11.45/2.01 ! [X0 : nat] : (vAPP(nat,nat,suc,X0) != X0)),
% 11.45/2.01 inference(rectify,[],[f30])).
% 11.45/2.01 thf(f30,axiom,(
% 11.45/2.01 ! [X2 : nat] : (vAPP(nat,nat,suc,X2) != X2)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_n__not__Suc__n)).
% 11.45/2.01 thf(f2375,plain,(
% 11.45/2.01 spl41_27),
% 11.45/2.01 inference(avatar_split_clause,[],[f1426,f2373])).
% 11.45/2.01 thf(f1426,plain,(
% 11.45/2.01 ( ! [X1 : $tType,X0 : $tType] : (($true = size(product_prod(X0,X1)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f696])).
% 11.45/2.01 thf(f696,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : ($true = size(product_prod(X0,X1)))),
% 11.45/2.01 inference(fool_elimination,[],[f695])).
% 11.45/2.01 thf(f695,plain,(
% 11.45/2.01 ! [X0 : $tType,X1 : $tType] : size(product_prod(X0,X1))),
% 11.45/2.01 inference(rectify,[],[f278])).
% 11.45/2.01 thf(f278,axiom,(
% 11.45/2.01 ! [X59 : $tType,X60 : $tType] : size(product_prod(X59,X60))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Nat_Osize_5)).
% 11.45/2.01 thf(f2371,plain,(
% 11.45/2.01 spl41_26),
% 11.45/2.01 inference(avatar_split_clause,[],[f284,f2369])).
% 11.45/2.01 thf(f284,plain,(
% 11.45/2.01 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 11.45/2.01 introduced(fool_axiom,[])).
% 11.45/2.01 thf(f2367,plain,(
% 11.45/2.01 spl41_25),
% 11.45/2.01 inference(avatar_split_clause,[],[f1355,f2365])).
% 11.45/2.01 thf(f1355,plain,(
% 11.45/2.01 ( ! [X0 : $tType] : (($true = size(list(X0)))) )),
% 11.45/2.01 inference(cnf_transformation,[],[f586])).
% 11.45/2.01 thf(f586,plain,(
% 11.45/2.01 ! [X0 : $tType] : ($true = size(list(X0)))),
% 11.45/2.01 inference(fool_elimination,[],[f585])).
% 11.45/2.01 thf(f585,plain,(
% 11.45/2.01 ! [X0 : $tType] : size(list(X0))),
% 11.45/2.01 inference(rectify,[],[f277])).
% 11.45/2.01 thf(f277,axiom,(
% 11.45/2.01 ! [X59 : $tType] : size(list(X59))),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_4)).
% 11.45/2.01 thf(f2363,plain,(
% 11.45/2.01 spl41_24),
% 11.45/2.01 inference(avatar_split_clause,[],[f1501,f2360])).
% 11.45/2.01 thf(f1501,plain,(
% 11.45/2.01 (linord20386208strict(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f796])).
% 11.45/2.01 thf(f796,plain,(
% 11.45/2.01 (linord20386208strict(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f795])).
% 11.45/2.01 thf(f795,plain,(
% 11.45/2.01 linord20386208strict(nat)),
% 11.45/2.01 inference(rectify,[],[f260])).
% 11.45/2.01 thf(f260,axiom,(
% 11.45/2.01 linord20386208strict(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semiring__strict)).
% 11.45/2.01 thf(f2358,plain,(
% 11.45/2.01 spl41_23),
% 11.45/2.01 inference(avatar_split_clause,[],[f1500,f2355])).
% 11.45/2.01 thf(f1500,plain,(
% 11.45/2.01 (canoni770627133id_add(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f794])).
% 11.45/2.01 thf(f794,plain,(
% 11.45/2.01 (canoni770627133id_add(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f793])).
% 11.45/2.01 thf(f793,plain,(
% 11.45/2.01 canoni770627133id_add(nat)),
% 11.45/2.01 inference(rectify,[],[f258])).
% 11.45/2.01 thf(f258,axiom,(
% 11.45/2.01 canoni770627133id_add(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add)).
% 11.45/2.01 thf(f2353,plain,(
% 11.45/2.01 spl41_22),
% 11.45/2.01 inference(avatar_split_clause,[],[f1499,f2350])).
% 11.45/2.01 thf(f1499,plain,(
% 11.45/2.01 (ordered_semiring_0(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f792])).
% 11.45/2.01 thf(f792,plain,(
% 11.45/2.01 (ordered_semiring_0(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f791])).
% 11.45/2.01 thf(f791,plain,(
% 11.45/2.01 ordered_semiring_0(nat)),
% 11.45/2.01 inference(rectify,[],[f263])).
% 11.45/2.01 thf(f263,axiom,(
% 11.45/2.01 ordered_semiring_0(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__semiring__0)).
% 11.45/2.01 thf(f2348,plain,(
% 11.45/2.01 spl41_21),
% 11.45/2.01 inference(avatar_split_clause,[],[f1498,f2345])).
% 11.45/2.01 thf(f1498,plain,(
% 11.45/2.01 (linorder(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f790])).
% 11.45/2.01 thf(f790,plain,(
% 11.45/2.01 (linorder(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f789])).
% 11.45/2.01 thf(f789,plain,(
% 11.45/2.01 linorder(nat)),
% 11.45/2.01 inference(rectify,[],[f270])).
% 11.45/2.01 thf(f270,axiom,(
% 11.45/2.01 linorder(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder)).
% 11.45/2.01 thf(f2343,plain,(
% 11.45/2.01 spl41_20),
% 11.45/2.01 inference(avatar_split_clause,[],[f1497,f2340])).
% 11.45/2.01 thf(f1497,plain,(
% 11.45/2.01 (order(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f788])).
% 11.45/2.01 thf(f788,plain,(
% 11.45/2.01 (order(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f787])).
% 11.45/2.01 thf(f787,plain,(
% 11.45/2.01 order(nat)),
% 11.45/2.01 inference(rectify,[],[f272])).
% 11.45/2.01 thf(f272,axiom,(
% 11.45/2.01 order(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_1)).
% 11.45/2.01 thf(f2338,plain,(
% 11.45/2.01 spl41_19),
% 11.45/2.01 inference(avatar_split_clause,[],[f1496,f2335])).
% 11.45/2.01 thf(f1496,plain,(
% 11.45/2.01 (linorder($o) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f786])).
% 11.45/2.01 thf(f786,plain,(
% 11.45/2.01 (linorder($o) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f785])).
% 11.45/2.01 thf(f785,plain,(
% 11.45/2.01 linorder($o)),
% 11.45/2.01 inference(rectify,[],[f275])).
% 11.45/2.01 thf(f275,axiom,(
% 11.45/2.01 linorder($o)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_2)).
% 11.45/2.01 thf(f2333,plain,(
% 11.45/2.01 spl41_18),
% 11.45/2.01 inference(avatar_split_clause,[],[f1495,f2330])).
% 11.45/2.01 thf(f1495,plain,(
% 11.45/2.01 (order($o) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f784])).
% 11.45/2.01 thf(f784,plain,(
% 11.45/2.01 (order($o) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f783])).
% 11.45/2.01 thf(f783,plain,(
% 11.45/2.01 order($o)),
% 11.45/2.01 inference(rectify,[],[f276])).
% 11.45/2.01 thf(f276,axiom,(
% 11.45/2.01 order($o)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_3)).
% 11.45/2.01 thf(f2328,plain,(
% 11.45/2.01 spl41_17),
% 11.45/2.01 inference(avatar_split_clause,[],[f1494,f2325])).
% 11.45/2.01 thf(f1494,plain,(
% 11.45/2.01 (semidom_divide(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f782])).
% 11.45/2.01 thf(f782,plain,(
% 11.45/2.01 (semidom_divide(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f781])).
% 11.45/2.01 thf(f781,plain,(
% 11.45/2.01 semidom_divide(nat)),
% 11.45/2.01 inference(rectify,[],[f267])).
% 11.45/2.01 thf(f267,axiom,(
% 11.45/2.01 semidom_divide(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__divide)).
% 11.45/2.01 thf(f2323,plain,(
% 11.45/2.01 spl41_16),
% 11.45/2.01 inference(avatar_split_clause,[],[f1493,f2320])).
% 11.45/2.01 thf(f1493,plain,(
% 11.45/2.01 (ordered_semiring(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f780])).
% 11.45/2.01 thf(f780,plain,(
% 11.45/2.01 (ordered_semiring(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f779])).
% 11.45/2.01 thf(f779,plain,(
% 11.45/2.01 ordered_semiring(nat)),
% 11.45/2.01 inference(rectify,[],[f265])).
% 11.45/2.01 thf(f265,axiom,(
% 11.45/2.01 ordered_semiring(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__semiring)).
% 11.45/2.01 thf(f2318,plain,(
% 11.45/2.01 spl41_15),
% 11.45/2.01 inference(avatar_split_clause,[],[f1492,f2315])).
% 11.45/2.01 thf(f1492,plain,(
% 11.45/2.01 (semiri1923998003cancel(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f778])).
% 11.45/2.01 thf(f778,plain,(
% 11.45/2.01 (semiri1923998003cancel(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f777])).
% 11.45/2.01 thf(f777,plain,(
% 11.45/2.01 semiri1923998003cancel(nat)),
% 11.45/2.01 inference(rectify,[],[f256])).
% 11.45/2.01 thf(f256,axiom,(
% 11.45/2.01 semiri1923998003cancel(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel)).
% 11.45/2.01 thf(f2313,plain,(
% 11.45/2.01 spl41_14),
% 11.45/2.01 inference(avatar_split_clause,[],[f1491,f2310])).
% 11.45/2.01 thf(f1491,plain,(
% 11.45/2.01 (euclid191655569cancel(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f776])).
% 11.45/2.01 thf(f776,plain,(
% 11.45/2.01 (euclid191655569cancel(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f775])).
% 11.45/2.01 thf(f775,plain,(
% 11.45/2.01 euclid191655569cancel(nat)),
% 11.45/2.01 inference(rectify,[],[f255])).
% 11.45/2.01 thf(f255,axiom,(
% 11.45/2.01 euclid191655569cancel(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Euclidean__Division_Oeuclidean__semiring__cancel)).
% 11.45/2.01 thf(f2308,plain,(
% 11.45/2.01 spl41_13),
% 11.45/2.01 inference(avatar_split_clause,[],[f1490,f2305])).
% 11.45/2.01 thf(f1490,plain,(
% 11.45/2.01 (semiri1193490041visors(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f774])).
% 11.45/2.01 thf(f774,plain,(
% 11.45/2.01 (semiri1193490041visors(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f773])).
% 11.45/2.01 thf(f773,plain,(
% 11.45/2.01 semiri1193490041visors(nat)),
% 11.45/2.01 inference(rectify,[],[f261])).
% 11.45/2.01 thf(f261,axiom,(
% 11.45/2.01 semiri1193490041visors(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors)).
% 11.45/2.01 thf(f2303,plain,(
% 11.45/2.01 spl41_12),
% 11.45/2.01 inference(avatar_split_clause,[],[f1489,f2300])).
% 11.45/2.01 thf(f1489,plain,(
% 11.45/2.01 (ab_semigroup_mult(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f772])).
% 11.45/2.01 thf(f772,plain,(
% 11.45/2.01 (ab_semigroup_mult(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f771])).
% 11.45/2.01 thf(f771,plain,(
% 11.45/2.01 ab_semigroup_mult(nat)),
% 11.45/2.01 inference(rectify,[],[f264])).
% 11.45/2.01 thf(f264,axiom,(
% 11.45/2.01 ab_semigroup_mult(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult)).
% 11.45/2.01 thf(f2298,plain,(
% 11.45/2.01 spl41_11),
% 11.45/2.01 inference(avatar_split_clause,[],[f1488,f2295])).
% 11.45/2.01 thf(f1488,plain,(
% 11.45/2.01 (mult_zero(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f770])).
% 11.45/2.01 thf(f770,plain,(
% 11.45/2.01 (mult_zero(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f769])).
% 11.45/2.01 thf(f769,plain,(
% 11.45/2.01 mult_zero(nat)),
% 11.45/2.01 inference(rectify,[],[f271])).
% 11.45/2.01 thf(f271,axiom,(
% 11.45/2.01 mult_zero(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Omult__zero)).
% 11.45/2.01 thf(f2293,plain,(
% 11.45/2.01 spl41_10),
% 11.45/2.01 inference(avatar_split_clause,[],[f1487,f2290])).
% 11.45/2.01 thf(f1487,plain,(
% 11.45/2.01 (size(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f768])).
% 11.45/2.01 thf(f768,plain,(
% 11.45/2.01 (size(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f767])).
% 11.45/2.01 thf(f767,plain,(
% 11.45/2.01 size(nat)),
% 11.45/2.01 inference(rectify,[],[f274])).
% 11.45/2.01 thf(f274,axiom,(
% 11.45/2.01 size(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize)).
% 11.45/2.01 thf(f2288,plain,(
% 11.45/2.01 spl41_9),
% 11.45/2.01 inference(avatar_split_clause,[],[f1486,f2285])).
% 11.45/2.01 thf(f1486,plain,(
% 11.45/2.01 (wellorder(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f766])).
% 11.45/2.01 thf(f766,plain,(
% 11.45/2.01 (wellorder(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f765])).
% 11.45/2.01 thf(f765,plain,(
% 11.45/2.01 wellorder(nat)),
% 11.45/2.01 inference(rectify,[],[f269])).
% 11.45/2.01 thf(f269,axiom,(
% 11.45/2.01 wellorder(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder)).
% 11.45/2.01 thf(f2283,plain,(
% 11.45/2.01 spl41_8),
% 11.45/2.01 inference(avatar_split_clause,[],[f1485,f2280])).
% 11.45/2.01 thf(f1485,plain,(
% 11.45/2.01 (semiring_bits(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f764])).
% 11.45/2.01 thf(f764,plain,(
% 11.45/2.01 (semiring_bits(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f763])).
% 11.45/2.01 thf(f763,plain,(
% 11.45/2.01 semiring_bits(nat)),
% 11.45/2.01 inference(rectify,[],[f268])).
% 11.45/2.01 thf(f268,axiom,(
% 11.45/2.01 semiring_bits(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Parity_Osemiring__bits)).
% 11.45/2.01 thf(f2278,plain,(
% 11.45/2.01 spl41_7),
% 11.45/2.01 inference(avatar_split_clause,[],[f1484,f2275])).
% 11.45/2.01 thf(f1484,plain,(
% 11.45/2.01 (linord1659791738miring(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f762])).
% 11.45/2.01 thf(f762,plain,(
% 11.45/2.01 (linord1659791738miring(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f761])).
% 11.45/2.01 thf(f761,plain,(
% 11.45/2.01 linord1659791738miring(nat)),
% 11.45/2.01 inference(rectify,[],[f259])).
% 11.45/2.01 thf(f259,axiom,(
% 11.45/2.01 linord1659791738miring(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring)).
% 11.45/2.01 thf(f2273,plain,(
% 11.45/2.01 spl41_6),
% 11.45/2.01 inference(avatar_split_clause,[],[f1483,f2270])).
% 11.45/2.01 thf(f1483,plain,(
% 11.45/2.01 (zero(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f760])).
% 11.45/2.01 thf(f760,plain,(
% 11.45/2.01 (zero(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f759])).
% 11.45/2.01 thf(f759,plain,(
% 11.45/2.01 zero(nat)),
% 11.45/2.01 inference(rectify,[],[f273])).
% 11.45/2.01 thf(f273,axiom,(
% 11.45/2.01 zero(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero)).
% 11.45/2.01 thf(f2268,plain,(
% 11.45/2.01 spl41_5),
% 11.45/2.01 inference(avatar_split_clause,[],[f1482,f2265])).
% 11.45/2.01 thf(f1482,plain,(
% 11.45/2.01 (semigroup_mult(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f758])).
% 11.45/2.01 thf(f758,plain,(
% 11.45/2.01 (semigroup_mult(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f757])).
% 11.45/2.01 thf(f757,plain,(
% 11.45/2.01 semigroup_mult(nat)),
% 11.45/2.01 inference(rectify,[],[f266])).
% 11.45/2.01 thf(f266,axiom,(
% 11.45/2.01 semigroup_mult(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult)).
% 11.45/2.01 thf(f2263,plain,(
% 11.45/2.01 spl41_4),
% 11.45/2.01 inference(avatar_split_clause,[],[f1481,f2260])).
% 11.45/2.01 thf(f1481,plain,(
% 11.45/2.01 (ordere1490568538miring(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f756])).
% 11.45/2.01 thf(f756,plain,(
% 11.45/2.01 (ordere1490568538miring(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f755])).
% 11.45/2.01 thf(f755,plain,(
% 11.45/2.01 ordere1490568538miring(nat)),
% 11.45/2.01 inference(rectify,[],[f262])).
% 11.45/2.01 thf(f262,axiom,(
% 11.45/2.01 ordere1490568538miring(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__comm__semiring)).
% 11.45/2.01 thf(f2258,plain,(
% 11.45/2.01 spl41_3),
% 11.45/2.01 inference(avatar_split_clause,[],[f1480,f2255])).
% 11.45/2.01 thf(f1480,plain,(
% 11.45/2.01 (linord893533164strict(nat) = $true)),
% 11.45/2.01 inference(cnf_transformation,[],[f754])).
% 11.45/2.01 thf(f754,plain,(
% 11.45/2.01 (linord893533164strict(nat) = $true)),
% 11.45/2.01 inference(fool_elimination,[],[f753])).
% 11.45/2.01 thf(f753,plain,(
% 11.45/2.01 linord893533164strict(nat)),
% 11.45/2.01 inference(rectify,[],[f257])).
% 11.45/2.01 thf(f257,axiom,(
% 11.45/2.01 linord893533164strict(nat)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict)).
% 11.45/2.01 thf(f2253,plain,(
% 11.45/2.01 ~spl41_2),
% 11.45/2.01 inference(avatar_split_clause,[],[f1183,f2250])).
% 11.45/2.01 thf(f1183,plain,(
% 11.45/2.01 (zero_zero(nat) != k)),
% 11.45/2.01 inference(cnf_transformation,[],[f280])).
% 11.45/2.01 thf(f280,axiom,(
% 11.45/2.01 (zero_zero(nat) != k)),
% 11.45/2.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 11.45/2.01 thf(f2248,plain,(
% 11.45/2.01 ~spl41_1),
% 11.45/2.01 inference(avatar_split_clause,[],[f283,f2245])).
% 11.45/2.01 thf(f283,plain,(
% 11.45/2.01 ($true != $false)),
% 11.45/2.01 introduced(fool_axiom,[])).
% 11.45/2.01 % SZS output end Proof for theBenchmark
% 11.45/2.01 % (26935)------------------------------
% 11.45/2.01 % (26935)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 11.45/2.01 % (26935)Termination reason: Refutation
% 11.45/2.01
% 11.45/2.01 % (26935)Memory used [KB]: 16387
% 11.45/2.01 % (26935)Time elapsed: 1.597 s
% 11.45/2.01 % (26935)Instructions burned: 5917 (million)
% 11.45/2.01 % (26920)Success in time 1.618 s
%------------------------------------------------------------------------------