TSTP Solution File: SWW470_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW470_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 : Tue Apr 30 17:33:19 EDT 2024
% Result : Theorem 4.58s 1.02s
% Output : Refutation 4.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW470_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 03:04:11 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (8371)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (8374)WARNING: value z3 for option sas not known
% 0.14/0.39 % (8375)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (8372)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (8376)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.39 % (8377)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39 % (8373)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (8374)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39 % (8378)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)
% 0.14/0.40 % (8378)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.41 % Exception at run slice level
% 0.14/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.41 % Exception at run slice level
% 0.14/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.41 % Exception at run slice level
% 0.14/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.42 % (8379)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.42 % (8380)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)
% 0.14/0.42 % (8381)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)
% 0.14/0.43 % (8379)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.43 % (8380)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.43 % Exception at run slice level
% 0.14/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.45 % (8382)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)
% 4.17/0.99 % (8376)First to succeed.
% 4.58/1.02 % (8376)Refutation found. Thanks to Tanya!
% 4.58/1.02 % SZS status Theorem for theBenchmark
% 4.58/1.02 % SZS output start Proof for theBenchmark
% 4.58/1.02 tff(type_def_5, type, a: $tType).
% 4.58/1.02 tff(type_def_6, type, com: $tType).
% 4.58/1.02 tff(type_def_7, type, state: $tType).
% 4.58/1.02 tff(type_def_8, type, bool: $tType).
% 4.58/1.02 tff(type_def_9, type, hoare_28830079triple: $tType > $tType).
% 4.58/1.02 tff(type_def_10, type, fun: ($tType * $tType) > $tType).
% 4.58/1.02 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,X1)) > fun(fun(X2,X0),fun(X2,X1)))).
% 4.58/1.02 tff(func_def_1, type, combc: !>[X0: $tType, X1: $tType, X2: $tType]:(fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))))).
% 4.58/1.02 tff(func_def_2, type, combk: !>[X0: $tType, X1: $tType]:((X0) > fun(X1,X0))).
% 4.58/1.02 tff(func_def_3, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:(fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))))).
% 4.58/1.02 tff(func_def_4, type, skip: com).
% 4.58/1.02 tff(func_def_5, type, semi: (com * com) > com).
% 4.58/1.02 tff(func_def_6, type, finite_fold1: !>[X0: $tType]:((fun(X0,fun(X0,X0))) > fun(fun(X0,bool),X0))).
% 4.58/1.02 tff(func_def_7, type, finite_fold1Set: !>[X0: $tType]:((fun(X0,fun(X0,X0)) * fun(X0,bool)) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_8, type, the: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_9, type, hoare_1841697145triple: !>[X0: $tType]:((fun(X0,fun(state,bool)) * com * fun(X0,fun(state,bool))) > hoare_28830079triple(X0))).
% 4.58/1.02 tff(func_def_10, type, hoare_376461865e_case: !>[X0: $tType, X1: $tType]:((fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0)) > X1)).
% 4.58/1.02 tff(func_def_11, type, hoare_678420151le_rec: !>[X0: $tType, X1: $tType]:((fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0)) > X1)).
% 4.58/1.02 tff(func_def_12, type, bot_bot: !>[X0: $tType]:(X0)).
% 4.58/1.02 tff(func_def_13, type, collect: !>[X0: $tType]:((fun(X0,bool)) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_14, type, insert: !>[X0: $tType]:(fun(X0,fun(fun(X0,bool),fun(X0,bool))))).
% 4.58/1.02 tff(func_def_15, type, the_elem: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_16, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 4.58/1.02 tff(func_def_17, type, fFalse: bool).
% 4.58/1.02 tff(func_def_18, type, fNot: fun(bool,bool)).
% 4.58/1.02 tff(func_def_19, type, fTrue: bool).
% 4.58/1.02 tff(func_def_20, type, fconj: fun(bool,fun(bool,bool))).
% 4.58/1.02 tff(func_def_21, type, fdisj: fun(bool,fun(bool,bool))).
% 4.58/1.02 tff(func_def_22, type, fequal: !>[X0: $tType]:(fun(X0,fun(X0,bool)))).
% 4.58/1.02 tff(func_def_23, type, fimplies: fun(bool,fun(bool,bool))).
% 4.58/1.02 tff(func_def_24, type, member: !>[X0: $tType]:(fun(X0,fun(fun(X0,bool),bool)))).
% 4.58/1.02 tff(func_def_25, type, g: fun(hoare_28830079triple(a),bool)).
% 4.58/1.02 tff(func_def_26, type, p: fun(a,fun(state,bool))).
% 4.58/1.02 tff(func_def_27, type, b: fun(state,bool)).
% 4.58/1.02 tff(func_def_28, type, c: com).
% 4.58/1.02 tff(func_def_29, type, sK4: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_30, type, sK5: !>[X0: $tType]:((fun(X0,bool) * X0) > X0)).
% 4.58/1.02 tff(func_def_31, type, sK6: !>[X0: $tType]:((fun(X0,bool)) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_32, type, sK7: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_33, type, sK8: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_34, type, sK9: !>[X0: $tType]:((fun(X0,bool)) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_35, type, sK10: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_36, type, sK11: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_37, type, sK12: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_38, type, sK13: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_39, type, sK14: !>[X0: $tType]:((hoare_28830079triple(X0)) > fun(X0,fun(state,bool)))).
% 4.58/1.02 tff(func_def_40, type, sK15: !>[X0: $tType]:((hoare_28830079triple(X0)) > com)).
% 4.58/1.02 tff(func_def_41, type, sK16: !>[X0: $tType]:((hoare_28830079triple(X0)) > fun(X0,fun(state,bool)))).
% 4.58/1.02 tff(func_def_42, type, sK17: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > X0)).
% 4.58/1.02 tff(func_def_43, type, sK18: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_44, type, sK19: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > X0)).
% 4.58/1.02 tff(func_def_45, type, sK20: !>[X0: $tType]:((fun(X0,fun(X0,X0)) * fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_46, type, sK21: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > X0)).
% 4.58/1.02 tff(func_def_47, type, sK22: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_48, type, sK23: !>[X0: $tType]:((X0 * fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_49, type, sK24: !>[X0: $tType]:((X0 * fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_50, type, sK25: !>[X0: $tType]:((fun(X0,bool) * X0) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_51, type, sK26: !>[X0: $tType]:((fun(X0,bool) * X0) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_52, type, sK27: !>[X0: $tType]:((fun(X0,bool) * X0) > X0)).
% 4.58/1.02 tff(func_def_53, type, sK28: !>[X0: $tType]:((fun(X0,bool) * fun(X0,bool)) > X0)).
% 4.58/1.02 tff(func_def_54, type, sK29: !>[X0: $tType]:((fun(X0,bool) * X0) > X0)).
% 4.58/1.02 tff(func_def_55, type, sK30: !>[X0: $tType, X1: $tType]:((fun(X1,X0) * fun(X1,X0)) > X1)).
% 4.58/1.02 tff(func_def_56, type, sK31: !>[X0: $tType]:((X0 * fun(X0,bool) * fun(X0,fun(X0,X0))) > X0)).
% 4.58/1.02 tff(func_def_57, type, sK32: !>[X0: $tType]:((X0 * fun(X0,bool) * fun(X0,fun(X0,X0))) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_58, type, sK33: !>[X0: $tType]:((X0 * fun(X0,bool) * fun(X0,fun(X0,X0))) > X0)).
% 4.58/1.02 tff(func_def_59, type, sK34: !>[X0: $tType, X1: $tType]:((X1 * fun(X0,fun(X1,X1)) * fun(X0,bool)) > X1)).
% 4.58/1.02 tff(func_def_60, type, sK35: !>[X0: $tType]:((X0 * fun(X0,bool) * X0 * fun(X0,bool)) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_61, type, sK36: !>[X0: $tType]:((X0 * fun(X0,bool) * X0 * fun(X0,fun(X0,X0))) > X0)).
% 4.58/1.02 tff(func_def_62, type, sK37: !>[X0: $tType]:((X0 * fun(X0,bool) * X0 * fun(X0,fun(X0,X0))) > fun(X0,bool))).
% 4.58/1.02 tff(func_def_63, type, sK38: !>[X0: $tType]:((fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool))) > X0)).
% 4.58/1.02 tff(func_def_64, type, sK39: !>[X0: $tType]:((fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool))) > state)).
% 4.58/1.02 tff(func_def_65, type, sK40: !>[X0: $tType]:((fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool))) > X0)).
% 4.58/1.02 tff(func_def_66, type, sK41: !>[X0: $tType]:((fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool))) > state)).
% 4.58/1.02 tff(func_def_67, type, sK42: !>[X0: $tType]:((fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool))) > state)).
% 4.58/1.02 tff(func_def_68, type, sK43: !>[X0: $tType]:((fun(X0,fun(state,bool)) * fun(X0,fun(state,bool))) > X0)).
% 4.58/1.02 tff(func_def_69, type, sK44: !>[X0: $tType]:((fun(X0,fun(state,bool)) * fun(X0,fun(state,bool))) > state)).
% 4.58/1.02 tff(func_def_70, type, sK45: !>[X0: $tType]:((fun(X0,fun(state,bool)) * fun(X0,fun(state,bool))) > X0)).
% 4.58/1.02 tff(func_def_71, type, sK46: !>[X0: $tType]:((fun(X0,fun(state,bool)) * fun(X0,fun(state,bool))) > state)).
% 4.58/1.02 tff(func_def_72, type, sK47: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(X0,X0)) * X0 * fun(X1,bool)) > X1)).
% 4.58/1.02 tff(func_def_73, type, sK48: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(X0,X0)) * X0 * fun(X1,bool)) > fun(X1,bool))).
% 4.58/1.02 tff(func_def_74, type, sK49: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(X0,X0)) * X0 * fun(X1,bool)) > X0)).
% 4.58/1.02 tff(func_def_75, type, sK50: !>[X0: $tType]:((fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool))) > X0)).
% 4.58/1.02 tff(func_def_76, type, sK51: !>[X0: $tType]:((fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool))) > state)).
% 4.58/1.02 tff(func_def_77, type, sK52: !>[X0: $tType]:((fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool))) > state)).
% 4.58/1.02 tff(pred_def_1, type, bot: !>[X0: $tType]:($o)).
% 4.58/1.02 tff(pred_def_2, type, finite_finite: !>[X0: $tType]:($o)).
% 4.58/1.02 tff(pred_def_3, type, finite_finite1: !>[X0: $tType]:((fun(X0,bool)) > $o)).
% 4.58/1.02 tff(pred_def_4, type, finite_fold_graph: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X1)) * X1 * fun(X0,bool) * X1) > $o)).
% 4.58/1.02 tff(pred_def_5, type, finite_folding_one: !>[X0: $tType]:((fun(X0,fun(X0,X0)) * fun(fun(X0,bool),X0)) > $o)).
% 4.58/1.02 tff(pred_def_6, type, finite2073411215e_idem: !>[X0: $tType]:((fun(X0,fun(X0,X0)) * fun(fun(X0,bool),X0)) > $o)).
% 4.58/1.02 tff(pred_def_7, type, hoare_992312373derivs: !>[X0: $tType]:((fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool)) > $o)).
% 4.58/1.02 tff(pred_def_8, type, pp: bool > $o).
% 4.58/1.02 tff(pred_def_9, type, sP0: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > $o)).
% 4.58/1.02 tff(pred_def_10, type, sP1: !>[X0: $tType]:((X0 * fun(X0,bool) * X0 * fun(X0,bool)) > $o)).
% 4.58/1.02 tff(pred_def_11, type, sP2: !>[X0: $tType]:((X0 * X0 * X0 * X0) > $o)).
% 4.58/1.02 tff(pred_def_12, type, sP3: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(X0,X0)) * X0 * fun(X1,bool)) > $o)).
% 4.58/1.02 tff(f10991,plain,(
% 4.58/1.02 $false),
% 4.58/1.02 inference(avatar_sat_refutation,[],[f755,f760,f765,f770,f774,f778,f782,f786,f790,f794,f798,f802,f809,f813,f817,f821,f825,f829,f833,f842,f846,f850,f854,f864,f869,f873,f877,f881,f885,f889,f893,f909,f914,f922,f926,f931,f935,f939,f944,f952,f961,f970,f974,f978,f982,f986,f990,f994,f998,f1002,f1006,f1021,f1028,f1033,f1042,f1046,f1050,f1054,f1059,f1063,f1067,f1071,f1075,f1080,f1085,f1099,f1112,f1116,f1151,f1155,f1162,f1166,f1170,f1178,f1182,f1186,f1190,f1393,f1398,f1402,f1406,f1410,f1450,f1464,f1469,f1475,f1479,f1484,f1488,f1492,f1496,f1543,f1616,f1620,f1636,f1660,f1664,f1668,f1680,f1684,f1723,f1734,f1738,f1743,f1748,f1753,f1758,f1763,f1767,f1794,f1798,f1802,f1806,f1810,f1889,f1920,f1936,f1941,f1945,f1949,f1989,f1993,f1997,f2025,f2030,f2034,f2038,f2042,f2172,f2176,f2180,f2184,f2189,f2240,f2256,f2261,f2265,f2269,f2273,f2277,f2317,f2321,f2341,f2345,f2357,f2398,f2403,f2408,f2412,f2448,f2453,f2460,f2469,f2473,f2523,f2527,f2568,f2573,f2577,f2594,f2598,f2642,f2646,f2704,f2786,f2790,f2794,f2798,f2802,f2806,f2822,f2830,f2835,f3035,f3066,f3071,f3075,f3127,f3131,f3136,f3140,f3144,f3204,f3230,f3234,f3269,f3273,f3305,f3309,f3313,f3346,f3404,f3408,f3438,f3500,f3504,f3534,f3586,f3594,f3602,f3608,f3624,f3628,f3632,f3636,f3729,f3747,f3751,f3780,f3785,f3803,f3809,f3815,f3831,f3836,f3840,f3847,f3869,f3874,f3880,f3902,f3909,f3949,f3955,f4010,f4021,f4041,f4055,f4059,f4064,f4073,f4077,f4081,f4173,f4225,f4229,f4253,f4257,f4261,f4266,f4304,f4308,f4312,f4316,f4320,f4325,f4329,f4333,f4337,f4341,f4345,f4349,f4360,f4619,f4624,f4628,f4632,f4650,f4654,f4668,f4732,f4736,f4741,f4765,f4773,f4828,f4980,f4984,f4988,f4999,f5033,f5037,f5062,f5066,f5073,f5113,f5188,f5192,f5196,f5200,f5204,f5208,f5212,f5216,f5220,f5384,f5418,f5422,f5426,f5434,f5455,f5488,f5568,f5592,f5596,f5600,f5604,f5608,f5624,f5628,f5632,f5636,f5640,f6099,f6103,f6107,f6111,f6115,f6322,f6326,f6330,f6334,f6338,f6342,f6346,f6382,f6689,f6693,f6700,f6744,f6749,f6809,f6925,f6929,f6933,f6973,f6974,f6986,f6990,f6995,f6999,f7003,f7007,f7011,f7015,f7194,f7513,f7517,f7571,f7575,f7579,f7583,f7587,f7689,f7693,f7697,f7701,f7705,f7709,f7713,f7717,f7721,f7739,f8032,f8036,f8040,f8067,f8071,f8075,f8079,f8083,f8087,f8091,f8095,f8142,f8492,f8515,f8519,f8523,f8527,f8531,f8986,f9041,f9047,f9051,f9055,f9059,f9063,f9067,f9299,f9303,f9307,f9311,f9315,f9602,f9606,f9610,f9614,f9999,f10089,f10093,f10097,f10101,f10105,f10109,f10336,f10340,f10344,f10348,f10352,f10357,f10361,f10365,f10369,f10373,f10377,f10381,f10385,f10389,f10393,f10397,f10411,f10415,f10419,f10423,f10427,f10565,f10990])).
% 4.58/1.02 tff(f10990,plain,(
% 4.58/1.02 spl53_1 | ~spl53_20 | spl53_153 | ~spl53_409),
% 4.58/1.02 inference(avatar_split_clause,[],[f10677,f10367,f2457,f840,f752])).
% 4.58/1.02 tff(f752,plain,(
% 4.58/1.02 spl53_1 <=> pp(fFalse)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_1])])).
% 4.58/1.02 tff(f840,plain,(
% 4.58/1.02 spl53_20 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : X0] : aa(X0,X1,combk(X1,X0,X3),X2) = X3),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_20])])).
% 4.58/1.02 tff(f2457,plain,(
% 4.58/1.02 spl53_153 <=> hoare_992312373derivs(a,g,aa(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b)))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_153])])).
% 4.58/1.02 tff(f10367,plain,(
% 4.58/1.02 spl53_409 <=> ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X3 : com,X1 : fun(state,bool)] : (pp(aa(state,bool,X1,sK39(X0,X2,X3,X4,combk(fun(state,bool),X0,X1)))) | hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,X1),X3,X2))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_409])])).
% 4.58/1.02 tff(f10677,plain,(
% 4.58/1.02 pp(fFalse) | (~spl53_20 | spl53_153 | ~spl53_409)),
% 4.58/1.02 inference(forward_demodulation,[],[f10657,f841])).
% 4.58/1.02 tff(f841,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (aa(X0,X1,combk(X1,X0,X3),X2) = X3) ) | ~spl53_20),
% 4.58/1.02 inference(avatar_component_clause,[],[f840])).
% 4.58/1.02 tff(f10657,plain,(
% 4.58/1.02 pp(aa(state,bool,combk(bool,state,fFalse),sK39(a,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b)),c,g,combk(fun(state,bool),a,combk(bool,state,fFalse))))) | (spl53_153 | ~spl53_409)),
% 4.58/1.02 inference(resolution,[],[f10368,f2459])).
% 4.58/1.02 tff(f2459,plain,(
% 4.58/1.02 ~hoare_992312373derivs(a,g,aa(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b))))) | spl53_153),
% 4.58/1.02 inference(avatar_component_clause,[],[f2457])).
% 4.58/1.02 tff(f10368,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(state,bool),X4 : fun(hoare_28830079triple(X0),bool)] : (pp(aa(state,bool,X1,sK39(X0,X2,X3,X4,combk(fun(state,bool),X0,X1)))) | hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,X1),X3,X2)))) ) | ~spl53_409),
% 4.58/1.02 inference(avatar_component_clause,[],[f10367])).
% 4.58/1.02 tff(f10565,plain,(
% 4.58/1.02 spl53_24 | ~spl53_422 | ~spl53_320),
% 4.58/1.02 inference(avatar_split_clause,[],[f9592,f6380,f10562,f858])).
% 4.58/1.02 tff(f858,plain,(
% 4.58/1.02 spl53_24 <=> ! [X0 : bool] : fTrue = X0),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_24])])).
% 4.58/1.02 tff(f10562,plain,(
% 4.58/1.02 spl53_422 <=> fTrue = the(bool,fNot)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_422])])).
% 4.58/1.02 tff(f6380,plain,(
% 4.58/1.02 spl53_320 <=> ! [X0 : bool] : (the(bool,fNot) = X0 | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_320])])).
% 4.58/1.02 tff(f9592,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (fTrue != the(bool,fNot) | fTrue = X0) ) | ~spl53_320),
% 4.58/1.02 inference(equality_factoring,[],[f6381])).
% 4.58/1.02 tff(f6381,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (the(bool,fNot) = X0 | fTrue = X0) ) | ~spl53_320),
% 4.58/1.02 inference(avatar_component_clause,[],[f6380])).
% 4.58/1.02 tff(f10427,plain,(
% 4.58/1.02 spl53_421 | ~spl53_56 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2763,f2702,f1040,f10425])).
% 4.58/1.02 tff(f10425,plain,(
% 4.58/1.02 spl53_421 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0)) | ~pp(aa(bool,bool,X1,X0)) | ~pp(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_421])])).
% 4.58/1.02 tff(f1040,plain,(
% 4.58/1.02 spl53_56 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_56])])).
% 4.58/1.02 tff(f2702,plain,(
% 4.58/1.02 spl53_165 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : fun(X2,fun(X1,X0)),X4 : fun(X2,X1),X3 : X2] : aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_165])])).
% 4.58/1.02 tff(f2763,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0)) | ~pp(aa(bool,bool,X1,X0)) | ~pp(X0)) ) | (~spl53_56 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f1041,f2703])).
% 4.58/1.02 tff(f2703,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : (aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))) ) | ~spl53_165),
% 4.58/1.02 inference(avatar_component_clause,[],[f2702])).
% 4.58/1.02 tff(f1041,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) ) | ~spl53_56),
% 4.58/1.02 inference(avatar_component_clause,[],[f1040])).
% 4.58/1.02 tff(f10423,plain,(
% 4.58/1.02 spl53_420 | ~spl53_58 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2760,f2702,f1048,f10421])).
% 4.58/1.02 tff(f10421,plain,(
% 4.58/1.02 spl53_420 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0)) | ~pp(X0) | pp(aa(bool,bool,X1,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_420])])).
% 4.58/1.02 tff(f1048,plain,(
% 4.58/1.02 spl53_58 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_58])])).
% 4.58/1.02 tff(f2760,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0)) | ~pp(X0) | pp(aa(bool,bool,X1,X0))) ) | (~spl53_58 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f1049,f2703])).
% 4.58/1.02 tff(f1049,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) | ~pp(X1) | pp(X0)) ) | ~spl53_58),
% 4.58/1.02 inference(avatar_component_clause,[],[f1048])).
% 4.58/1.02 tff(f10419,plain,(
% 4.58/1.02 spl53_419 | ~spl53_57 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2757,f2702,f1044,f10417])).
% 4.58/1.02 tff(f10417,plain,(
% 4.58/1.02 spl53_419 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0)) | pp(X0) | pp(aa(bool,bool,X1,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_419])])).
% 4.58/1.02 tff(f1044,plain,(
% 4.58/1.02 spl53_57 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_57])])).
% 4.58/1.02 tff(f2757,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0)) | pp(X0) | pp(aa(bool,bool,X1,X0))) ) | (~spl53_57 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f1045,f2703])).
% 4.58/1.02 tff(f1045,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | pp(X1) | pp(X0)) ) | ~spl53_57),
% 4.58/1.02 inference(avatar_component_clause,[],[f1044])).
% 4.58/1.02 tff(f10415,plain,(
% 4.58/1.02 spl53_418 | ~spl53_61 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2752,f2702,f1061,f10413])).
% 4.58/1.02 tff(f10413,plain,(
% 4.58/1.02 spl53_418 <=> ! [X0 : $tType,X2 : fun(X0,X0),X1 : X0] : (~pp(aa(X0,bool,aa(fun(X0,X0),fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(fun(X0,X0),fun(X0,bool)),combs(X0,X0,bool),fequal(X0)),X2),X1)) | aa(X0,X0,X2,X1) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_418])])).
% 4.58/1.02 tff(f1061,plain,(
% 4.58/1.02 spl53_61 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_61])])).
% 4.58/1.02 tff(f2752,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,X0),X1 : X0] : (~pp(aa(X0,bool,aa(fun(X0,X0),fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(fun(X0,X0),fun(X0,bool)),combs(X0,X0,bool),fequal(X0)),X2),X1)) | aa(X0,X0,X2,X1) = X1) ) | (~spl53_61 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f1062,f2703])).
% 4.58/1.02 tff(f1062,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) | X1 = X2) ) | ~spl53_61),
% 4.58/1.02 inference(avatar_component_clause,[],[f1061])).
% 4.58/1.02 tff(f10411,plain,(
% 4.58/1.02 spl53_417 | ~spl53_135 | ~spl53_163),
% 4.58/1.02 inference(avatar_split_clause,[],[f2658,f2640,f2238,f10409])).
% 4.58/1.02 tff(f10409,plain,(
% 4.58/1.02 spl53_417 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (~pp(aa(X0,bool,finite_fold1Set(X0,X2,aa(X0,fun(X0,bool),fequal(X0),X1)),X3)) | finite_fold_graph(X0,X0,X2,sK36(X0,X3,combk(bool,X0,fFalse),X1,X2),sK37(X0,X3,combk(bool,X0,fFalse),X1,X2),X3))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_417])])).
% 4.58/1.02 tff(f2238,plain,(
% 4.58/1.02 spl53_135 <=> ! [X0 : $tType,X1 : X0] : aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),combk(bool,X0,fFalse))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_135])])).
% 4.58/1.02 tff(f2640,plain,(
% 4.58/1.02 spl53_163 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,X0)),X3 : X0,X2 : fun(X0,bool),X1 : X0] : (finite_fold_graph(X0,X0,X4,sK36(X0,X1,X2,X3,X4),sK37(X0,X1,X2,X3,X4),X1) | ~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_163])])).
% 4.58/1.02 tff(f2658,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X3 : X0,X1 : X0] : (~pp(aa(X0,bool,finite_fold1Set(X0,X2,aa(X0,fun(X0,bool),fequal(X0),X1)),X3)) | finite_fold_graph(X0,X0,X2,sK36(X0,X3,combk(bool,X0,fFalse),X1,X2),sK37(X0,X3,combk(bool,X0,fFalse),X1,X2),X3)) ) | (~spl53_135 | ~spl53_163)),
% 4.58/1.02 inference(superposition,[],[f2641,f2239])).
% 4.58/1.02 tff(f2239,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),combk(bool,X0,fFalse))) ) | ~spl53_135),
% 4.58/1.02 inference(avatar_component_clause,[],[f2238])).
% 4.58/1.02 tff(f2641,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1)) | finite_fold_graph(X0,X0,X4,sK36(X0,X1,X2,X3,X4),sK37(X0,X1,X2,X3,X4),X1)) ) | ~spl53_163),
% 4.58/1.02 inference(avatar_component_clause,[],[f2640])).
% 4.58/1.02 tff(f10397,plain,(
% 4.58/1.02 spl53_416 | ~spl53_113 | ~spl53_162),
% 4.58/1.02 inference(avatar_split_clause,[],[f2622,f2596,f1800,f10395])).
% 4.58/1.02 tff(f10395,plain,(
% 4.58/1.02 spl53_416 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK13(X0,X1)),sK26(X0,X1,sK13(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_416])])).
% 4.58/1.02 tff(f1800,plain,(
% 4.58/1.02 spl53_113 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1)),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_113])])).
% 4.58/1.02 tff(f2596,plain,(
% 4.58/1.02 spl53_162 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK26(X0,X1,X2)) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_162])])).
% 4.58/1.02 tff(f2622,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK13(X0,X1)),sK26(X0,X1,sK13(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_113 | ~spl53_162)),
% 4.58/1.02 inference(resolution,[],[f2597,f1801])).
% 4.58/1.02 tff(f1801,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1)),X1)) | combk(bool,X0,fFalse) = X1) ) | ~spl53_113),
% 4.58/1.02 inference(avatar_component_clause,[],[f1800])).
% 4.58/1.02 tff(f2597,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK26(X0,X1,X2)) = X1) ) | ~spl53_162),
% 4.58/1.02 inference(avatar_component_clause,[],[f2596])).
% 4.58/1.02 tff(f10393,plain,(
% 4.58/1.02 spl53_415 | ~spl53_112 | ~spl53_162),
% 4.58/1.02 inference(avatar_split_clause,[],[f2621,f2596,f1796,f10391])).
% 4.58/1.02 tff(f10391,plain,(
% 4.58/1.02 spl53_415 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK12(X0,X1)),sK26(X0,X1,sK12(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_415])])).
% 4.58/1.02 tff(f1796,plain,(
% 4.58/1.02 spl53_112 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK12(X0,X1)),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_112])])).
% 4.58/1.02 tff(f2621,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK12(X0,X1)),sK26(X0,X1,sK12(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_112 | ~spl53_162)),
% 4.58/1.02 inference(resolution,[],[f2597,f1797])).
% 4.58/1.02 tff(f1797,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK12(X0,X1)),X1)) | combk(bool,X0,fFalse) = X1) ) | ~spl53_112),
% 4.58/1.02 inference(avatar_component_clause,[],[f1796])).
% 4.58/1.02 tff(f10389,plain,(
% 4.58/1.02 spl53_414 | ~spl53_111 | ~spl53_162),
% 4.58/1.02 inference(avatar_split_clause,[],[f2620,f2596,f1792,f10387])).
% 4.58/1.02 tff(f10387,plain,(
% 4.58/1.02 spl53_414 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK4(X0,X1)),sK26(X0,X1,sK4(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_414])])).
% 4.58/1.02 tff(f1792,plain,(
% 4.58/1.02 spl53_111 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_111])])).
% 4.58/1.02 tff(f2620,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK4(X0,X1)),sK26(X0,X1,sK4(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_111 | ~spl53_162)),
% 4.58/1.02 inference(resolution,[],[f2597,f1793])).
% 4.58/1.02 tff(f1793,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),X1)) | combk(bool,X0,fFalse) = X1) ) | ~spl53_111),
% 4.58/1.02 inference(avatar_component_clause,[],[f1792])).
% 4.58/1.02 tff(f10385,plain,(
% 4.58/1.02 spl53_413 | ~spl53_113 | ~spl53_161),
% 4.58/1.02 inference(avatar_split_clause,[],[f2602,f2592,f1800,f10383])).
% 4.58/1.02 tff(f10383,plain,(
% 4.58/1.02 spl53_413 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK13(X0,X1)),sK25(X0,X1,sK13(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_413])])).
% 4.58/1.02 tff(f2592,plain,(
% 4.58/1.02 spl53_161 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK25(X0,X1,X2)) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_161])])).
% 4.58/1.02 tff(f2602,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK13(X0,X1)),sK25(X0,X1,sK13(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_113 | ~spl53_161)),
% 4.58/1.02 inference(resolution,[],[f2593,f1801])).
% 4.58/1.02 tff(f2593,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK25(X0,X1,X2)) = X1) ) | ~spl53_161),
% 4.58/1.02 inference(avatar_component_clause,[],[f2592])).
% 4.58/1.02 tff(f10381,plain,(
% 4.58/1.02 spl53_412 | ~spl53_112 | ~spl53_161),
% 4.58/1.02 inference(avatar_split_clause,[],[f2601,f2592,f1796,f10379])).
% 4.58/1.02 tff(f10379,plain,(
% 4.58/1.02 spl53_412 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK12(X0,X1)),sK25(X0,X1,sK12(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_412])])).
% 4.58/1.02 tff(f2601,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK12(X0,X1)),sK25(X0,X1,sK12(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_112 | ~spl53_161)),
% 4.58/1.02 inference(resolution,[],[f2593,f1797])).
% 4.58/1.02 tff(f10377,plain,(
% 4.58/1.02 spl53_411 | ~spl53_111 | ~spl53_161),
% 4.58/1.02 inference(avatar_split_clause,[],[f2600,f2592,f1792,f10375])).
% 4.58/1.02 tff(f10375,plain,(
% 4.58/1.02 spl53_411 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK4(X0,X1)),sK25(X0,X1,sK4(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_411])])).
% 4.58/1.02 tff(f2600,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK4(X0,X1)),sK25(X0,X1,sK4(X0,X1))) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_111 | ~spl53_161)),
% 4.58/1.02 inference(resolution,[],[f2593,f1793])).
% 4.58/1.02 tff(f10373,plain,(
% 4.58/1.02 spl53_410 | ~spl53_20 | ~spl53_155),
% 4.58/1.02 inference(avatar_split_clause,[],[f2510,f2471,f840,f10371])).
% 4.58/1.02 tff(f10371,plain,(
% 4.58/1.02 spl53_410 <=> ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X3 : com,X1 : fun(state,bool)] : (pp(aa(state,bool,X1,sK41(X0,X2,X3,X4,combk(fun(state,bool),X0,X1)))) | hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,X1),X3,X2))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_410])])).
% 4.58/1.02 tff(f2471,plain,(
% 4.58/1.02 spl53_155 <=> ! [X0 : $tType,X4 : fun(X0,fun(state,bool)),X3 : fun(hoare_28830079triple(X0),bool),X2 : com,X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK40(X0,X1,X2,X3,X4)),sK41(X0,X1,X2,X3,X4))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_155])])).
% 4.58/1.02 tff(f2510,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(state,bool),X4 : fun(hoare_28830079triple(X0),bool)] : (pp(aa(state,bool,X1,sK41(X0,X2,X3,X4,combk(fun(state,bool),X0,X1)))) | hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,X1),X3,X2)))) ) | (~spl53_20 | ~spl53_155)),
% 4.58/1.02 inference(superposition,[],[f2472,f841])).
% 4.58/1.02 tff(f2472,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK40(X0,X1,X2,X3,X4)),sK41(X0,X1,X2,X3,X4)))) ) | ~spl53_155),
% 4.58/1.02 inference(avatar_component_clause,[],[f2471])).
% 4.58/1.02 tff(f10369,plain,(
% 4.58/1.02 spl53_409 | ~spl53_20 | ~spl53_154),
% 4.58/1.02 inference(avatar_split_clause,[],[f2487,f2467,f840,f10367])).
% 4.58/1.02 tff(f2467,plain,(
% 4.58/1.02 spl53_154 <=> ! [X0 : $tType,X4 : fun(X0,fun(state,bool)),X3 : fun(hoare_28830079triple(X0),bool),X2 : com,X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK38(X0,X1,X2,X3,X4)),sK39(X0,X1,X2,X3,X4))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_154])])).
% 4.58/1.02 tff(f2487,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(state,bool),X4 : fun(hoare_28830079triple(X0),bool)] : (pp(aa(state,bool,X1,sK39(X0,X2,X3,X4,combk(fun(state,bool),X0,X1)))) | hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,X1),X3,X2)))) ) | (~spl53_20 | ~spl53_154)),
% 4.58/1.02 inference(superposition,[],[f2468,f841])).
% 4.58/1.02 tff(f2468,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK38(X0,X1,X2,X3,X4)),sK39(X0,X1,X2,X3,X4)))) ) | ~spl53_154),
% 4.58/1.02 inference(avatar_component_clause,[],[f2467])).
% 4.58/1.02 tff(f10365,plain,(
% 4.58/1.02 spl53_408 | ~spl53_8 | ~spl53_140),
% 4.58/1.02 inference(avatar_split_clause,[],[f2306,f2271,f784,f10363])).
% 4.58/1.02 tff(f10363,plain,(
% 4.58/1.02 spl53_408 <=> ! [X0 : fun(bool,bool)] : (aa(fun(bool,bool),fun(bool,bool),aa(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),fFalse),sK9(bool,X0)) = X0 | combk(bool,bool,fFalse) = X0 | fTrue = sK8(bool,X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_408])])).
% 4.58/1.02 tff(f784,plain,(
% 4.58/1.02 spl53_8 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_8])])).
% 4.58/1.02 tff(f2271,plain,(
% 4.58/1.02 spl53_140 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),sK9(X0,X1)) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_140])])).
% 4.58/1.02 tff(f2306,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool)] : (aa(fun(bool,bool),fun(bool,bool),aa(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),fFalse),sK9(bool,X0)) = X0 | combk(bool,bool,fFalse) = X0 | fTrue = sK8(bool,X0)) ) | (~spl53_8 | ~spl53_140)),
% 4.58/1.02 inference(superposition,[],[f2272,f785])).
% 4.58/1.02 tff(f785,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) ) | ~spl53_8),
% 4.58/1.02 inference(avatar_component_clause,[],[f784])).
% 4.58/1.02 tff(f2272,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),sK9(X0,X1)) = X1 | combk(bool,X0,fFalse) = X1) ) | ~spl53_140),
% 4.58/1.02 inference(avatar_component_clause,[],[f2271])).
% 4.58/1.02 tff(f10361,plain,(
% 4.58/1.02 spl53_407 | ~spl53_8 | ~spl53_138),
% 4.58/1.02 inference(avatar_split_clause,[],[f2294,f2263,f784,f10359])).
% 4.58/1.02 tff(f10359,plain,(
% 4.58/1.02 spl53_407 <=> ! [X0 : $tType,X4 : fun(bool,bool),X3 : X0,X2 : fun(bool,fun(X0,X0)),X1 : X0] : (~pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),sK48(X0,bool,X1,X2,X3,X4))) | ~sP3(X0,bool,X1,X2,X3,X4) | fTrue = sK47(X0,bool,X1,X2,X3,X4))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_407])])).
% 4.58/1.02 tff(f2263,plain,(
% 4.58/1.02 spl53_138 <=> ! [X3 : $tType,X2 : $tType,X4 : X2,X0 : X2,X5 : fun(X3,bool),X1 : fun(X3,fun(X2,X2))] : (~pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),sK47(X2,X3,X0,X1,X4,X5)),sK48(X2,X3,X0,X1,X4,X5))) | ~sP3(X2,X3,X0,X1,X4,X5))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_138])])).
% 4.58/1.02 tff(f2294,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(bool,fun(X0,X0)),X3 : X0,X1 : X0,X4 : fun(bool,bool)] : (~pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),sK48(X0,bool,X1,X2,X3,X4))) | ~sP3(X0,bool,X1,X2,X3,X4) | fTrue = sK47(X0,bool,X1,X2,X3,X4)) ) | (~spl53_8 | ~spl53_138)),
% 4.58/1.02 inference(superposition,[],[f2264,f785])).
% 4.58/1.02 tff(f2264,plain,(
% 4.58/1.02 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (~pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),sK47(X2,X3,X0,X1,X4,X5)),sK48(X2,X3,X0,X1,X4,X5))) | ~sP3(X2,X3,X0,X1,X4,X5)) ) | ~spl53_138),
% 4.58/1.02 inference(avatar_component_clause,[],[f2263])).
% 4.58/1.02 tff(f10357,plain,(
% 4.58/1.02 spl53_24 | ~spl53_406 | ~spl53_261),
% 4.58/1.02 inference(avatar_split_clause,[],[f6313,f4666,f10354,f858])).
% 4.58/1.02 tff(f10354,plain,(
% 4.58/1.02 spl53_406 <=> fTrue = sK11(bool,fNot)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_406])])).
% 4.58/1.02 tff(f4666,plain,(
% 4.58/1.02 spl53_261 <=> ! [X0 : bool] : (sK11(bool,fNot) = X0 | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_261])])).
% 4.58/1.02 tff(f6313,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (fTrue != sK11(bool,fNot) | fTrue = X0) ) | ~spl53_261),
% 4.58/1.02 inference(equality_factoring,[],[f4667])).
% 4.58/1.02 tff(f4667,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (sK11(bool,fNot) = X0 | fTrue = X0) ) | ~spl53_261),
% 4.58/1.02 inference(avatar_component_clause,[],[f4666])).
% 4.58/1.02 tff(f10352,plain,(
% 4.58/1.02 spl53_405 | ~spl53_60 | ~spl53_130),
% 4.58/1.02 inference(avatar_split_clause,[],[f2204,f2170,f1057,f10350])).
% 4.58/1.02 tff(f10350,plain,(
% 4.58/1.02 spl53_405 <=> ! [X0 : fun(bool,fun(bool,bool))] : (~pp(the(bool,finite_fold1Set(bool,X0,aa(fun(bool,bool),fun(bool,bool),aa(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),sK17(bool,finite_fold1(bool,X0))),sK18(bool,finite_fold1(bool,X0)))))) | ~sP0(bool,finite_fold1(bool,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_405])])).
% 4.58/1.02 tff(f1057,plain,(
% 4.58/1.02 spl53_60 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : fun(X0,bool)] : aa(fun(X0,bool),X0,finite_fold1(X0,X2),X1) = the(X0,finite_fold1Set(X0,X2,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_60])])).
% 4.58/1.02 tff(f2170,plain,(
% 4.58/1.02 spl53_130 <=> ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK17(X0,X1)),sK18(X0,X1)))) | ~sP0(X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_130])])).
% 4.58/1.02 tff(f2204,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool))] : (~pp(the(bool,finite_fold1Set(bool,X0,aa(fun(bool,bool),fun(bool,bool),aa(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),sK17(bool,finite_fold1(bool,X0))),sK18(bool,finite_fold1(bool,X0)))))) | ~sP0(bool,finite_fold1(bool,X0))) ) | (~spl53_60 | ~spl53_130)),
% 4.58/1.02 inference(superposition,[],[f2171,f1058])).
% 4.58/1.02 tff(f1058,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : fun(X0,bool)] : (aa(fun(X0,bool),X0,finite_fold1(X0,X2),X1) = the(X0,finite_fold1Set(X0,X2,X1))) ) | ~spl53_60),
% 4.58/1.02 inference(avatar_component_clause,[],[f1057])).
% 4.58/1.02 tff(f2171,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK17(X0,X1)),sK18(X0,X1)))) | ~sP0(X0,X1)) ) | ~spl53_130),
% 4.58/1.02 inference(avatar_component_clause,[],[f2170])).
% 4.58/1.02 tff(f10348,plain,(
% 4.58/1.02 spl53_404 | ~spl53_71 | ~spl53_117),
% 4.58/1.02 inference(avatar_split_clause,[],[f1922,f1918,f1153,f10346])).
% 4.58/1.02 tff(f10346,plain,(
% 4.58/1.02 spl53_404 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (~pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3)) | sK33(X0,X3,X2,X1) = sK31(X0,X3,X2,X1) | sP3(X0,X0,sK31(X0,X3,X2,X1),X1,sK33(X0,X3,X2,X1),sK32(X0,X3,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_404])])).
% 4.58/1.02 tff(f1153,plain,(
% 4.58/1.02 spl53_71 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1)),X2 : X1] : (sP3(X1,X0,X4,X5,X2,X3) | X2 = X4 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_71])])).
% 4.58/1.02 tff(f1918,plain,(
% 4.58/1.02 spl53_117 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool),X1 : X0] : (finite_fold_graph(X0,X0,X3,sK31(X0,X1,X2,X3),sK32(X0,X1,X2,X3),sK33(X0,X1,X2,X3)) | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_117])])).
% 4.58/1.02 tff(f1922,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,fun(X0,X0))] : (~pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3)) | sK33(X0,X3,X2,X1) = sK31(X0,X3,X2,X1) | sP3(X0,X0,sK31(X0,X3,X2,X1),X1,sK33(X0,X3,X2,X1),sK32(X0,X3,X2,X1))) ) | (~spl53_71 | ~spl53_117)),
% 4.58/1.02 inference(resolution,[],[f1919,f1154])).
% 4.58/1.02 tff(f1154,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (~finite_fold_graph(X0,X1,X5,X4,X3,X2) | X2 = X4 | sP3(X1,X0,X4,X5,X2,X3)) ) | ~spl53_71),
% 4.58/1.02 inference(avatar_component_clause,[],[f1153])).
% 4.58/1.02 tff(f1919,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (finite_fold_graph(X0,X0,X3,sK31(X0,X1,X2,X3),sK32(X0,X1,X2,X3),sK33(X0,X1,X2,X3)) | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1))) ) | ~spl53_117),
% 4.58/1.02 inference(avatar_component_clause,[],[f1918])).
% 4.58/1.02 tff(f10344,plain,(
% 4.58/1.02 spl53_403 | ~spl53_60 | ~spl53_100),
% 4.58/1.02 inference(avatar_split_clause,[],[f1714,f1678,f1057,f10342])).
% 4.58/1.02 tff(f10342,plain,(
% 4.58/1.02 spl53_403 <=> ! [X2 : fun(bool,bool),X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,sK27(fun(bool,bool),finite_fold1(bool,X0),X1)))) | ~pp(the(bool,finite_fold1Set(bool,X0,X2))) | ~pp(the(bool,finite_fold1Set(bool,X0,X1))) | the(fun(bool,bool),finite_fold1(bool,X0)) = X2)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_403])])).
% 4.58/1.02 tff(f1678,plain,(
% 4.58/1.02 spl53_100 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : X0] : (the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X1)) | pp(aa(X0,bool,X2,sK27(X0,X2,X3))) | ~pp(aa(X0,bool,X2,X3)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_100])])).
% 4.58/1.02 tff(f1714,plain,(
% 4.58/1.02 ( ! [X2 : fun(bool,bool),X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,sK27(fun(bool,bool),finite_fold1(bool,X0),X1)))) | ~pp(the(bool,finite_fold1Set(bool,X0,X2))) | ~pp(the(bool,finite_fold1Set(bool,X0,X1))) | the(fun(bool,bool),finite_fold1(bool,X0)) = X2) ) | (~spl53_60 | ~spl53_100)),
% 4.58/1.02 inference(forward_demodulation,[],[f1713,f1058])).
% 4.58/1.02 tff(f1713,plain,(
% 4.58/1.02 ( ! [X2 : fun(bool,bool),X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,finite_fold1Set(bool,X0,X2))) | ~pp(the(bool,finite_fold1Set(bool,X0,X1))) | pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),sK27(fun(bool,bool),finite_fold1(bool,X0),X1))) | the(fun(bool,bool),finite_fold1(bool,X0)) = X2) ) | (~spl53_60 | ~spl53_100)),
% 4.58/1.02 inference(forward_demodulation,[],[f1708,f1058])).
% 4.58/1.02 tff(f1708,plain,(
% 4.58/1.02 ( ! [X2 : fun(bool,bool),X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,finite_fold1Set(bool,X0,X1))) | ~pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),X2)) | pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),sK27(fun(bool,bool),finite_fold1(bool,X0),X1))) | the(fun(bool,bool),finite_fold1(bool,X0)) = X2) ) | (~spl53_60 | ~spl53_100)),
% 4.58/1.02 inference(superposition,[],[f1679,f1058])).
% 4.58/1.02 tff(f1679,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (~pp(aa(X0,bool,X2,X3)) | ~pp(aa(X0,bool,X2,X1)) | pp(aa(X0,bool,X2,sK27(X0,X2,X3))) | the(X0,X2) = X1) ) | ~spl53_100),
% 4.58/1.02 inference(avatar_component_clause,[],[f1678])).
% 4.58/1.02 tff(f10340,plain,(
% 4.58/1.02 spl53_402 | ~spl53_60 | ~spl53_95),
% 4.58/1.02 inference(avatar_split_clause,[],[f1649,f1618,f1057,f10338])).
% 4.58/1.02 tff(f10338,plain,(
% 4.58/1.02 spl53_402 <=> ! [X0 : $tType,X2 : fun(fun(X0,bool),X0),X1 : fun(X0,fun(X0,X0))] : (the(X0,finite_fold1Set(X0,X1,sK30(X0,fun(X0,bool),finite_fold1(X0,X1),X2))) != aa(fun(X0,bool),X0,X2,sK30(X0,fun(X0,bool),finite_fold1(X0,X1),X2)) | finite_fold1(X0,X1) = X2)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_402])])).
% 4.58/1.02 tff(f1618,plain,(
% 4.58/1.02 spl53_95 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X1,X0),X2 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK30(X0,X1,X2,X3)) != aa(X1,X0,X2,sK30(X0,X1,X2,X3)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_95])])).
% 4.58/1.02 tff(f1649,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(fun(X0,bool),X0),X1 : fun(X0,fun(X0,X0))] : (the(X0,finite_fold1Set(X0,X1,sK30(X0,fun(X0,bool),finite_fold1(X0,X1),X2))) != aa(fun(X0,bool),X0,X2,sK30(X0,fun(X0,bool),finite_fold1(X0,X1),X2)) | finite_fold1(X0,X1) = X2) ) | (~spl53_60 | ~spl53_95)),
% 4.58/1.02 inference(superposition,[],[f1619,f1058])).
% 4.58/1.02 tff(f1619,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (aa(X1,X0,X3,sK30(X0,X1,X2,X3)) != aa(X1,X0,X2,sK30(X0,X1,X2,X3)) | X2 = X3) ) | ~spl53_95),
% 4.58/1.02 inference(avatar_component_clause,[],[f1618])).
% 4.58/1.02 tff(f10336,plain,(
% 4.58/1.02 spl53_401 | ~spl53_60 | ~spl53_95),
% 4.58/1.02 inference(avatar_split_clause,[],[f1637,f1618,f1057,f10334])).
% 4.58/1.02 tff(f10334,plain,(
% 4.58/1.02 spl53_401 <=> ! [X0 : $tType,X2 : fun(fun(X0,bool),X0),X1 : fun(X0,fun(X0,X0))] : (the(X0,finite_fold1Set(X0,X1,sK30(X0,fun(X0,bool),X2,finite_fold1(X0,X1)))) != aa(fun(X0,bool),X0,X2,sK30(X0,fun(X0,bool),X2,finite_fold1(X0,X1))) | finite_fold1(X0,X1) = X2)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_401])])).
% 4.58/1.02 tff(f1637,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(fun(X0,bool),X0),X1 : fun(X0,fun(X0,X0))] : (the(X0,finite_fold1Set(X0,X1,sK30(X0,fun(X0,bool),X2,finite_fold1(X0,X1)))) != aa(fun(X0,bool),X0,X2,sK30(X0,fun(X0,bool),X2,finite_fold1(X0,X1))) | finite_fold1(X0,X1) = X2) ) | (~spl53_60 | ~spl53_95)),
% 4.58/1.02 inference(superposition,[],[f1619,f1058])).
% 4.58/1.02 tff(f10109,plain,(
% 4.58/1.02 spl53_400 | ~spl53_135 | ~spl53_193),
% 4.58/1.02 inference(avatar_split_clause,[],[f3410,f3402,f2238,f10107])).
% 4.58/1.02 tff(f10107,plain,(
% 4.58/1.02 spl53_400 <=> ! [X0 : $tType,X1 : X0] : aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),aa(X0,fun(X0,bool),fequal(X0),X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_400])])).
% 4.58/1.02 tff(f3402,plain,(
% 4.58/1.02 spl53_193 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_193])])).
% 4.58/1.02 tff(f3410,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),aa(X0,fun(X0,bool),fequal(X0),X1))) ) | (~spl53_135 | ~spl53_193)),
% 4.58/1.02 inference(superposition,[],[f3403,f2239])).
% 4.58/1.02 tff(f3403,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) ) | ~spl53_193),
% 4.58/1.02 inference(avatar_component_clause,[],[f3402])).
% 4.58/1.02 tff(f10105,plain,(
% 4.58/1.02 spl53_399 | ~spl53_74 | ~spl53_186),
% 4.58/1.02 inference(avatar_split_clause,[],[f3262,f3232,f1168,f10103])).
% 4.58/1.02 tff(f10103,plain,(
% 4.58/1.02 spl53_399 <=> ! [X0 : $tType,X4 : fun(X0,fun(state,bool)),X3 : com,X2 : fun(X0,fun(state,bool)),X1 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X1,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X3,X4))) | hoare_992312373derivs(X0,X1,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,semi(skip,X3),X4))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_399])])).
% 4.58/1.02 tff(f1168,plain,(
% 4.58/1.02 spl53_74 <=> ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : hoare_992312373derivs(X0,X2,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_74])])).
% 4.58/1.02 tff(f3232,plain,(
% 4.58/1.02 spl53_186 <=> ! [X0 : $tType,X2 : com,X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3))) | ~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,semi(X4,X2),X1))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_186])])).
% 4.58/1.02 tff(f3262,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X1,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X3,X4))) | hoare_992312373derivs(X0,X1,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,semi(skip,X3),X4)))) ) | (~spl53_74 | ~spl53_186)),
% 4.58/1.02 inference(resolution,[],[f3233,f1169])).
% 4.58/1.02 tff(f1169,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X2,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1)))) ) | ~spl53_74),
% 4.58/1.02 inference(avatar_component_clause,[],[f1168])).
% 4.58/1.02 tff(f3233,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3))) | ~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,semi(X4,X2),X1)))) ) | ~spl53_186),
% 4.58/1.02 inference(avatar_component_clause,[],[f3232])).
% 4.58/1.02 tff(f10101,plain,(
% 4.58/1.02 spl53_398 | ~spl53_140 | ~spl53_171),
% 4.58/1.02 inference(avatar_split_clause,[],[f2817,f2804,f2271,f10099])).
% 4.58/1.02 tff(f10099,plain,(
% 4.58/1.02 spl53_398 <=> ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X2,X1) | ~hoare_992312373derivs(X0,X2,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),sK8(hoare_28830079triple(X0),X1))) | ~hoare_992312373derivs(X0,X2,sK9(hoare_28830079triple(X0),X1)) | combk(bool,hoare_28830079triple(X0),fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_398])])).
% 4.58/1.02 tff(f2804,plain,(
% 4.58/1.02 spl53_171 <=> ! [X0 : $tType,X3 : fun(hoare_28830079triple(X0),bool),X2 : hoare_28830079triple(X0),X1 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),X2)) | hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1)) | ~hoare_992312373derivs(X0,X3,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_171])])).
% 4.58/1.02 tff(f2817,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X2,X1) | ~hoare_992312373derivs(X0,X2,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),sK8(hoare_28830079triple(X0),X1))) | ~hoare_992312373derivs(X0,X2,sK9(hoare_28830079triple(X0),X1)) | combk(bool,hoare_28830079triple(X0),fFalse) = X1) ) | (~spl53_140 | ~spl53_171)),
% 4.58/1.02 inference(superposition,[],[f2805,f2272])).
% 4.58/1.02 tff(f2805,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1)) | ~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),X2)) | ~hoare_992312373derivs(X0,X3,X1)) ) | ~spl53_171),
% 4.58/1.02 inference(avatar_component_clause,[],[f2804])).
% 4.58/1.02 tff(f10097,plain,(
% 4.58/1.02 spl53_397 | ~spl53_5 | ~spl53_149),
% 4.58/1.02 inference(avatar_split_clause,[],[f2413,f2406,f772,f10095])).
% 4.58/1.02 tff(f10095,plain,(
% 4.58/1.02 spl53_397 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1 | combk(bool,X0,fFalse) = X1 | ~finite_finite(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_397])])).
% 4.58/1.02 tff(f772,plain,(
% 4.58/1.02 spl53_5 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_5])])).
% 4.58/1.02 tff(f2406,plain,(
% 4.58/1.02 spl53_149 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1 | ~finite_finite1(X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_149])])).
% 4.58/1.02 tff(f2413,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1 | combk(bool,X0,fFalse) = X1 | ~finite_finite(X0)) ) | (~spl53_5 | ~spl53_149)),
% 4.58/1.02 inference(resolution,[],[f2407,f773])).
% 4.58/1.02 tff(f773,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite(X0)) ) | ~spl53_5),
% 4.58/1.02 inference(avatar_component_clause,[],[f772])).
% 4.58/1.02 tff(f2407,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (~finite_finite1(X0,X1) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1 | combk(bool,X0,fFalse) = X1) ) | ~spl53_149),
% 4.58/1.02 inference(avatar_component_clause,[],[f2406])).
% 4.58/1.02 tff(f10093,plain,(
% 4.58/1.02 spl53_396 | ~spl53_126 | ~spl53_127),
% 4.58/1.02 inference(avatar_split_clause,[],[f2135,f2032,f2028,f10091])).
% 4.58/1.02 tff(f10091,plain,(
% 4.58/1.02 spl53_396 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X1))) | pp(aa(X0,bool,X1,sK29(X0,X1,X2))) | ~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK29(X0,X1,X3))) | ~pp(aa(X0,bool,X1,X3)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_396])])).
% 4.58/1.02 tff(f2028,plain,(
% 4.58/1.02 spl53_126 <=> ! [X0 : $tType,X4 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X2))) | pp(aa(X0,bool,X2,sK28(X0,X1,X2))) | pp(aa(X0,bool,X2,sK29(X0,X2,X4))) | ~pp(aa(X0,bool,X2,X4)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_126])])).
% 4.58/1.02 tff(f2032,plain,(
% 4.58/1.02 spl53_127 <=> ! [X0 : $tType,X4 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X2))) | ~pp(aa(X0,bool,X1,sK28(X0,X1,X2))) | pp(aa(X0,bool,X2,sK29(X0,X2,X4))) | ~pp(aa(X0,bool,X2,X4)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_127])])).
% 4.58/1.02 tff(f2135,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X1))) | pp(aa(X0,bool,X1,sK29(X0,X1,X2))) | ~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK29(X0,X1,X3))) | ~pp(aa(X0,bool,X1,X3))) ) | (~spl53_126 | ~spl53_127)),
% 4.58/1.02 inference(duplicate_literal_removal,[],[f2119])).
% 4.58/1.02 tff(f2119,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X1))) | pp(aa(X0,bool,X1,sK29(X0,X1,X2))) | ~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK29(X0,X1,X3))) | pp(aa(X0,bool,X1,the(X0,X1))) | ~pp(aa(X0,bool,X1,X3))) ) | (~spl53_126 | ~spl53_127)),
% 4.58/1.02 inference(resolution,[],[f2033,f2029])).
% 4.58/1.02 tff(f2029,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,X2,sK29(X0,X2,X4))) | pp(aa(X0,bool,X2,sK28(X0,X1,X2))) | pp(aa(X0,bool,X1,the(X0,X2))) | ~pp(aa(X0,bool,X2,X4))) ) | ~spl53_126),
% 4.58/1.02 inference(avatar_component_clause,[],[f2028])).
% 4.58/1.02 tff(f2033,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (~pp(aa(X0,bool,X1,sK28(X0,X1,X2))) | pp(aa(X0,bool,X1,the(X0,X2))) | pp(aa(X0,bool,X2,sK29(X0,X2,X4))) | ~pp(aa(X0,bool,X2,X4))) ) | ~spl53_127),
% 4.58/1.02 inference(avatar_component_clause,[],[f2032])).
% 4.58/1.02 tff(f10089,plain,(
% 4.58/1.02 spl53_395 | ~spl53_77 | ~spl53_93),
% 4.58/1.02 inference(avatar_split_clause,[],[f1601,f1541,f1184,f10087])).
% 4.58/1.02 tff(f10087,plain,(
% 4.58/1.02 spl53_395 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | ~finite_finite1(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) | sK20(X0,X2,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_395])])).
% 4.58/1.02 tff(f1184,plain,(
% 4.58/1.02 spl53_77 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : X0,X1 : X0] : (~pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(X0,fun(X0,bool),fequal(X0),X2)),X1)) | X1 = X2)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_77])])).
% 4.58/1.02 tff(f1541,plain,(
% 4.58/1.02 spl53_93 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = X2 | pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),sK20(X0,X1,X2))) | ~finite_finite1(X0,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_93])])).
% 4.58/1.02 tff(f1601,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | ~finite_finite1(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) | sK20(X0,X2,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) ) | (~spl53_77 | ~spl53_93)),
% 4.58/1.02 inference(resolution,[],[f1542,f1185])).
% 4.58/1.02 tff(f1185,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(X0,fun(X0,bool),fequal(X0),X2)),X1)) | X1 = X2) ) | ~spl53_77),
% 4.58/1.02 inference(avatar_component_clause,[],[f1184])).
% 4.58/1.02 tff(f1542,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),sK20(X0,X1,X2))) | combk(bool,X0,fFalse) = X2 | ~finite_finite1(X0,X2)) ) | ~spl53_93),
% 4.58/1.02 inference(avatar_component_clause,[],[f1541])).
% 4.58/1.02 tff(f9999,plain,(
% 4.58/1.02 spl53_24 | ~spl53_394 | ~spl53_236),
% 4.58/1.02 inference(avatar_split_clause,[],[f5927,f4171,f9996,f858])).
% 4.58/1.02 tff(f9996,plain,(
% 4.58/1.02 spl53_394 <=> fTrue = sK10(bool,fNot)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_394])])).
% 4.58/1.02 tff(f4171,plain,(
% 4.58/1.02 spl53_236 <=> ! [X0 : bool] : (sK10(bool,fNot) = X0 | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_236])])).
% 4.58/1.02 tff(f5927,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (fTrue != sK10(bool,fNot) | fTrue = X0) ) | ~spl53_236),
% 4.58/1.02 inference(equality_factoring,[],[f4172])).
% 4.58/1.02 tff(f4172,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (sK10(bool,fNot) = X0 | fTrue = X0) ) | ~spl53_236),
% 4.58/1.02 inference(avatar_component_clause,[],[f4171])).
% 4.58/1.02 tff(f9614,plain,(
% 4.58/1.02 spl53_393 | ~spl53_135 | ~spl53_175),
% 4.58/1.02 inference(avatar_split_clause,[],[f3055,f3033,f2238,f9612])).
% 4.58/1.02 tff(f9612,plain,(
% 4.58/1.02 spl53_393 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),combk(bool,X0,fFalse)) | X1 = X2)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_393])])).
% 4.58/1.02 tff(f3033,plain,(
% 4.58/1.02 spl53_175 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),combk(bool,X0,fFalse)) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),combk(bool,X0,fFalse)) | X1 = X2)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_175])])).
% 4.58/1.02 tff(f3055,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),combk(bool,X0,fFalse)) | X1 = X2) ) | (~spl53_135 | ~spl53_175)),
% 4.58/1.02 inference(superposition,[],[f3034,f2239])).
% 4.58/1.02 tff(f3034,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),combk(bool,X0,fFalse)) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),combk(bool,X0,fFalse)) | X1 = X2) ) | ~spl53_175),
% 4.58/1.02 inference(avatar_component_clause,[],[f3033])).
% 4.58/1.02 tff(f9610,plain,(
% 4.58/1.02 spl53_392 | ~spl53_49 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2764,f2702,f992,f9608])).
% 4.58/1.02 tff(f9608,plain,(
% 4.58/1.02 spl53_392 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0)) | pp(aa(bool,bool,X1,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_392])])).
% 4.58/1.02 tff(f992,plain,(
% 4.58/1.02 spl53_49 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_49])])).
% 4.58/1.02 tff(f2764,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0)) | pp(aa(bool,bool,X1,X0))) ) | (~spl53_49 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f993,f2703])).
% 4.58/1.02 tff(f993,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | pp(X0)) ) | ~spl53_49),
% 4.58/1.02 inference(avatar_component_clause,[],[f992])).
% 4.58/1.02 tff(f9606,plain,(
% 4.58/1.02 spl53_391 | ~spl53_46 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2762,f2702,f980,f9604])).
% 4.58/1.02 tff(f9604,plain,(
% 4.58/1.02 spl53_391 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0)) | ~pp(aa(bool,bool,X1,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_391])])).
% 4.58/1.02 tff(f980,plain,(
% 4.58/1.02 spl53_46 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_46])])).
% 4.58/1.02 tff(f2762,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0)) | ~pp(aa(bool,bool,X1,X0))) ) | (~spl53_46 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f981,f2703])).
% 4.58/1.02 tff(f981,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X1)) ) | ~spl53_46),
% 4.58/1.02 inference(avatar_component_clause,[],[f980])).
% 4.58/1.02 tff(f9602,plain,(
% 4.58/1.02 spl53_390 | ~spl53_44 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2759,f2702,f972,f9600])).
% 4.58/1.02 tff(f9600,plain,(
% 4.58/1.02 spl53_390 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0)) | ~pp(aa(bool,bool,X1,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_390])])).
% 4.58/1.02 tff(f972,plain,(
% 4.58/1.02 spl53_44 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_44])])).
% 4.58/1.02 tff(f2759,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0)) | ~pp(aa(bool,bool,X1,X0))) ) | (~spl53_44 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f973,f2703])).
% 4.58/1.02 tff(f973,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1)) ) | ~spl53_44),
% 4.58/1.02 inference(avatar_component_clause,[],[f972])).
% 4.58/1.02 tff(f9315,plain,(
% 4.58/1.02 spl53_389 | ~spl53_8 | ~spl53_135),
% 4.58/1.02 inference(avatar_split_clause,[],[f2241,f2238,f784,f9313])).
% 4.58/1.02 tff(f9313,plain,(
% 4.58/1.02 spl53_389 <=> ! [X1 : $tType,X2 : X1,X0 : bool] : (aa(X1,fun(X1,bool),fequal(X1),X2) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),combk(bool,X1,X0)) | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_389])])).
% 4.58/1.02 tff(f2241,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X2 : X1,X0 : bool] : (aa(X1,fun(X1,bool),fequal(X1),X2) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),combk(bool,X1,X0)) | fTrue = X0) ) | (~spl53_8 | ~spl53_135)),
% 4.58/1.02 inference(superposition,[],[f2239,f785])).
% 4.58/1.02 tff(f9311,plain,(
% 4.58/1.02 spl53_388 | ~spl53_8 | ~spl53_131),
% 4.58/1.02 inference(avatar_split_clause,[],[f2214,f2174,f784,f9309])).
% 4.58/1.02 tff(f9309,plain,(
% 4.58/1.02 spl53_388 <=> ! [X2 : fun(bool,fun(bool,bool)),X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),sK32(bool,X0,X1,X2))) | ~pp(aa(bool,bool,finite_fold1Set(bool,X2,X1),X0)) | fTrue = sK31(bool,X0,X1,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_388])])).
% 4.58/1.02 tff(f2174,plain,(
% 4.58/1.02 spl53_131 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool),X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3))) | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_131])])).
% 4.58/1.02 tff(f2214,plain,(
% 4.58/1.02 ( ! [X2 : fun(bool,fun(bool,bool)),X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),sK32(bool,X0,X1,X2))) | ~pp(aa(bool,bool,finite_fold1Set(bool,X2,X1),X0)) | fTrue = sK31(bool,X0,X1,X2)) ) | (~spl53_8 | ~spl53_131)),
% 4.58/1.02 inference(superposition,[],[f2175,f785])).
% 4.58/1.02 tff(f2175,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3))) | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1))) ) | ~spl53_131),
% 4.58/1.02 inference(avatar_component_clause,[],[f2174])).
% 4.58/1.02 tff(f9307,plain,(
% 4.58/1.02 spl53_387 | ~spl53_8 | ~spl53_130),
% 4.58/1.02 inference(avatar_split_clause,[],[f2198,f2170,f784,f9305])).
% 4.58/1.02 tff(f9305,plain,(
% 4.58/1.02 spl53_387 <=> ! [X0 : fun(fun(bool,bool),bool)] : (~pp(aa(fun(bool,bool),bool,X0,aa(fun(bool,bool),fun(bool,bool),aa(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),fFalse),sK18(bool,X0)))) | ~sP0(bool,X0) | fTrue = sK17(bool,X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_387])])).
% 4.58/1.02 tff(f2198,plain,(
% 4.58/1.02 ( ! [X0 : fun(fun(bool,bool),bool)] : (~pp(aa(fun(bool,bool),bool,X0,aa(fun(bool,bool),fun(bool,bool),aa(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),fFalse),sK18(bool,X0)))) | ~sP0(bool,X0) | fTrue = sK17(bool,X0)) ) | (~spl53_8 | ~spl53_130)),
% 4.58/1.02 inference(superposition,[],[f2171,f785])).
% 4.58/1.02 tff(f9303,plain,(
% 4.58/1.02 spl53_386 | ~spl53_89 | ~spl53_100),
% 4.58/1.02 inference(avatar_split_clause,[],[f1701,f1678,f1482,f9301])).
% 4.58/1.02 tff(f9301,plain,(
% 4.58/1.02 spl53_386 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK24(X0,X3,X1)))) | the(X0,X1) = X2 | pp(aa(X0,bool,X1,the(X0,X1))) | ~pp(aa(X0,bool,X1,X3)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_386])])).
% 4.58/1.02 tff(f1482,plain,(
% 4.58/1.02 spl53_89 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (pp(aa(X0,bool,X2,the(X0,X2))) | pp(aa(X0,bool,X2,sK24(X0,X1,X2))) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_89])])).
% 4.58/1.02 tff(f1701,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK24(X0,X3,X1)))) | the(X0,X1) = X2 | pp(aa(X0,bool,X1,the(X0,X1))) | ~pp(aa(X0,bool,X1,X3))) ) | (~spl53_89 | ~spl53_100)),
% 4.58/1.02 inference(resolution,[],[f1679,f1483])).
% 4.58/1.02 tff(f1483,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (pp(aa(X0,bool,X2,sK24(X0,X1,X2))) | pp(aa(X0,bool,X2,the(X0,X2))) | ~pp(aa(X0,bool,X2,X1))) ) | ~spl53_89),
% 4.58/1.02 inference(avatar_component_clause,[],[f1482])).
% 4.58/1.02 tff(f9299,plain,(
% 4.58/1.02 spl53_385 | ~spl53_87 | ~spl53_100),
% 4.58/1.02 inference(avatar_split_clause,[],[f1697,f1678,f1473,f9297])).
% 4.58/1.02 tff(f9297,plain,(
% 4.58/1.02 spl53_385 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK5(X0,X1,X3)))) | the(X0,X1) = X2 | pp(aa(X0,bool,X1,the(X0,X1))) | ~pp(aa(X0,bool,X1,X3)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_385])])).
% 4.58/1.02 tff(f1473,plain,(
% 4.58/1.02 spl53_87 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X1))) | pp(aa(X0,bool,X1,sK5(X0,X1,X2))) | ~pp(aa(X0,bool,X1,X2)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_87])])).
% 4.58/1.02 tff(f1697,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK5(X0,X1,X3)))) | the(X0,X1) = X2 | pp(aa(X0,bool,X1,the(X0,X1))) | ~pp(aa(X0,bool,X1,X3))) ) | (~spl53_87 | ~spl53_100)),
% 4.58/1.02 inference(resolution,[],[f1679,f1474])).
% 4.58/1.02 tff(f1474,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,sK5(X0,X1,X2))) | pp(aa(X0,bool,X1,the(X0,X1))) | ~pp(aa(X0,bool,X1,X2))) ) | ~spl53_87),
% 4.58/1.02 inference(avatar_component_clause,[],[f1473])).
% 4.58/1.02 tff(f9067,plain,(
% 4.58/1.02 spl53_384 | ~spl53_74 | ~spl53_183),
% 4.58/1.02 inference(avatar_split_clause,[],[f3197,f3142,f1168,f9065])).
% 4.58/1.02 tff(f9065,plain,(
% 4.58/1.02 spl53_384 <=> ! [X0 : $tType,X3 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,skip,X3))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK45(X0,X3,X2)),sK46(X0,X3,X2))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_384])])).
% 4.58/1.02 tff(f3142,plain,(
% 4.58/1.02 spl53_183 <=> ! [X0 : $tType,X5 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool)),X3 : com,X2 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK45(X0,X1,X2)),sK46(X0,X1,X2))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_183])])).
% 4.58/1.02 tff(f3197,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,skip,X3))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK45(X0,X3,X2)),sK46(X0,X3,X2)))) ) | (~spl53_74 | ~spl53_183)),
% 4.58/1.02 inference(resolution,[],[f3143,f1169])).
% 4.58/1.02 tff(f3143,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK45(X0,X1,X2)),sK46(X0,X1,X2)))) ) | ~spl53_183),
% 4.58/1.02 inference(avatar_component_clause,[],[f3142])).
% 4.58/1.02 tff(f9063,plain,(
% 4.58/1.02 spl53_383 | ~spl53_74 | ~spl53_180),
% 4.58/1.02 inference(avatar_split_clause,[],[f3169,f3129,f1168,f9061])).
% 4.58/1.02 tff(f9061,plain,(
% 4.58/1.02 spl53_383 <=> ! [X0 : $tType,X3 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,skip,X3))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK43(X0,X2,X3)),sK44(X0,X2,X3))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_383])])).
% 4.58/1.02 tff(f3129,plain,(
% 4.58/1.02 spl53_180 <=> ! [X0 : $tType,X5 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool)),X3 : com,X2 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2))) | pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK43(X0,X1,X4)),sK44(X0,X1,X4))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_180])])).
% 4.58/1.02 tff(f3169,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,skip,X3))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK43(X0,X2,X3)),sK44(X0,X2,X3)))) ) | (~spl53_74 | ~spl53_180)),
% 4.58/1.02 inference(resolution,[],[f3130,f1169])).
% 4.58/1.02 tff(f3130,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2))) | pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK43(X0,X1,X4)),sK44(X0,X1,X4)))) ) | ~spl53_180),
% 4.58/1.02 inference(avatar_component_clause,[],[f3129])).
% 4.58/1.02 tff(f9059,plain,(
% 4.58/1.02 spl53_382 | ~spl53_62 | ~spl53_81),
% 4.58/1.02 inference(avatar_split_clause,[],[f1423,f1400,f1065,f9057])).
% 4.58/1.02 tff(f9057,plain,(
% 4.58/1.02 spl53_382 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (the(X0,finite_fold1Set(X0,X1,X2)) = X3 | ~pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3)) | sK23(X0,X3,finite_fold1Set(X0,X1,X2)) = sK33(X0,sK23(X0,X3,finite_fold1Set(X0,X1,X2)),X2,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_382])])).
% 4.58/1.02 tff(f1065,plain,(
% 4.58/1.02 spl53_62 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool),X1 : X0] : (sK33(X0,X1,X2,X3) = X1 | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_62])])).
% 4.58/1.02 tff(f1400,plain,(
% 4.58/1.02 spl53_81 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (the(X0,X2) = X1 | pp(aa(X0,bool,X2,sK23(X0,X1,X2))) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_81])])).
% 4.58/1.02 tff(f1423,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,fun(X0,X0))] : (the(X0,finite_fold1Set(X0,X1,X2)) = X3 | ~pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3)) | sK23(X0,X3,finite_fold1Set(X0,X1,X2)) = sK33(X0,sK23(X0,X3,finite_fold1Set(X0,X1,X2)),X2,X1)) ) | (~spl53_62 | ~spl53_81)),
% 4.58/1.02 inference(resolution,[],[f1401,f1066])).
% 4.58/1.02 tff(f1066,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)) | sK33(X0,X1,X2,X3) = X1) ) | ~spl53_62),
% 4.58/1.02 inference(avatar_component_clause,[],[f1065])).
% 4.58/1.02 tff(f1401,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (pp(aa(X0,bool,X2,sK23(X0,X1,X2))) | the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X1))) ) | ~spl53_81),
% 4.58/1.02 inference(avatar_component_clause,[],[f1400])).
% 4.58/1.02 tff(f9055,plain,(
% 4.58/1.02 spl53_381 | ~spl53_58 | ~spl53_81),
% 4.58/1.02 inference(avatar_split_clause,[],[f1420,f1400,f1048,f9053])).
% 4.58/1.02 tff(f9053,plain,(
% 4.58/1.02 spl53_381 <=> ! [X0 : bool,X1 : bool] : (the(bool,aa(bool,fun(bool,bool),fimplies,X0)) = X1 | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X0) | pp(sK23(bool,X1,aa(bool,fun(bool,bool),fimplies,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_381])])).
% 4.58/1.02 tff(f1420,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (the(bool,aa(bool,fun(bool,bool),fimplies,X0)) = X1 | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X0) | pp(sK23(bool,X1,aa(bool,fun(bool,bool),fimplies,X0)))) ) | (~spl53_58 | ~spl53_81)),
% 4.58/1.02 inference(resolution,[],[f1401,f1049])).
% 4.58/1.02 tff(f9051,plain,(
% 4.58/1.02 spl53_380 | ~spl53_57 | ~spl53_81),
% 4.58/1.02 inference(avatar_split_clause,[],[f1419,f1400,f1044,f9049])).
% 4.58/1.02 tff(f9049,plain,(
% 4.58/1.02 spl53_380 <=> ! [X0 : bool,X1 : bool] : (the(bool,aa(bool,fun(bool,bool),fdisj,X0)) = X1 | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | pp(X0) | pp(sK23(bool,X1,aa(bool,fun(bool,bool),fdisj,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_380])])).
% 4.58/1.02 tff(f1419,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (the(bool,aa(bool,fun(bool,bool),fdisj,X0)) = X1 | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | pp(X0) | pp(sK23(bool,X1,aa(bool,fun(bool,bool),fdisj,X0)))) ) | (~spl53_57 | ~spl53_81)),
% 4.58/1.02 inference(resolution,[],[f1401,f1045])).
% 4.58/1.02 tff(f9047,plain,(
% 4.58/1.02 spl53_379 | ~spl53_38 | ~spl53_61),
% 4.58/1.02 inference(avatar_split_clause,[],[f1102,f1061,f933,f9045])).
% 4.58/1.02 tff(f9045,plain,(
% 4.58/1.02 spl53_379 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (sK18(X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)) = X1 | ~sP0(X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_379])])).
% 4.58/1.02 tff(f933,plain,(
% 4.58/1.02 spl53_38 <=> ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,sK18(X0,X1))) | ~sP0(X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_38])])).
% 4.58/1.02 tff(f1102,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (sK18(X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)) = X1 | ~sP0(X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1))) ) | (~spl53_38 | ~spl53_61)),
% 4.58/1.02 inference(resolution,[],[f1062,f934])).
% 4.58/1.02 tff(f934,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,sK18(X0,X1))) | ~sP0(X0,X1)) ) | ~spl53_38),
% 4.58/1.02 inference(avatar_component_clause,[],[f933])).
% 4.58/1.02 tff(f9041,plain,(
% 4.58/1.02 spl53_378 | ~spl53_8 | spl53_153),
% 4.58/1.02 inference(avatar_split_clause,[],[f2461,f2457,f784,f9039])).
% 4.58/1.02 tff(f9039,plain,(
% 4.58/1.02 spl53_378 <=> ! [X0 : bool] : (~hoare_992312373derivs(a,g,aa(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,X0)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b))))) | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_378])])).
% 4.58/1.02 tff(f2461,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~hoare_992312373derivs(a,g,aa(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,X0)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b))))) | fTrue = X0) ) | (~spl53_8 | spl53_153)),
% 4.58/1.02 inference(superposition,[],[f2459,f785])).
% 4.58/1.02 tff(f8986,plain,(
% 4.58/1.02 ~spl53_377 | ~spl53_27 | ~spl53_34 | ~spl53_238 | ~spl53_325),
% 4.58/1.02 inference(avatar_split_clause,[],[f6804,f6739,f4227,f912,f871,f8983])).
% 4.58/1.02 tff(f8983,plain,(
% 4.58/1.02 spl53_377 <=> pp(sK28(bool,combk(bool,bool,fFalse),fNot))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_377])])).
% 4.58/1.02 tff(f871,plain,(
% 4.58/1.02 spl53_27 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : ~pp(aa(X0,bool,finite_fold1Set(X0,X2,bot_bot(fun(X0,bool))),X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_27])])).
% 4.58/1.02 tff(f912,plain,(
% 4.58/1.02 spl53_34 <=> ! [X0 : $tType] : bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_34])])).
% 4.58/1.02 tff(f4227,plain,(
% 4.58/1.02 spl53_238 <=> ! [X0 : $tType,X1 : fun(X0,fun(X0,X0))] : combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,combk(bool,X0,fFalse))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_238])])).
% 4.58/1.02 tff(f6739,plain,(
% 4.58/1.02 spl53_325 <=> ! [X0 : fun(bool,bool)] : (pp(aa(bool,bool,X0,the(bool,fNot))) | ~pp(sK28(bool,X0,fNot)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_325])])).
% 4.58/1.02 tff(f6804,plain,(
% 4.58/1.02 ~pp(sK28(bool,combk(bool,bool,fFalse),fNot)) | (~spl53_27 | ~spl53_34 | ~spl53_238 | ~spl53_325)),
% 4.58/1.02 inference(forward_demodulation,[],[f6803,f4228])).
% 4.58/1.02 tff(f4228,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,combk(bool,X0,fFalse))) ) | ~spl53_238),
% 4.58/1.02 inference(avatar_component_clause,[],[f4227])).
% 4.58/1.02 tff(f6803,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool))] : (~pp(sK28(bool,finite_fold1Set(bool,X0,combk(bool,bool,fFalse)),fNot))) ) | (~spl53_27 | ~spl53_34 | ~spl53_325)),
% 4.58/1.02 inference(forward_demodulation,[],[f6768,f913])).
% 4.58/1.02 tff(f913,plain,(
% 4.58/1.02 ( ! [X0 : $tType] : (bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse)) ) | ~spl53_34),
% 4.58/1.02 inference(avatar_component_clause,[],[f912])).
% 4.58/1.02 tff(f6768,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool))] : (~pp(sK28(bool,finite_fold1Set(bool,X0,bot_bot(fun(bool,bool))),fNot))) ) | (~spl53_27 | ~spl53_325)),
% 4.58/1.02 inference(resolution,[],[f6740,f872])).
% 4.58/1.02 tff(f872,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (~pp(aa(X0,bool,finite_fold1Set(X0,X2,bot_bot(fun(X0,bool))),X1))) ) | ~spl53_27),
% 4.58/1.02 inference(avatar_component_clause,[],[f871])).
% 4.58/1.02 tff(f6740,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool)] : (pp(aa(bool,bool,X0,the(bool,fNot))) | ~pp(sK28(bool,X0,fNot))) ) | ~spl53_325),
% 4.58/1.02 inference(avatar_component_clause,[],[f6739])).
% 4.58/1.02 tff(f8531,plain,(
% 4.58/1.02 spl53_376 | ~spl53_8 | ~spl53_129),
% 4.58/1.02 inference(avatar_split_clause,[],[f2149,f2040,f784,f8529])).
% 4.58/1.02 tff(f8529,plain,(
% 4.58/1.02 spl53_376 <=> ! [X1 : $tType,X0 : bool,X3 : fun(X1,bool),X2 : fun(fun(X1,bool),bool)] : (~pp(aa(fun(X1,bool),bool,X2,combk(bool,X1,X0))) | pp(aa(fun(X1,bool),bool,X2,X3)) | pp(aa(fun(X1,bool),bool,X2,sK22(X1,X2))) | ~finite_finite1(X1,X3) | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_376])])).
% 4.58/1.02 tff(f2040,plain,(
% 4.58/1.02 spl53_129 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | pp(aa(fun(X0,bool),bool,X1,sK22(X0,X1))) | ~finite_finite1(X0,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_129])])).
% 4.58/1.02 tff(f2149,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X2 : fun(fun(X1,bool),bool),X3 : fun(X1,bool),X0 : bool] : (~pp(aa(fun(X1,bool),bool,X2,combk(bool,X1,X0))) | pp(aa(fun(X1,bool),bool,X2,X3)) | pp(aa(fun(X1,bool),bool,X2,sK22(X1,X2))) | ~finite_finite1(X1,X3) | fTrue = X0) ) | (~spl53_8 | ~spl53_129)),
% 4.58/1.02 inference(superposition,[],[f2041,f785])).
% 4.58/1.02 tff(f2041,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | pp(aa(fun(X0,bool),bool,X1,sK22(X0,X1))) | ~finite_finite1(X0,X2)) ) | ~spl53_129),
% 4.58/1.02 inference(avatar_component_clause,[],[f2040])).
% 4.58/1.02 tff(f8527,plain,(
% 4.58/1.02 spl53_375 | ~spl53_8 | ~spl53_127),
% 4.58/1.02 inference(avatar_split_clause,[],[f2126,f2032,f784,f8525])).
% 4.58/1.02 tff(f8525,plain,(
% 4.58/1.02 spl53_375 <=> ! [X2 : bool,X0 : fun(bool,bool),X1 : fun(bool,bool)] : (~pp(aa(bool,bool,X0,fFalse)) | pp(aa(bool,bool,X0,the(bool,X1))) | pp(aa(bool,bool,X1,sK29(bool,X1,X2))) | ~pp(aa(bool,bool,X1,X2)) | fTrue = sK28(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_375])])).
% 4.58/1.02 tff(f2126,plain,(
% 4.58/1.02 ( ! [X2 : bool,X0 : fun(bool,bool),X1 : fun(bool,bool)] : (~pp(aa(bool,bool,X0,fFalse)) | pp(aa(bool,bool,X0,the(bool,X1))) | pp(aa(bool,bool,X1,sK29(bool,X1,X2))) | ~pp(aa(bool,bool,X1,X2)) | fTrue = sK28(bool,X0,X1)) ) | (~spl53_8 | ~spl53_127)),
% 4.58/1.02 inference(superposition,[],[f2033,f785])).
% 4.58/1.02 tff(f8523,plain,(
% 4.58/1.02 spl53_374 | ~spl53_8 | ~spl53_126),
% 4.58/1.02 inference(avatar_split_clause,[],[f2084,f2028,f784,f8521])).
% 4.58/1.02 tff(f8521,plain,(
% 4.58/1.02 spl53_374 <=> ! [X2 : bool,X0 : fun(bool,bool),X1 : fun(bool,bool)] : (pp(aa(bool,bool,X1,fFalse)) | pp(aa(bool,bool,X1,sK29(bool,X1,X2))) | pp(aa(bool,bool,X0,the(bool,X1))) | ~pp(aa(bool,bool,X1,X2)) | fTrue = sK28(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_374])])).
% 4.58/1.02 tff(f2084,plain,(
% 4.58/1.02 ( ! [X2 : bool,X0 : fun(bool,bool),X1 : fun(bool,bool)] : (pp(aa(bool,bool,X1,fFalse)) | pp(aa(bool,bool,X1,sK29(bool,X1,X2))) | pp(aa(bool,bool,X0,the(bool,X1))) | ~pp(aa(bool,bool,X1,X2)) | fTrue = sK28(bool,X0,X1)) ) | (~spl53_8 | ~spl53_126)),
% 4.58/1.02 inference(superposition,[],[f2029,f785])).
% 4.58/1.02 tff(f8519,plain,(
% 4.58/1.02 spl53_373 | ~spl53_8 | ~spl53_126),
% 4.58/1.02 inference(avatar_split_clause,[],[f2071,f2028,f784,f8517])).
% 4.58/1.02 tff(f8517,plain,(
% 4.58/1.02 spl53_373 <=> ! [X2 : fun(bool,bool),X0 : fun(bool,bool),X1 : bool] : (pp(aa(bool,bool,X0,fFalse)) | pp(aa(bool,bool,X0,sK28(bool,X2,X0))) | pp(aa(bool,bool,X2,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK29(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_373])])).
% 4.58/1.02 tff(f2071,plain,(
% 4.58/1.02 ( ! [X2 : fun(bool,bool),X0 : fun(bool,bool),X1 : bool] : (pp(aa(bool,bool,X0,fFalse)) | pp(aa(bool,bool,X0,sK28(bool,X2,X0))) | pp(aa(bool,bool,X2,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK29(bool,X0,X1)) ) | (~spl53_8 | ~spl53_126)),
% 4.58/1.02 inference(superposition,[],[f2029,f785])).
% 4.58/1.02 tff(f8515,plain,(
% 4.58/1.02 spl53_372 | ~spl53_71 | ~spl53_101),
% 4.58/1.02 inference(avatar_split_clause,[],[f1725,f1682,f1153,f8513])).
% 4.58/1.02 tff(f8513,plain,(
% 4.58/1.02 spl53_372 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X1,fun(X0,X0)),X4 : X0,X5 : fun(X1,bool),X2 : X0] : (~sP3(X0,X1,X2,X3,X4,X5) | sK49(X0,X1,X2,X3,X4,X5) = X2 | sP3(X0,X1,X2,X3,sK49(X0,X1,X2,X3,X4,X5),sK48(X0,X1,X2,X3,X4,X5)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_372])])).
% 4.58/1.02 tff(f1682,plain,(
% 4.58/1.02 spl53_101 <=> ! [X3 : $tType,X2 : $tType,X4 : X2,X0 : X2,X5 : fun(X3,bool),X1 : fun(X3,fun(X2,X2))] : (finite_fold_graph(X3,X2,X1,X0,sK48(X2,X3,X0,X1,X4,X5),sK49(X2,X3,X0,X1,X4,X5)) | ~sP3(X2,X3,X0,X1,X4,X5))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_101])])).
% 4.58/1.02 tff(f1725,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : fun(X1,fun(X0,X0)),X4 : X0,X5 : fun(X1,bool)] : (~sP3(X0,X1,X2,X3,X4,X5) | sK49(X0,X1,X2,X3,X4,X5) = X2 | sP3(X0,X1,X2,X3,sK49(X0,X1,X2,X3,X4,X5),sK48(X0,X1,X2,X3,X4,X5))) ) | (~spl53_71 | ~spl53_101)),
% 4.58/1.02 inference(resolution,[],[f1683,f1154])).
% 4.58/1.02 tff(f1683,plain,(
% 4.58/1.02 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (finite_fold_graph(X3,X2,X1,X0,sK48(X2,X3,X0,X1,X4,X5),sK49(X2,X3,X0,X1,X4,X5)) | ~sP3(X2,X3,X0,X1,X4,X5)) ) | ~spl53_101),
% 4.58/1.02 inference(avatar_component_clause,[],[f1682])).
% 4.58/1.02 tff(f8492,plain,(
% 4.58/1.02 spl53_371 | ~spl53_38 | ~spl53_100),
% 4.58/1.02 inference(avatar_split_clause,[],[f1691,f1678,f933,f8490])).
% 4.58/1.02 tff(f8490,plain,(
% 4.58/1.02 spl53_371 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,X2)) | pp(aa(fun(X0,bool),bool,X1,sK27(fun(X0,bool),X1,sK18(X0,X1)))) | the(fun(X0,bool),X1) = X2 | ~sP0(X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_371])])).
% 4.58/1.02 tff(f1691,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,X2)) | pp(aa(fun(X0,bool),bool,X1,sK27(fun(X0,bool),X1,sK18(X0,X1)))) | the(fun(X0,bool),X1) = X2 | ~sP0(X0,X1)) ) | (~spl53_38 | ~spl53_100)),
% 4.58/1.02 inference(resolution,[],[f1679,f934])).
% 4.58/1.02 tff(f8142,plain,(
% 4.58/1.02 ~spl53_370 | ~spl53_4 | ~spl53_116 | ~spl53_266),
% 4.58/1.02 inference(avatar_split_clause,[],[f4816,f4767,f1886,f767,f8139])).
% 4.58/1.02 tff(f8139,plain,(
% 4.58/1.02 spl53_370 <=> pp(sK5(bool,fNot,fFalse))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_370])])).
% 4.58/1.02 tff(f767,plain,(
% 4.58/1.02 spl53_4 <=> pp(fTrue)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_4])])).
% 4.58/1.02 tff(f1886,plain,(
% 4.58/1.02 spl53_116 <=> fTrue = aa(bool,bool,fNot,fFalse)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_116])])).
% 4.58/1.02 tff(f4767,plain,(
% 4.58/1.02 spl53_266 <=> ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | ~pp(sK5(bool,fNot,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_266])])).
% 4.58/1.02 tff(f4816,plain,(
% 4.58/1.02 ~pp(fTrue) | ~pp(sK5(bool,fNot,fFalse)) | (~spl53_116 | ~spl53_266)),
% 4.58/1.02 inference(superposition,[],[f4768,f1888])).
% 4.58/1.02 tff(f1888,plain,(
% 4.58/1.02 fTrue = aa(bool,bool,fNot,fFalse) | ~spl53_116),
% 4.58/1.02 inference(avatar_component_clause,[],[f1886])).
% 4.58/1.02 tff(f4768,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | ~pp(sK5(bool,fNot,X0))) ) | ~spl53_266),
% 4.58/1.02 inference(avatar_component_clause,[],[f4767])).
% 4.58/1.02 tff(f8095,plain,(
% 4.58/1.02 spl53_369 | ~spl53_140 | ~spl53_193),
% 4.58/1.02 inference(avatar_split_clause,[],[f3412,f3402,f2271,f8093])).
% 4.58/1.02 tff(f8093,plain,(
% 4.58/1.02 spl53_369 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),X1) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_369])])).
% 4.58/1.02 tff(f3412,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),X1) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_140 | ~spl53_193)),
% 4.58/1.02 inference(superposition,[],[f3403,f2272])).
% 4.58/1.02 tff(f8091,plain,(
% 4.58/1.02 spl53_368 | ~spl53_113 | ~spl53_156),
% 4.58/1.02 inference(avatar_split_clause,[],[f2531,f2521,f1800,f8089])).
% 4.58/1.02 tff(f8089,plain,(
% 4.58/1.02 spl53_368 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK13(X0,X1)),X1) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_368])])).
% 4.58/1.02 tff(f2521,plain,(
% 4.58/1.02 spl53_156 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_156])])).
% 4.58/1.02 tff(f2531,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK13(X0,X1)),X1) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_113 | ~spl53_156)),
% 4.58/1.02 inference(resolution,[],[f2522,f1801])).
% 4.58/1.02 tff(f2522,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = X1) ) | ~spl53_156),
% 4.58/1.02 inference(avatar_component_clause,[],[f2521])).
% 4.58/1.02 tff(f8087,plain,(
% 4.58/1.02 spl53_367 | ~spl53_112 | ~spl53_156),
% 4.58/1.02 inference(avatar_split_clause,[],[f2530,f2521,f1796,f8085])).
% 4.58/1.02 tff(f8085,plain,(
% 4.58/1.02 spl53_367 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK12(X0,X1)),X1) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_367])])).
% 4.58/1.02 tff(f2530,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK12(X0,X1)),X1) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_112 | ~spl53_156)),
% 4.58/1.02 inference(resolution,[],[f2522,f1797])).
% 4.58/1.02 tff(f8083,plain,(
% 4.58/1.02 spl53_366 | ~spl53_111 | ~spl53_156),
% 4.58/1.02 inference(avatar_split_clause,[],[f2529,f2521,f1792,f8081])).
% 4.58/1.02 tff(f8081,plain,(
% 4.58/1.02 spl53_366 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK4(X0,X1)),X1) = X1 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_366])])).
% 4.58/1.02 tff(f2529,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK4(X0,X1)),X1) = X1 | combk(bool,X0,fFalse) = X1) ) | (~spl53_111 | ~spl53_156)),
% 4.58/1.02 inference(resolution,[],[f2522,f1793])).
% 4.58/1.02 tff(f8079,plain,(
% 4.58/1.02 spl53_365 | ~spl53_61 | ~spl53_155),
% 4.58/1.02 inference(avatar_split_clause,[],[f2499,f2471,f1061,f8077])).
% 4.58/1.02 tff(f8077,plain,(
% 4.58/1.02 spl53_365 <=> ! [X2 : fun(hoare_28830079triple(state),bool),X0 : fun(state,fun(state,bool)),X1 : com] : (hoare_992312373derivs(state,X2,aa(hoare_28830079triple(state),fun(hoare_28830079triple(state),bool),fequal(hoare_28830079triple(state)),hoare_1841697145triple(state,fequal(state),X1,X0))) | sK40(state,X0,X1,X2,fequal(state)) = sK41(state,X0,X1,X2,fequal(state)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_365])])).
% 4.58/1.02 tff(f2499,plain,(
% 4.58/1.02 ( ! [X2 : fun(hoare_28830079triple(state),bool),X0 : fun(state,fun(state,bool)),X1 : com] : (hoare_992312373derivs(state,X2,aa(hoare_28830079triple(state),fun(hoare_28830079triple(state),bool),fequal(hoare_28830079triple(state)),hoare_1841697145triple(state,fequal(state),X1,X0))) | sK40(state,X0,X1,X2,fequal(state)) = sK41(state,X0,X1,X2,fequal(state))) ) | (~spl53_61 | ~spl53_155)),
% 4.58/1.02 inference(resolution,[],[f2472,f1062])).
% 4.58/1.02 tff(f8075,plain,(
% 4.58/1.02 spl53_364 | ~spl53_61 | ~spl53_154),
% 4.58/1.02 inference(avatar_split_clause,[],[f2476,f2467,f1061,f8073])).
% 4.58/1.02 tff(f8073,plain,(
% 4.58/1.02 spl53_364 <=> ! [X2 : fun(hoare_28830079triple(state),bool),X0 : fun(state,fun(state,bool)),X1 : com] : (hoare_992312373derivs(state,X2,aa(hoare_28830079triple(state),fun(hoare_28830079triple(state),bool),fequal(hoare_28830079triple(state)),hoare_1841697145triple(state,fequal(state),X1,X0))) | sK38(state,X0,X1,X2,fequal(state)) = sK39(state,X0,X1,X2,fequal(state)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_364])])).
% 4.58/1.02 tff(f2476,plain,(
% 4.58/1.02 ( ! [X2 : fun(hoare_28830079triple(state),bool),X0 : fun(state,fun(state,bool)),X1 : com] : (hoare_992312373derivs(state,X2,aa(hoare_28830079triple(state),fun(hoare_28830079triple(state),bool),fequal(hoare_28830079triple(state)),hoare_1841697145triple(state,fequal(state),X1,X0))) | sK38(state,X0,X1,X2,fequal(state)) = sK39(state,X0,X1,X2,fequal(state))) ) | (~spl53_61 | ~spl53_154)),
% 4.58/1.02 inference(resolution,[],[f2468,f1062])).
% 4.58/1.02 tff(f8071,plain,(
% 4.58/1.02 spl53_363 | ~spl53_14 | ~spl53_139),
% 4.58/1.02 inference(avatar_split_clause,[],[f2300,f2267,f811,f8069])).
% 4.58/1.02 tff(f8069,plain,(
% 4.58/1.02 spl53_363 <=> ! [X0 : $tType,X1 : X0] : aa(X0,fun(X0,bool),fequal(X0),X1) = aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_363])])).
% 4.58/1.02 tff(f811,plain,(
% 4.58/1.02 spl53_14 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : collect(X0,X1) = X1),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_14])])).
% 4.58/1.02 tff(f2267,plain,(
% 4.58/1.02 spl53_139 <=> ! [X0 : $tType,X1 : X0] : aa(X0,fun(X0,bool),fequal(X0),X1) = collect(X0,aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_139])])).
% 4.58/1.02 tff(f2300,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) ) | (~spl53_14 | ~spl53_139)),
% 4.58/1.02 inference(superposition,[],[f2268,f812])).
% 4.58/1.02 tff(f812,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (collect(X0,X1) = X1) ) | ~spl53_14),
% 4.58/1.02 inference(avatar_component_clause,[],[f811])).
% 4.58/1.02 tff(f2268,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = collect(X0,aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))) ) | ~spl53_139),
% 4.58/1.02 inference(avatar_component_clause,[],[f2267])).
% 4.58/1.02 tff(f8067,plain,(
% 4.58/1.02 spl53_362 | ~spl53_81 | ~spl53_100),
% 4.58/1.02 inference(avatar_split_clause,[],[f1700,f1678,f1400,f8065])).
% 4.58/1.02 tff(f8065,plain,(
% 4.58/1.02 spl53_362 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK23(X0,X3,X1)))) | the(X0,X1) = X2 | the(X0,X1) = X3 | ~pp(aa(X0,bool,X1,X3)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_362])])).
% 4.58/1.02 tff(f1700,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK23(X0,X3,X1)))) | the(X0,X1) = X2 | the(X0,X1) = X3 | ~pp(aa(X0,bool,X1,X3))) ) | (~spl53_81 | ~spl53_100)),
% 4.58/1.02 inference(resolution,[],[f1679,f1401])).
% 4.58/1.02 tff(f8040,plain,(
% 4.58/1.02 spl53_361 | ~spl53_60 | ~spl53_89),
% 4.58/1.02 inference(avatar_split_clause,[],[f1569,f1482,f1057,f8038])).
% 4.58/1.02 tff(f8038,plain,(
% 4.58/1.02 spl53_361 <=> ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,finite_fold1Set(bool,X0,X1))) | pp(the(bool,finite_fold1Set(bool,X0,the(fun(bool,bool),finite_fold1(bool,X0))))) | pp(the(bool,finite_fold1Set(bool,X0,sK24(fun(bool,bool),X1,finite_fold1(bool,X0))))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_361])])).
% 4.58/1.02 tff(f1569,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,finite_fold1Set(bool,X0,X1))) | pp(the(bool,finite_fold1Set(bool,X0,the(fun(bool,bool),finite_fold1(bool,X0))))) | pp(the(bool,finite_fold1Set(bool,X0,sK24(fun(bool,bool),X1,finite_fold1(bool,X0)))))) ) | (~spl53_60 | ~spl53_89)),
% 4.58/1.02 inference(forward_demodulation,[],[f1568,f1058])).
% 4.58/1.02 tff(f1568,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,the(fun(bool,bool),finite_fold1(bool,X0))))) | pp(the(bool,finite_fold1Set(bool,X0,sK24(fun(bool,bool),X1,finite_fold1(bool,X0))))) | ~pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1))) ) | (~spl53_60 | ~spl53_89)),
% 4.58/1.02 inference(forward_demodulation,[],[f1564,f1058])).
% 4.58/1.02 tff(f1564,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,sK24(fun(bool,bool),X1,finite_fold1(bool,X0))))) | pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),the(fun(bool,bool),finite_fold1(bool,X0)))) | ~pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1))) ) | (~spl53_60 | ~spl53_89)),
% 4.58/1.02 inference(superposition,[],[f1483,f1058])).
% 4.58/1.02 tff(f8036,plain,(
% 4.58/1.02 spl53_360 | ~spl53_60 | ~spl53_87),
% 4.58/1.02 inference(avatar_split_clause,[],[f1536,f1473,f1057,f8034])).
% 4.58/1.02 tff(f8034,plain,(
% 4.58/1.02 spl53_360 <=> ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,finite_fold1Set(bool,X0,X1))) | pp(the(bool,finite_fold1Set(bool,X0,the(fun(bool,bool),finite_fold1(bool,X0))))) | pp(the(bool,finite_fold1Set(bool,X0,sK5(fun(bool,bool),finite_fold1(bool,X0),X1)))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_360])])).
% 4.58/1.02 tff(f1536,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,finite_fold1Set(bool,X0,X1))) | pp(the(bool,finite_fold1Set(bool,X0,the(fun(bool,bool),finite_fold1(bool,X0))))) | pp(the(bool,finite_fold1Set(bool,X0,sK5(fun(bool,bool),finite_fold1(bool,X0),X1))))) ) | (~spl53_60 | ~spl53_87)),
% 4.58/1.02 inference(forward_demodulation,[],[f1535,f1058])).
% 4.58/1.02 tff(f1535,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,the(fun(bool,bool),finite_fold1(bool,X0))))) | pp(the(bool,finite_fold1Set(bool,X0,sK5(fun(bool,bool),finite_fold1(bool,X0),X1)))) | ~pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1))) ) | (~spl53_60 | ~spl53_87)),
% 4.58/1.02 inference(forward_demodulation,[],[f1531,f1058])).
% 4.58/1.02 tff(f1531,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,sK5(fun(bool,bool),finite_fold1(bool,X0),X1)))) | pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),the(fun(bool,bool),finite_fold1(bool,X0)))) | ~pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1))) ) | (~spl53_60 | ~spl53_87)),
% 4.58/1.02 inference(superposition,[],[f1474,f1058])).
% 4.58/1.02 tff(f8032,plain,(
% 4.58/1.02 spl53_359 | ~spl53_49 | ~spl53_81),
% 4.58/1.02 inference(avatar_split_clause,[],[f1417,f1400,f992,f8030])).
% 4.58/1.02 tff(f8030,plain,(
% 4.58/1.02 spl53_359 <=> ! [X0 : bool,X1 : bool] : (the(bool,aa(bool,fun(bool,bool),fconj,X0)) = X1 | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X0),X1)) | pp(sK23(bool,X1,aa(bool,fun(bool,bool),fconj,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_359])])).
% 4.58/1.02 tff(f1417,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (the(bool,aa(bool,fun(bool,bool),fconj,X0)) = X1 | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X0),X1)) | pp(sK23(bool,X1,aa(bool,fun(bool,bool),fconj,X0)))) ) | (~spl53_49 | ~spl53_81)),
% 4.58/1.02 inference(resolution,[],[f1401,f993])).
% 4.58/1.02 tff(f7739,plain,(
% 4.58/1.02 spl53_358 | ~spl53_15 | ~spl53_323),
% 4.58/1.02 inference(avatar_split_clause,[],[f6701,f6695,f815,f7737])).
% 4.58/1.02 tff(f7737,plain,(
% 4.58/1.02 spl53_358 <=> ! [X0 : bool] : (~pp(sK29(bool,fNot,X0)) | pp(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_358])])).
% 4.58/1.02 tff(f815,plain,(
% 4.58/1.02 spl53_15 <=> ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_15])])).
% 4.58/1.02 tff(f6695,plain,(
% 4.58/1.02 spl53_323 <=> ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | ~pp(sK29(bool,fNot,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_323])])).
% 4.58/1.02 tff(f6701,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~pp(sK29(bool,fNot,X0)) | pp(X0)) ) | (~spl53_15 | ~spl53_323)),
% 4.58/1.02 inference(resolution,[],[f6696,f816])).
% 4.58/1.02 tff(f816,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0)) ) | ~spl53_15),
% 4.58/1.02 inference(avatar_component_clause,[],[f815])).
% 4.58/1.02 tff(f6696,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | ~pp(sK29(bool,fNot,X0))) ) | ~spl53_323),
% 4.58/1.02 inference(avatar_component_clause,[],[f6695])).
% 4.58/1.02 tff(f7721,plain,(
% 4.58/1.02 spl53_357 | ~spl53_48 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2765,f2702,f988,f7719])).
% 4.58/1.02 tff(f7719,plain,(
% 4.58/1.02 spl53_357 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0)) | pp(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_357])])).
% 4.58/1.02 tff(f988,plain,(
% 4.58/1.02 spl53_48 <=> ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_48])])).
% 4.58/1.02 tff(f2765,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (~pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0)) | pp(X0)) ) | (~spl53_48 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f989,f2703])).
% 4.58/1.02 tff(f989,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | pp(X1)) ) | ~spl53_48),
% 4.58/1.02 inference(avatar_component_clause,[],[f988])).
% 4.58/1.02 tff(f7717,plain,(
% 4.58/1.02 spl53_356 | ~spl53_47 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2761,f2702,f984,f7715])).
% 4.58/1.02 tff(f7715,plain,(
% 4.58/1.02 spl53_356 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0)) | pp(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_356])])).
% 4.58/1.02 tff(f984,plain,(
% 4.58/1.02 spl53_47 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) | pp(X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_47])])).
% 4.58/1.02 tff(f2761,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0)) | pp(X0)) ) | (~spl53_47 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f985,f2703])).
% 4.58/1.02 tff(f985,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) | pp(X1)) ) | ~spl53_47),
% 4.58/1.02 inference(avatar_component_clause,[],[f984])).
% 4.58/1.02 tff(f7713,plain,(
% 4.58/1.02 spl53_355 | ~spl53_45 | ~spl53_165),
% 4.58/1.02 inference(avatar_split_clause,[],[f2758,f2702,f976,f7711])).
% 4.58/1.02 tff(f7711,plain,(
% 4.58/1.02 spl53_355 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0)) | ~pp(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_355])])).
% 4.58/1.02 tff(f976,plain,(
% 4.58/1.02 spl53_45 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_45])])).
% 4.58/1.02 tff(f2758,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0)) | ~pp(X0)) ) | (~spl53_45 | ~spl53_165)),
% 4.58/1.02 inference(superposition,[],[f977,f2703])).
% 4.58/1.02 tff(f977,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1)) ) | ~spl53_45),
% 4.58/1.02 inference(avatar_component_clause,[],[f976])).
% 4.58/1.02 tff(f7709,plain,(
% 4.58/1.02 spl53_354 | ~spl53_92 | ~spl53_162),
% 4.58/1.02 inference(avatar_split_clause,[],[f2619,f2596,f1494,f7707])).
% 4.58/1.02 tff(f7707,plain,(
% 4.58/1.02 spl53_354 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),sK26(X0,X2,X1)) = X2 | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_354])])).
% 4.58/1.02 tff(f1494,plain,(
% 4.58/1.02 spl53_92 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | ~pp(aa(X0,bool,X1,X2)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_92])])).
% 4.58/1.02 tff(f2619,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),sK26(X0,X2,X1)) = X2 | ~pp(aa(X0,bool,X2,X1))) ) | (~spl53_92 | ~spl53_162)),
% 4.58/1.02 inference(resolution,[],[f2597,f1495])).
% 4.58/1.02 tff(f1495,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | ~pp(aa(X0,bool,X1,X2))) ) | ~spl53_92),
% 4.58/1.02 inference(avatar_component_clause,[],[f1494])).
% 4.58/1.02 tff(f7705,plain,(
% 4.58/1.02 spl53_353 | ~spl53_92 | ~spl53_161),
% 4.58/1.02 inference(avatar_split_clause,[],[f2599,f2592,f1494,f7703])).
% 4.58/1.02 tff(f7703,plain,(
% 4.58/1.02 spl53_353 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),sK25(X0,X2,X1)) = X2 | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_353])])).
% 4.58/1.02 tff(f2599,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),sK25(X0,X2,X1)) = X2 | ~pp(aa(X0,bool,X2,X1))) ) | (~spl53_92 | ~spl53_161)),
% 4.58/1.02 inference(resolution,[],[f2593,f1495])).
% 4.58/1.02 tff(f7701,plain,(
% 4.58/1.02 spl53_352 | ~spl53_69 | ~spl53_77),
% 4.58/1.02 inference(avatar_split_clause,[],[f1378,f1184,f1114,f7699])).
% 4.58/1.02 tff(f7699,plain,(
% 4.58/1.02 spl53_352 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : (sK11(X0,finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2))) = X2 | combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_352])])).
% 4.58/1.02 tff(f1114,plain,(
% 4.58/1.02 spl53_69 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK11(X0,X1))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_69])])).
% 4.58/1.02 tff(f1378,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : (sK11(X0,finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2))) = X2 | combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2))) ) | (~spl53_69 | ~spl53_77)),
% 4.58/1.02 inference(resolution,[],[f1185,f1115])).
% 4.58/1.02 tff(f1115,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,sK11(X0,X1))) | combk(bool,X0,fFalse) = X1) ) | ~spl53_69),
% 4.58/1.02 inference(avatar_component_clause,[],[f1114])).
% 4.58/1.02 tff(f7697,plain,(
% 4.58/1.02 spl53_351 | ~spl53_68 | ~spl53_77),
% 4.58/1.02 inference(avatar_split_clause,[],[f1377,f1184,f1110,f7695])).
% 4.58/1.02 tff(f7695,plain,(
% 4.58/1.02 spl53_351 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : (sK10(X0,finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2))) = X2 | combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_351])])).
% 4.58/1.02 tff(f1110,plain,(
% 4.58/1.02 spl53_68 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK10(X0,X1))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_68])])).
% 4.58/1.02 tff(f1377,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : (sK10(X0,finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2))) = X2 | combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2))) ) | (~spl53_68 | ~spl53_77)),
% 4.58/1.02 inference(resolution,[],[f1185,f1111])).
% 4.58/1.02 tff(f1111,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,sK10(X0,X1))) | combk(bool,X0,fFalse) = X1) ) | ~spl53_68),
% 4.58/1.02 inference(avatar_component_clause,[],[f1110])).
% 4.58/1.02 tff(f7693,plain,(
% 4.58/1.02 spl53_350 | ~spl53_38 | ~spl53_62),
% 4.58/1.02 inference(avatar_split_clause,[],[f1105,f1065,f933,f7691])).
% 4.58/1.02 tff(f7691,plain,(
% 4.58/1.02 spl53_350 <=> ! [X0 : $tType,X2 : fun(fun(X0,bool),bool),X1 : fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)))] : (sK18(X0,finite_fold1Set(fun(X0,bool),X1,X2)) = sK33(fun(X0,bool),sK18(X0,finite_fold1Set(fun(X0,bool),X1,X2)),X2,X1) | ~sP0(X0,finite_fold1Set(fun(X0,bool),X1,X2)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_350])])).
% 4.58/1.02 tff(f1105,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(fun(X0,bool),bool),X1 : fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)))] : (sK18(X0,finite_fold1Set(fun(X0,bool),X1,X2)) = sK33(fun(X0,bool),sK18(X0,finite_fold1Set(fun(X0,bool),X1,X2)),X2,X1) | ~sP0(X0,finite_fold1Set(fun(X0,bool),X1,X2))) ) | (~spl53_38 | ~spl53_62)),
% 4.58/1.02 inference(resolution,[],[f1066,f934])).
% 4.58/1.02 tff(f7689,plain,(
% 4.58/1.02 spl53_349 | ~spl53_15 | ~spl53_268),
% 4.58/1.02 inference(avatar_split_clause,[],[f6460,f4826,f815,f7687])).
% 4.58/1.02 tff(f7687,plain,(
% 4.58/1.02 spl53_349 <=> ! [X0 : bool] : (~pp(sK24(bool,X0,fNot)) | pp(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_349])])).
% 4.58/1.02 tff(f4826,plain,(
% 4.58/1.02 spl53_268 <=> ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | ~pp(sK24(bool,X0,fNot)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_268])])).
% 4.58/1.02 tff(f6460,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~pp(sK24(bool,X0,fNot)) | pp(X0)) ) | (~spl53_15 | ~spl53_268)),
% 4.58/1.02 inference(resolution,[],[f4827,f816])).
% 4.58/1.02 tff(f4827,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | ~pp(sK24(bool,X0,fNot))) ) | ~spl53_268),
% 4.58/1.02 inference(avatar_component_clause,[],[f4826])).
% 4.58/1.02 tff(f7587,plain,(
% 4.58/1.02 spl53_348 | ~spl53_92 | ~spl53_160),
% 4.58/1.02 inference(avatar_split_clause,[],[f2578,f2575,f1494,f7585])).
% 4.58/1.02 tff(f7585,plain,(
% 4.58/1.02 spl53_348 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | ~finite_finite1(X0,X2) | ~pp(aa(X0,bool,sK22(X0,X1),sK21(X0,X1))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_348])])).
% 4.58/1.02 tff(f2575,plain,(
% 4.58/1.02 spl53_160 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK21(X0,X1)),sK22(X0,X1))) | ~finite_finite1(X0,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_160])])).
% 4.58/1.02 tff(f2578,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | ~finite_finite1(X0,X2) | ~pp(aa(X0,bool,sK22(X0,X1),sK21(X0,X1)))) ) | (~spl53_92 | ~spl53_160)),
% 4.58/1.02 inference(resolution,[],[f2576,f1495])).
% 4.58/1.02 tff(f2576,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK21(X0,X1)),sK22(X0,X1))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | ~finite_finite1(X0,X2)) ) | ~spl53_160),
% 4.58/1.02 inference(avatar_component_clause,[],[f2575])).
% 4.58/1.02 tff(f7583,plain,(
% 4.58/1.02 spl53_347 | ~spl53_8 | ~spl53_121),
% 4.58/1.02 inference(avatar_split_clause,[],[f1980,f1947,f784,f7581])).
% 4.58/1.02 tff(f7581,plain,(
% 4.58/1.02 spl53_347 <=> ! [X0 : fun(bool,bool)] : (~pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),sK9(bool,X0))) | combk(bool,bool,fFalse) = X0 | fTrue = sK8(bool,X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_347])])).
% 4.58/1.02 tff(f1947,plain,(
% 4.58/1.02 spl53_121 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),sK9(X0,X1))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_121])])).
% 4.58/1.02 tff(f1980,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool)] : (~pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),sK9(bool,X0))) | combk(bool,bool,fFalse) = X0 | fTrue = sK8(bool,X0)) ) | (~spl53_8 | ~spl53_121)),
% 4.58/1.02 inference(superposition,[],[f1948,f785])).
% 4.58/1.02 tff(f1948,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),sK9(X0,X1))) | combk(bool,X0,fFalse) = X1) ) | ~spl53_121),
% 4.58/1.02 inference(avatar_component_clause,[],[f1947])).
% 4.58/1.02 tff(f7579,plain,(
% 4.58/1.02 spl53_346 | ~spl53_8 | ~spl53_120),
% 4.58/1.02 inference(avatar_split_clause,[],[f1959,f1943,f784,f7577])).
% 4.58/1.02 tff(f7577,plain,(
% 4.58/1.02 spl53_346 <=> ! [X2 : fun(bool,bool),X0 : fun(bool,bool),X1 : bool] : (fFalse != X1 | ~pp(aa(bool,bool,X2,sK28(bool,X2,X0))) | pp(aa(bool,bool,X2,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK29(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_346])])).
% 4.58/1.02 tff(f1943,plain,(
% 4.58/1.02 spl53_120 <=> ! [X0 : $tType,X4 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X2))) | ~pp(aa(X0,bool,X1,sK28(X0,X1,X2))) | sK29(X0,X2,X4) != X4 | ~pp(aa(X0,bool,X2,X4)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_120])])).
% 4.58/1.02 tff(f1959,plain,(
% 4.58/1.02 ( ! [X2 : fun(bool,bool),X0 : fun(bool,bool),X1 : bool] : (fFalse != X1 | ~pp(aa(bool,bool,X2,sK28(bool,X2,X0))) | pp(aa(bool,bool,X2,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK29(bool,X0,X1)) ) | (~spl53_8 | ~spl53_120)),
% 4.58/1.02 inference(superposition,[],[f1944,f785])).
% 4.58/1.02 tff(f1944,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (sK29(X0,X2,X4) != X4 | ~pp(aa(X0,bool,X1,sK28(X0,X1,X2))) | pp(aa(X0,bool,X1,the(X0,X2))) | ~pp(aa(X0,bool,X2,X4))) ) | ~spl53_120),
% 4.58/1.02 inference(avatar_component_clause,[],[f1943])).
% 4.58/1.02 tff(f7575,plain,(
% 4.58/1.02 spl53_345 | ~spl53_8 | ~spl53_119),
% 4.58/1.02 inference(avatar_split_clause,[],[f1954,f1939,f784,f7573])).
% 4.58/1.02 tff(f7573,plain,(
% 4.58/1.02 spl53_345 <=> ! [X2 : fun(bool,bool),X0 : fun(bool,bool),X1 : bool] : (fFalse != X1 | pp(aa(bool,bool,X0,sK28(bool,X2,X0))) | pp(aa(bool,bool,X2,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK29(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_345])])).
% 4.58/1.02 tff(f1939,plain,(
% 4.58/1.02 spl53_119 <=> ! [X0 : $tType,X4 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X2))) | pp(aa(X0,bool,X2,sK28(X0,X1,X2))) | sK29(X0,X2,X4) != X4 | ~pp(aa(X0,bool,X2,X4)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_119])])).
% 4.58/1.02 tff(f1954,plain,(
% 4.58/1.02 ( ! [X2 : fun(bool,bool),X0 : fun(bool,bool),X1 : bool] : (fFalse != X1 | pp(aa(bool,bool,X0,sK28(bool,X2,X0))) | pp(aa(bool,bool,X2,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK29(bool,X0,X1)) ) | (~spl53_8 | ~spl53_119)),
% 4.58/1.02 inference(superposition,[],[f1940,f785])).
% 4.58/1.02 tff(f1940,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (sK29(X0,X2,X4) != X4 | pp(aa(X0,bool,X2,sK28(X0,X1,X2))) | pp(aa(X0,bool,X1,the(X0,X2))) | ~pp(aa(X0,bool,X2,X4))) ) | ~spl53_119),
% 4.58/1.02 inference(avatar_component_clause,[],[f1939])).
% 4.58/1.02 tff(f7571,plain,(
% 4.58/1.02 spl53_344 | ~spl53_60 | ~spl53_81),
% 4.58/1.02 inference(avatar_split_clause,[],[f1440,f1400,f1057,f7569])).
% 4.58/1.02 tff(f7569,plain,(
% 4.58/1.02 spl53_344 <=> ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,finite_fold1Set(bool,X0,X1))) | pp(the(bool,finite_fold1Set(bool,X0,sK23(fun(bool,bool),X1,finite_fold1(bool,X0))))) | the(fun(bool,bool),finite_fold1(bool,X0)) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_344])])).
% 4.58/1.02 tff(f1440,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,finite_fold1Set(bool,X0,X1))) | pp(the(bool,finite_fold1Set(bool,X0,sK23(fun(bool,bool),X1,finite_fold1(bool,X0))))) | the(fun(bool,bool),finite_fold1(bool,X0)) = X1) ) | (~spl53_60 | ~spl53_81)),
% 4.58/1.02 inference(forward_demodulation,[],[f1436,f1058])).
% 4.58/1.02 tff(f1436,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,sK23(fun(bool,bool),X1,finite_fold1(bool,X0))))) | the(fun(bool,bool),finite_fold1(bool,X0)) = X1 | ~pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1))) ) | (~spl53_60 | ~spl53_81)),
% 4.58/1.02 inference(superposition,[],[f1401,f1058])).
% 4.58/1.02 tff(f7517,plain,(
% 4.58/1.02 spl53_343 | ~spl53_8 | ~spl53_117),
% 4.58/1.02 inference(avatar_split_clause,[],[f1932,f1918,f784,f7515])).
% 4.58/1.02 tff(f7515,plain,(
% 4.58/1.02 spl53_343 <=> ! [X2 : fun(bool,fun(bool,bool)),X0 : bool,X1 : fun(bool,bool)] : (finite_fold_graph(bool,bool,X2,sK31(bool,X0,X1,X2),sK32(bool,X0,X1,X2),fFalse) | ~pp(aa(bool,bool,finite_fold1Set(bool,X2,X1),X0)) | fTrue = sK33(bool,X0,X1,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_343])])).
% 4.58/1.02 tff(f1932,plain,(
% 4.58/1.02 ( ! [X2 : fun(bool,fun(bool,bool)),X0 : bool,X1 : fun(bool,bool)] : (finite_fold_graph(bool,bool,X2,sK31(bool,X0,X1,X2),sK32(bool,X0,X1,X2),fFalse) | ~pp(aa(bool,bool,finite_fold1Set(bool,X2,X1),X0)) | fTrue = sK33(bool,X0,X1,X2)) ) | (~spl53_8 | ~spl53_117)),
% 4.58/1.02 inference(superposition,[],[f1919,f785])).
% 4.58/1.02 tff(f7513,plain,(
% 4.58/1.02 spl53_342 | ~spl53_8 | ~spl53_117),
% 4.58/1.02 inference(avatar_split_clause,[],[f1927,f1918,f784,f7511])).
% 4.58/1.02 tff(f7511,plain,(
% 4.58/1.02 spl53_342 <=> ! [X2 : fun(bool,fun(bool,bool)),X0 : bool,X1 : fun(bool,bool)] : (finite_fold_graph(bool,bool,X2,fFalse,sK32(bool,X0,X1,X2),sK33(bool,X0,X1,X2)) | ~pp(aa(bool,bool,finite_fold1Set(bool,X2,X1),X0)) | fTrue = sK31(bool,X0,X1,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_342])])).
% 4.58/1.02 tff(f1927,plain,(
% 4.58/1.02 ( ! [X2 : fun(bool,fun(bool,bool)),X0 : bool,X1 : fun(bool,bool)] : (finite_fold_graph(bool,bool,X2,fFalse,sK32(bool,X0,X1,X2),sK33(bool,X0,X1,X2)) | ~pp(aa(bool,bool,finite_fold1Set(bool,X2,X1),X0)) | fTrue = sK31(bool,X0,X1,X2)) ) | (~spl53_8 | ~spl53_117)),
% 4.58/1.02 inference(superposition,[],[f1919,f785])).
% 4.58/1.02 tff(f7194,plain,(
% 4.58/1.02 ~spl53_341 | ~spl53_266 | ~spl53_267),
% 4.58/1.02 inference(avatar_split_clause,[],[f4829,f4770,f4767,f7191])).
% 4.58/1.02 tff(f7191,plain,(
% 4.58/1.02 spl53_341 <=> pp(sK5(bool,fNot,the(bool,fNot)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_341])])).
% 4.58/1.02 tff(f4770,plain,(
% 4.58/1.02 spl53_267 <=> pp(aa(bool,bool,fNot,the(bool,fNot)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_267])])).
% 4.58/1.02 tff(f4829,plain,(
% 4.58/1.02 ~pp(sK5(bool,fNot,the(bool,fNot))) | (~spl53_266 | ~spl53_267)),
% 4.58/1.02 inference(resolution,[],[f4772,f4768])).
% 4.58/1.02 tff(f4772,plain,(
% 4.58/1.02 pp(aa(bool,bool,fNot,the(bool,fNot))) | ~spl53_267),
% 4.58/1.02 inference(avatar_component_clause,[],[f4770])).
% 4.58/1.02 tff(f7015,plain,(
% 4.58/1.02 spl53_340 | ~spl53_92 | ~spl53_156),
% 4.58/1.02 inference(avatar_split_clause,[],[f2528,f2521,f1494,f7013])).
% 4.58/1.02 tff(f7013,plain,(
% 4.58/1.02 spl53_340 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = X2 | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_340])])).
% 4.58/1.02 tff(f2528,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = X2 | ~pp(aa(X0,bool,X2,X1))) ) | (~spl53_92 | ~spl53_156)),
% 4.58/1.02 inference(resolution,[],[f2522,f1495])).
% 4.58/1.02 tff(f7011,plain,(
% 4.58/1.02 spl53_339 | ~spl53_8 | ~spl53_115),
% 4.58/1.02 inference(avatar_split_clause,[],[f1899,f1808,f784,f7009])).
% 4.58/1.02 tff(f7009,plain,(
% 4.58/1.02 spl53_339 <=> ! [X1 : $tType,X0 : bool,X3 : fun(X1,bool),X2 : fun(fun(X1,bool),bool)] : (~pp(aa(fun(X1,bool),bool,X2,combk(bool,X1,X0))) | pp(aa(fun(X1,bool),bool,X2,X3)) | finite_finite1(X1,sK22(X1,X2)) | ~finite_finite1(X1,X3) | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_339])])).
% 4.58/1.02 tff(f1808,plain,(
% 4.58/1.02 spl53_115 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | finite_finite1(X0,sK22(X0,X1)) | ~finite_finite1(X0,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_115])])).
% 4.58/1.02 tff(f1899,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X2 : fun(fun(X1,bool),bool),X3 : fun(X1,bool),X0 : bool] : (~pp(aa(fun(X1,bool),bool,X2,combk(bool,X1,X0))) | pp(aa(fun(X1,bool),bool,X2,X3)) | finite_finite1(X1,sK22(X1,X2)) | ~finite_finite1(X1,X3) | fTrue = X0) ) | (~spl53_8 | ~spl53_115)),
% 4.58/1.02 inference(superposition,[],[f1809,f785])).
% 4.58/1.02 tff(f1809,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | finite_finite1(X0,sK22(X0,X1)) | ~finite_finite1(X0,X2)) ) | ~spl53_115),
% 4.58/1.02 inference(avatar_component_clause,[],[f1808])).
% 4.58/1.02 tff(f7007,plain,(
% 4.58/1.02 spl53_338 | ~spl53_8 | ~spl53_113),
% 4.58/1.02 inference(avatar_split_clause,[],[f1879,f1800,f784,f7005])).
% 4.58/1.02 tff(f7005,plain,(
% 4.58/1.02 spl53_338 <=> ! [X0 : fun(bool,bool)] : (pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0)) | combk(bool,bool,fFalse) = X0 | fTrue = sK13(bool,X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_338])])).
% 4.58/1.02 tff(f1879,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool)] : (pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0)) | combk(bool,bool,fFalse) = X0 | fTrue = sK13(bool,X0)) ) | (~spl53_8 | ~spl53_113)),
% 4.58/1.02 inference(superposition,[],[f1801,f785])).
% 4.58/1.02 tff(f7003,plain,(
% 4.58/1.02 spl53_337 | ~spl53_8 | ~spl53_112),
% 4.58/1.02 inference(avatar_split_clause,[],[f1864,f1796,f784,f7001])).
% 4.58/1.02 tff(f7001,plain,(
% 4.58/1.02 spl53_337 <=> ! [X0 : fun(bool,bool)] : (pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0)) | combk(bool,bool,fFalse) = X0 | fTrue = sK12(bool,X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_337])])).
% 4.58/1.02 tff(f1864,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool)] : (pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0)) | combk(bool,bool,fFalse) = X0 | fTrue = sK12(bool,X0)) ) | (~spl53_8 | ~spl53_112)),
% 4.58/1.02 inference(superposition,[],[f1797,f785])).
% 4.58/1.02 tff(f6999,plain,(
% 4.58/1.02 spl53_336 | ~spl53_8 | ~spl53_111),
% 4.58/1.02 inference(avatar_split_clause,[],[f1849,f1792,f784,f6997])).
% 4.58/1.02 tff(f6997,plain,(
% 4.58/1.02 spl53_336 <=> ! [X0 : fun(bool,bool)] : (pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0)) | combk(bool,bool,fFalse) = X0 | fTrue = sK4(bool,X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_336])])).
% 4.58/1.02 tff(f1849,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool)] : (pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0)) | combk(bool,bool,fFalse) = X0 | fTrue = sK4(bool,X0)) ) | (~spl53_8 | ~spl53_111)),
% 4.58/1.02 inference(superposition,[],[f1793,f785])).
% 4.58/1.02 tff(f6995,plain,(
% 4.58/1.02 spl53_335 | ~spl53_8 | ~spl53_109),
% 4.58/1.02 inference(avatar_split_clause,[],[f1815,f1761,f784,f6993])).
% 4.58/1.02 tff(f6993,plain,(
% 4.58/1.02 spl53_335 <=> ! [X1 : $tType,X0 : $tType,X2 : fun(X1,bool),X4 : X0,X3 : fun(X0,X1)] : (fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) | fTrue = aa(X0,bool,aa(fun(X0,X1),fun(X0,bool),combb(X1,bool,X0,X2),X3),X4))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_335])])).
% 4.58/1.02 tff(f1761,plain,(
% 4.58/1.02 spl53_109 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : fun(X1,X0),X4 : fun(X2,X1),X3 : X2] : aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),combb(X1,X0,X2,X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_109])])).
% 4.58/1.02 tff(f1815,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,bool),X3 : fun(X0,X1),X4 : X0] : (fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) | fTrue = aa(X0,bool,aa(fun(X0,X1),fun(X0,bool),combb(X1,bool,X0,X2),X3),X4)) ) | (~spl53_8 | ~spl53_109)),
% 4.58/1.02 inference(superposition,[],[f1762,f785])).
% 4.58/1.02 tff(f1762,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : (aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),combb(X1,X0,X2,X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))) ) | ~spl53_109),
% 4.58/1.02 inference(avatar_component_clause,[],[f1761])).
% 4.58/1.02 tff(f6990,plain,(
% 4.58/1.02 spl53_334 | ~spl53_8 | ~spl53_103),
% 4.58/1.02 inference(avatar_split_clause,[],[f1772,f1732,f784,f6988])).
% 4.58/1.02 tff(f6988,plain,(
% 4.58/1.02 spl53_334 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = the(bool,aa(bool,fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combc(bool,bool,bool),fequal(bool)),X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_334])])).
% 4.58/1.02 tff(f1732,plain,(
% 4.58/1.02 spl53_103 <=> ! [X0 : $tType,X1 : X0] : the(X0,aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) = X1),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_103])])).
% 4.58/1.02 tff(f1772,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (fFalse = X0 | fTrue = the(bool,aa(bool,fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combc(bool,bool,bool),fequal(bool)),X0))) ) | (~spl53_8 | ~spl53_103)),
% 4.58/1.02 inference(superposition,[],[f1733,f785])).
% 4.58/1.02 tff(f1733,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (the(X0,aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) = X1) ) | ~spl53_103),
% 4.58/1.02 inference(avatar_component_clause,[],[f1732])).
% 4.58/1.02 tff(f6986,plain,(
% 4.58/1.02 spl53_333 | ~spl53_69 | ~spl53_100),
% 4.58/1.02 inference(avatar_split_clause,[],[f1699,f1678,f1114,f6984])).
% 4.58/1.02 tff(f6984,plain,(
% 4.58/1.02 spl53_333 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK11(X0,X1)))) | the(X0,X1) = X2 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_333])])).
% 4.58/1.02 tff(f1699,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK11(X0,X1)))) | the(X0,X1) = X2 | combk(bool,X0,fFalse) = X1) ) | (~spl53_69 | ~spl53_100)),
% 4.58/1.02 inference(resolution,[],[f1679,f1115])).
% 4.58/1.02 tff(f6974,plain,(
% 4.58/1.02 spl53_272 | ~spl53_15 | spl53_267),
% 4.58/1.02 inference(avatar_split_clause,[],[f6397,f4770,f815,f4996])).
% 4.58/1.02 tff(f4996,plain,(
% 4.58/1.02 spl53_272 <=> pp(the(bool,fNot))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_272])])).
% 4.58/1.02 tff(f6397,plain,(
% 4.58/1.02 pp(the(bool,fNot)) | (~spl53_15 | spl53_267)),
% 4.58/1.02 inference(resolution,[],[f4771,f816])).
% 4.58/1.02 tff(f4771,plain,(
% 4.58/1.02 ~pp(aa(bool,bool,fNot,the(bool,fNot))) | spl53_267),
% 4.58/1.02 inference(avatar_component_clause,[],[f4770])).
% 4.58/1.02 tff(f6973,plain,(
% 4.58/1.02 spl53_332 | ~spl53_68 | ~spl53_100),
% 4.58/1.02 inference(avatar_split_clause,[],[f1698,f1678,f1110,f6971])).
% 4.58/1.02 tff(f6971,plain,(
% 4.58/1.02 spl53_332 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK10(X0,X1)))) | the(X0,X1) = X2 | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_332])])).
% 4.58/1.02 tff(f1698,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | pp(aa(X0,bool,X1,sK27(X0,X1,sK10(X0,X1)))) | the(X0,X1) = X2 | combk(bool,X0,fFalse) = X1) ) | (~spl53_68 | ~spl53_100)),
% 4.58/1.02 inference(resolution,[],[f1679,f1111])).
% 4.58/1.02 tff(f6933,plain,(
% 4.58/1.02 spl53_331 | ~spl53_60 | ~spl53_73 | ~spl53_150),
% 4.58/1.02 inference(avatar_split_clause,[],[f2439,f2410,f1164,f1057,f6931])).
% 4.58/1.02 tff(f6931,plain,(
% 4.58/1.02 spl53_331 <=> ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,X1))) | ~pp(sK19(bool,finite_fold1(bool,X0))) | combk(bool,bool,fFalse) = X1 | sP0(bool,finite_fold1(bool,X0)) | ~finite_finite1(bool,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_331])])).
% 4.58/1.02 tff(f1164,plain,(
% 4.58/1.02 spl53_73 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : aa(fun(X0,bool),X0,finite_fold1(X0,X2),aa(X0,fun(X0,bool),fequal(X0),X1)) = X1),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_73])])).
% 4.58/1.02 tff(f2410,plain,(
% 4.58/1.02 spl53_150 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (combk(bool,X0,fFalse) = X2 | ~pp(aa(fun(X0,bool),bool,X1,aa(X0,fun(X0,bool),fequal(X0),sK19(X0,X1)))) | pp(aa(fun(X0,bool),bool,X1,X2)) | sP0(X0,X1) | ~finite_finite1(X0,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_150])])).
% 4.58/1.02 tff(f2439,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,X1))) | ~pp(sK19(bool,finite_fold1(bool,X0))) | combk(bool,bool,fFalse) = X1 | sP0(bool,finite_fold1(bool,X0)) | ~finite_finite1(bool,X1)) ) | (~spl53_60 | ~spl53_73 | ~spl53_150)),
% 4.58/1.02 inference(forward_demodulation,[],[f2434,f1058])).
% 4.58/1.02 tff(f2434,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(sK19(bool,finite_fold1(bool,X0))) | combk(bool,bool,fFalse) = X1 | pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1)) | sP0(bool,finite_fold1(bool,X0)) | ~finite_finite1(bool,X1)) ) | (~spl53_73 | ~spl53_150)),
% 4.58/1.02 inference(superposition,[],[f2411,f1165])).
% 4.58/1.02 tff(f1165,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (aa(fun(X0,bool),X0,finite_fold1(X0,X2),aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) ) | ~spl53_73),
% 4.58/1.02 inference(avatar_component_clause,[],[f1164])).
% 4.58/1.02 tff(f2411,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(X0,fun(X0,bool),fequal(X0),sK19(X0,X1)))) | combk(bool,X0,fFalse) = X2 | pp(aa(fun(X0,bool),bool,X1,X2)) | sP0(X0,X1) | ~finite_finite1(X0,X2)) ) | ~spl53_150),
% 4.58/1.02 inference(avatar_component_clause,[],[f2410])).
% 4.58/1.02 tff(f6929,plain,(
% 4.58/1.02 spl53_330 | ~spl53_8 | ~spl53_101),
% 4.58/1.02 inference(avatar_split_clause,[],[f1730,f1682,f784,f6927])).
% 4.58/1.02 tff(f6927,plain,(
% 4.58/1.02 spl53_330 <=> ! [X0 : $tType,X4 : fun(X0,bool),X3 : bool,X2 : fun(X0,fun(bool,bool)),X1 : bool] : (finite_fold_graph(X0,bool,X2,X1,sK48(bool,X0,X1,X2,X3,X4),fFalse) | ~sP3(bool,X0,X1,X2,X3,X4) | fTrue = sK49(bool,X0,X1,X2,X3,X4))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_330])])).
% 4.58/1.02 tff(f1730,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(bool,bool)),X3 : bool,X1 : bool,X4 : fun(X0,bool)] : (finite_fold_graph(X0,bool,X2,X1,sK48(bool,X0,X1,X2,X3,X4),fFalse) | ~sP3(bool,X0,X1,X2,X3,X4) | fTrue = sK49(bool,X0,X1,X2,X3,X4)) ) | (~spl53_8 | ~spl53_101)),
% 4.58/1.02 inference(superposition,[],[f1683,f785])).
% 4.58/1.02 tff(f6925,plain,(
% 4.58/1.02 spl53_329 | ~spl53_38 | ~spl53_91),
% 4.58/1.02 inference(avatar_split_clause,[],[f1578,f1490,f933,f6923])).
% 4.58/1.02 tff(f6923,plain,(
% 4.58/1.02 spl53_329 <=> ! [X0 : $tType,X1 : X0] : (pp(aa(X0,bool,sK18(X0,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)),X1)) | ~sP0(X0,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_329])])).
% 4.58/1.02 tff(f1490,plain,(
% 4.58/1.02 spl53_91 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_91])])).
% 4.58/1.02 tff(f1578,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (pp(aa(X0,bool,sK18(X0,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)),X1)) | ~sP0(X0,aa(X0,fun(fun(X0,bool),bool),member(X0),X1))) ) | (~spl53_38 | ~spl53_91)),
% 4.58/1.02 inference(resolution,[],[f1491,f934])).
% 4.58/1.02 tff(f1491,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(X0,bool,X1,X2))) ) | ~spl53_91),
% 4.58/1.02 inference(avatar_component_clause,[],[f1490])).
% 4.58/1.02 tff(f6809,plain,(
% 4.58/1.02 spl53_328 | ~spl53_15 | ~spl53_127),
% 4.58/1.02 inference(avatar_split_clause,[],[f2111,f2032,f815,f6807])).
% 4.58/1.02 tff(f6807,plain,(
% 4.58/1.02 spl53_328 <=> ! [X0 : fun(bool,bool),X1 : bool] : (pp(aa(bool,bool,fNot,the(bool,X0))) | pp(aa(bool,bool,X0,sK29(bool,X0,X1))) | ~pp(aa(bool,bool,X0,X1)) | pp(sK28(bool,fNot,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_328])])).
% 4.58/1.02 tff(f2111,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool),X1 : bool] : (pp(aa(bool,bool,fNot,the(bool,X0))) | pp(aa(bool,bool,X0,sK29(bool,X0,X1))) | ~pp(aa(bool,bool,X0,X1)) | pp(sK28(bool,fNot,X0))) ) | (~spl53_15 | ~spl53_127)),
% 4.58/1.02 inference(resolution,[],[f2033,f816])).
% 4.58/1.02 tff(f6749,plain,(
% 4.58/1.02 spl53_327 | ~spl53_13 | ~spl53_272 | ~spl53_325),
% 4.58/1.02 inference(avatar_split_clause,[],[f6745,f6739,f4996,f807,f6747])).
% 4.58/1.02 tff(f6747,plain,(
% 4.58/1.02 spl53_327 <=> ! [X0 : fun(bool,bool)] : (pp(aa(bool,bool,X0,fTrue)) | ~pp(sK28(bool,X0,fNot)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_327])])).
% 4.58/1.02 tff(f807,plain,(
% 4.58/1.02 spl53_13 <=> ! [X0 : bool] : (~pp(X0) | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_13])])).
% 4.58/1.02 tff(f6745,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool)] : (pp(aa(bool,bool,X0,fTrue)) | ~pp(sK28(bool,X0,fNot))) ) | (~spl53_13 | ~spl53_272 | ~spl53_325)),
% 4.58/1.02 inference(forward_demodulation,[],[f6740,f6619])).
% 4.58/1.02 tff(f6619,plain,(
% 4.58/1.02 fTrue = the(bool,fNot) | (~spl53_13 | ~spl53_272)),
% 4.58/1.02 inference(resolution,[],[f4997,f808])).
% 4.58/1.02 tff(f808,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | ~spl53_13),
% 4.58/1.02 inference(avatar_component_clause,[],[f807])).
% 4.58/1.02 tff(f4997,plain,(
% 4.58/1.02 pp(the(bool,fNot)) | ~spl53_272),
% 4.58/1.02 inference(avatar_component_clause,[],[f4996])).
% 4.58/1.02 tff(f6744,plain,(
% 4.58/1.02 spl53_325 | spl53_326 | ~spl53_16 | ~spl53_126),
% 4.58/1.02 inference(avatar_split_clause,[],[f2055,f2028,f819,f6742,f6739])).
% 4.58/1.02 tff(f6742,plain,(
% 4.58/1.02 spl53_326 <=> ! [X1 : bool] : (pp(aa(bool,bool,fNot,sK29(bool,fNot,X1))) | ~pp(aa(bool,bool,fNot,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_326])])).
% 4.58/1.02 tff(f819,plain,(
% 4.58/1.02 spl53_16 <=> ! [X0 : bool] : (~pp(X0) | ~pp(aa(bool,bool,fNot,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_16])])).
% 4.58/1.02 tff(f2055,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool),X1 : bool] : (pp(aa(bool,bool,fNot,sK29(bool,fNot,X1))) | pp(aa(bool,bool,X0,the(bool,fNot))) | ~pp(aa(bool,bool,fNot,X1)) | ~pp(sK28(bool,X0,fNot))) ) | (~spl53_16 | ~spl53_126)),
% 4.58/1.02 inference(resolution,[],[f2029,f820])).
% 4.58/1.02 tff(f820,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | ~pp(X0)) ) | ~spl53_16),
% 4.58/1.02 inference(avatar_component_clause,[],[f819])).
% 4.58/1.02 tff(f6700,plain,(
% 4.58/1.02 spl53_323 | spl53_324 | ~spl53_16 | ~spl53_126),
% 4.58/1.02 inference(avatar_split_clause,[],[f2043,f2028,f819,f6698,f6695])).
% 4.58/1.02 tff(f6698,plain,(
% 4.58/1.02 spl53_324 <=> ! [X1 : fun(bool,bool)] : (pp(aa(bool,bool,fNot,sK28(bool,X1,fNot))) | pp(aa(bool,bool,X1,the(bool,fNot))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_324])])).
% 4.58/1.02 tff(f2043,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,fNot,sK28(bool,X1,fNot))) | pp(aa(bool,bool,X1,the(bool,fNot))) | ~pp(aa(bool,bool,fNot,X0)) | ~pp(sK29(bool,fNot,X0))) ) | (~spl53_16 | ~spl53_126)),
% 4.58/1.02 inference(resolution,[],[f2029,f820])).
% 4.58/1.02 tff(f6693,plain,(
% 4.58/1.02 spl53_322 | ~spl53_62 | ~spl53_69),
% 4.58/1.02 inference(avatar_split_clause,[],[f1141,f1114,f1065,f6691])).
% 4.58/1.02 tff(f6691,plain,(
% 4.58/1.02 spl53_322 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,X2) | sK11(X0,finite_fold1Set(X0,X1,X2)) = sK33(X0,sK11(X0,finite_fold1Set(X0,X1,X2)),X2,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_322])])).
% 4.58/1.02 tff(f1141,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,X2) | sK11(X0,finite_fold1Set(X0,X1,X2)) = sK33(X0,sK11(X0,finite_fold1Set(X0,X1,X2)),X2,X1)) ) | (~spl53_62 | ~spl53_69)),
% 4.58/1.02 inference(resolution,[],[f1115,f1066])).
% 4.58/1.02 tff(f6689,plain,(
% 4.58/1.02 spl53_321 | ~spl53_62 | ~spl53_68),
% 4.58/1.02 inference(avatar_split_clause,[],[f1127,f1110,f1065,f6687])).
% 4.58/1.02 tff(f6687,plain,(
% 4.58/1.02 spl53_321 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,X2) | sK10(X0,finite_fold1Set(X0,X1,X2)) = sK33(X0,sK10(X0,finite_fold1Set(X0,X1,X2)),X2,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_321])])).
% 4.58/1.02 tff(f1127,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,X2) | sK10(X0,finite_fold1Set(X0,X1,X2)) = sK33(X0,sK10(X0,finite_fold1Set(X0,X1,X2)),X2,X1)) ) | (~spl53_62 | ~spl53_68)),
% 4.58/1.02 inference(resolution,[],[f1111,f1066])).
% 4.58/1.02 tff(f6382,plain,(
% 4.58/1.02 spl53_320 | ~spl53_84 | spl53_272),
% 4.58/1.02 inference(avatar_split_clause,[],[f5101,f4996,f1448,f6380])).
% 4.58/1.02 tff(f1448,plain,(
% 4.58/1.02 spl53_84 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | X0 = X1 | fTrue = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_84])])).
% 4.58/1.02 tff(f5101,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (the(bool,fNot) = X0 | fTrue = X0) ) | (~spl53_84 | spl53_272)),
% 4.58/1.02 inference(resolution,[],[f4998,f1449])).
% 4.58/1.02 tff(f1449,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (pp(X0) | X0 = X1 | fTrue = X1) ) | ~spl53_84),
% 4.58/1.02 inference(avatar_component_clause,[],[f1448])).
% 4.58/1.02 tff(f4998,plain,(
% 4.58/1.02 ~pp(the(bool,fNot)) | spl53_272),
% 4.58/1.02 inference(avatar_component_clause,[],[f4996])).
% 4.58/1.02 tff(f6346,plain,(
% 4.58/1.02 spl53_319 | ~spl53_137 | ~spl53_140),
% 4.58/1.02 inference(avatar_split_clause,[],[f2313,f2271,f2259,f6344])).
% 4.58/1.02 tff(f6344,plain,(
% 4.58/1.02 spl53_319 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1)) | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_319])])).
% 4.58/1.02 tff(f2259,plain,(
% 4.58/1.02 spl53_137 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_137])])).
% 4.58/1.02 tff(f2313,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1)) | combk(bool,X0,fFalse) = X1) ) | (~spl53_137 | ~spl53_140)),
% 4.58/1.02 inference(superposition,[],[f2260,f2272])).
% 4.58/1.02 tff(f2260,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))) ) | ~spl53_137),
% 4.58/1.02 inference(avatar_component_clause,[],[f2259])).
% 4.58/1.02 tff(f6342,plain,(
% 4.58/1.02 spl53_318 | ~spl53_132 | ~spl53_140),
% 4.58/1.02 inference(avatar_split_clause,[],[f2312,f2271,f2178,f6340])).
% 4.58/1.02 tff(f6340,plain,(
% 4.58/1.02 spl53_318 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | sK8(X0,X1) = X2 | pp(aa(X0,bool,sK9(X0,X1),X2)) | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_318])])).
% 4.58/1.02 tff(f2178,plain,(
% 4.58/1.02 spl53_132 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : X0] : (pp(aa(X0,bool,X2,X1)) | X1 = X3 | ~pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_132])])).
% 4.58/1.02 tff(f2312,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | sK8(X0,X1) = X2 | pp(aa(X0,bool,sK9(X0,X1),X2)) | combk(bool,X0,fFalse) = X1) ) | (~spl53_132 | ~spl53_140)),
% 4.58/1.02 inference(superposition,[],[f2179,f2272])).
% 4.58/1.02 tff(f2179,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (~pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1)) | X1 = X3 | pp(aa(X0,bool,X2,X1))) ) | ~spl53_132),
% 4.58/1.02 inference(avatar_component_clause,[],[f2178])).
% 4.58/1.02 tff(f6338,plain,(
% 4.58/1.02 spl53_317 | ~spl53_110 | ~spl53_113),
% 4.58/1.02 inference(avatar_split_clause,[],[f1872,f1800,f1765,f6336])).
% 4.58/1.02 tff(f6336,plain,(
% 4.58/1.02 spl53_317 <=> ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK13(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_317])])).
% 4.58/1.02 tff(f1765,plain,(
% 4.58/1.02 spl53_110 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(X0,fun(X0,bool),fequal(X0),X1))) | X1 = X2)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_110])])).
% 4.58/1.02 tff(f1872,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK13(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) ) | (~spl53_110 | ~spl53_113)),
% 4.58/1.02 inference(resolution,[],[f1801,f1766])).
% 4.58/1.02 tff(f1766,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(X0,fun(X0,bool),fequal(X0),X1))) | X1 = X2) ) | ~spl53_110),
% 4.58/1.02 inference(avatar_component_clause,[],[f1765])).
% 4.58/1.02 tff(f6334,plain,(
% 4.58/1.02 spl53_316 | ~spl53_110 | ~spl53_112),
% 4.58/1.02 inference(avatar_split_clause,[],[f1857,f1796,f1765,f6332])).
% 4.58/1.02 tff(f6332,plain,(
% 4.58/1.02 spl53_316 <=> ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK12(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_316])])).
% 4.58/1.02 tff(f1857,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK12(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) ) | (~spl53_110 | ~spl53_112)),
% 4.58/1.02 inference(resolution,[],[f1797,f1766])).
% 4.58/1.02 tff(f6330,plain,(
% 4.58/1.02 spl53_315 | ~spl53_110 | ~spl53_111),
% 4.58/1.02 inference(avatar_split_clause,[],[f1842,f1792,f1765,f6328])).
% 4.58/1.02 tff(f6328,plain,(
% 4.58/1.02 spl53_315 <=> ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK4(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_315])])).
% 4.58/1.02 tff(f1842,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK4(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) ) | (~spl53_110 | ~spl53_111)),
% 4.58/1.02 inference(resolution,[],[f1793,f1766])).
% 4.58/1.02 tff(f6326,plain,(
% 4.58/1.02 spl53_314 | ~spl53_8 | ~spl53_95),
% 4.58/1.02 inference(avatar_split_clause,[],[f1655,f1618,f784,f6324])).
% 4.58/1.02 tff(f6324,plain,(
% 4.58/1.02 spl53_314 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (fFalse != aa(X0,bool,X2,sK30(bool,X0,X1,X2)) | X1 = X2 | fTrue = aa(X0,bool,X1,sK30(bool,X0,X1,X2)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_314])])).
% 4.58/1.02 tff(f1655,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (fFalse != aa(X0,bool,X2,sK30(bool,X0,X1,X2)) | X1 = X2 | fTrue = aa(X0,bool,X1,sK30(bool,X0,X1,X2))) ) | (~spl53_8 | ~spl53_95)),
% 4.58/1.02 inference(superposition,[],[f1619,f785])).
% 4.58/1.02 tff(f6322,plain,(
% 4.58/1.02 spl53_313 | ~spl53_8 | ~spl53_95),
% 4.58/1.02 inference(avatar_split_clause,[],[f1643,f1618,f784,f6320])).
% 4.58/1.02 tff(f6320,plain,(
% 4.58/1.02 spl53_313 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (fFalse != aa(X0,bool,X2,sK30(bool,X0,X2,X1)) | X1 = X2 | fTrue = aa(X0,bool,X1,sK30(bool,X0,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_313])])).
% 4.58/1.02 tff(f1643,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (fFalse != aa(X0,bool,X2,sK30(bool,X0,X2,X1)) | X1 = X2 | fTrue = aa(X0,bool,X1,sK30(bool,X0,X2,X1))) ) | (~spl53_8 | ~spl53_95)),
% 4.58/1.02 inference(superposition,[],[f1619,f785])).
% 4.58/1.02 tff(f6115,plain,(
% 4.58/1.02 spl53_312 | ~spl53_8 | ~spl53_94),
% 4.58/1.02 inference(avatar_split_clause,[],[f1627,f1614,f784,f6113])).
% 4.58/1.02 tff(f6113,plain,(
% 4.58/1.02 spl53_312 <=> ! [X0 : fun(fun(bool,bool),bool)] : (~pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),sK18(bool,X0))) | ~sP0(bool,X0) | fTrue = sK17(bool,X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_312])])).
% 4.58/1.02 tff(f1614,plain,(
% 4.58/1.02 spl53_94 <=> ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK17(X0,X1)),sK18(X0,X1))) | ~sP0(X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_94])])).
% 4.58/1.02 tff(f1627,plain,(
% 4.58/1.02 ( ! [X0 : fun(fun(bool,bool),bool)] : (~pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),sK18(bool,X0))) | ~sP0(bool,X0) | fTrue = sK17(bool,X0)) ) | (~spl53_8 | ~spl53_94)),
% 4.58/1.02 inference(superposition,[],[f1615,f785])).
% 4.58/1.02 tff(f1615,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK17(X0,X1)),sK18(X0,X1))) | ~sP0(X0,X1)) ) | ~spl53_94),
% 4.58/1.02 inference(avatar_component_clause,[],[f1614])).
% 4.58/1.02 tff(f6111,plain,(
% 4.58/1.02 spl53_311 | ~spl53_60 | ~spl53_69),
% 4.58/1.02 inference(avatar_split_clause,[],[f1145,f1114,f1057,f6109])).
% 4.58/1.02 tff(f6109,plain,(
% 4.58/1.02 spl53_311 <=> ! [X0 : fun(bool,fun(bool,bool))] : (pp(the(bool,finite_fold1Set(bool,X0,sK11(fun(bool,bool),finite_fold1(bool,X0))))) | finite_fold1(bool,X0) = combk(bool,fun(bool,bool),fFalse))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_311])])).
% 4.58/1.02 tff(f1145,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool))] : (pp(the(bool,finite_fold1Set(bool,X0,sK11(fun(bool,bool),finite_fold1(bool,X0))))) | finite_fold1(bool,X0) = combk(bool,fun(bool,bool),fFalse)) ) | (~spl53_60 | ~spl53_69)),
% 4.58/1.02 inference(superposition,[],[f1115,f1058])).
% 4.58/1.02 tff(f6107,plain,(
% 4.58/1.02 spl53_310 | ~spl53_61 | ~spl53_69),
% 4.58/1.02 inference(avatar_split_clause,[],[f1140,f1114,f1061,f6105])).
% 4.58/1.02 tff(f6105,plain,(
% 4.58/1.02 spl53_310 <=> ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK11(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_310])])).
% 4.58/1.02 tff(f1140,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK11(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) ) | (~spl53_61 | ~spl53_69)),
% 4.58/1.02 inference(resolution,[],[f1115,f1062])).
% 4.58/1.02 tff(f6103,plain,(
% 4.58/1.02 spl53_309 | ~spl53_60 | ~spl53_68),
% 4.58/1.02 inference(avatar_split_clause,[],[f1131,f1110,f1057,f6101])).
% 4.58/1.02 tff(f6101,plain,(
% 4.58/1.02 spl53_309 <=> ! [X0 : fun(bool,fun(bool,bool))] : (pp(the(bool,finite_fold1Set(bool,X0,sK10(fun(bool,bool),finite_fold1(bool,X0))))) | finite_fold1(bool,X0) = combk(bool,fun(bool,bool),fFalse))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_309])])).
% 4.58/1.02 tff(f1131,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool))] : (pp(the(bool,finite_fold1Set(bool,X0,sK10(fun(bool,bool),finite_fold1(bool,X0))))) | finite_fold1(bool,X0) = combk(bool,fun(bool,bool),fFalse)) ) | (~spl53_60 | ~spl53_68)),
% 4.58/1.02 inference(superposition,[],[f1111,f1058])).
% 4.58/1.02 tff(f6099,plain,(
% 4.58/1.02 spl53_308 | ~spl53_61 | ~spl53_68),
% 4.58/1.02 inference(avatar_split_clause,[],[f1126,f1110,f1061,f6097])).
% 4.58/1.02 tff(f6097,plain,(
% 4.58/1.02 spl53_308 <=> ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK10(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_308])])).
% 4.58/1.02 tff(f1126,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) | sK10(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) ) | (~spl53_61 | ~spl53_68)),
% 4.58/1.02 inference(resolution,[],[f1111,f1062])).
% 4.58/1.02 tff(f5640,plain,(
% 4.58/1.02 spl53_307 | ~spl53_92 | ~spl53_143),
% 4.58/1.02 inference(avatar_split_clause,[],[f2330,f2319,f1494,f5638])).
% 4.58/1.02 tff(f5638,plain,(
% 4.58/1.02 spl53_307 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) | ~pp(aa(X0,bool,sK26(X0,X2,X1),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_307])])).
% 4.58/1.02 tff(f2319,plain,(
% 4.58/1.02 spl53_143 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK26(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_143])])).
% 4.58/1.02 tff(f2330,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) | ~pp(aa(X0,bool,sK26(X0,X2,X1),X1))) ) | (~spl53_92 | ~spl53_143)),
% 4.58/1.02 inference(resolution,[],[f2320,f1495])).
% 4.58/1.02 tff(f2320,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK26(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | ~spl53_143),
% 4.58/1.02 inference(avatar_component_clause,[],[f2319])).
% 4.58/1.02 tff(f5636,plain,(
% 4.58/1.02 spl53_306 | ~spl53_92 | ~spl53_142),
% 4.58/1.02 inference(avatar_split_clause,[],[f2322,f2315,f1494,f5634])).
% 4.58/1.02 tff(f5634,plain,(
% 4.58/1.02 spl53_306 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) | ~pp(aa(X0,bool,sK25(X0,X2,X1),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_306])])).
% 4.58/1.02 tff(f2315,plain,(
% 4.58/1.02 spl53_142 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK25(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_142])])).
% 4.58/1.02 tff(f2322,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) | ~pp(aa(X0,bool,sK25(X0,X2,X1),X1))) ) | (~spl53_92 | ~spl53_142)),
% 4.58/1.02 inference(resolution,[],[f2316,f1495])).
% 4.58/1.02 tff(f2316,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK25(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | ~spl53_142),
% 4.58/1.02 inference(avatar_component_clause,[],[f2315])).
% 4.58/1.02 tff(f5632,plain,(
% 4.58/1.02 spl53_305 | ~spl53_8 | ~spl53_93),
% 4.58/1.02 inference(avatar_split_clause,[],[f1607,f1541,f784,f5630])).
% 4.58/1.02 tff(f5630,plain,(
% 4.58/1.02 spl53_305 <=> ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(aa(bool,bool,finite_fold1Set(bool,X0,X1),fFalse)) | combk(bool,bool,fFalse) = X1 | ~finite_finite1(bool,X1) | fTrue = sK20(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_305])])).
% 4.58/1.02 tff(f1607,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(aa(bool,bool,finite_fold1Set(bool,X0,X1),fFalse)) | combk(bool,bool,fFalse) = X1 | ~finite_finite1(bool,X1) | fTrue = sK20(bool,X0,X1)) ) | (~spl53_8 | ~spl53_93)),
% 4.58/1.02 inference(superposition,[],[f1542,f785])).
% 4.58/1.02 tff(f5628,plain,(
% 4.58/1.02 spl53_304 | ~spl53_8 | ~spl53_90),
% 4.58/1.02 inference(avatar_split_clause,[],[f1577,f1486,f784,f5626])).
% 4.58/1.02 tff(f5626,plain,(
% 4.58/1.02 spl53_304 <=> ! [X2 : bool,X0 : fun(bool,bool),X1 : bool] : (fFalse != X1 | ~pp(aa(bool,bool,X0,X2)) | the(bool,X0) = X2 | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK27(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_304])])).
% 4.58/1.02 tff(f1486,plain,(
% 4.58/1.02 spl53_90 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : X0] : (the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X1)) | sK27(X0,X2,X3) != X3 | ~pp(aa(X0,bool,X2,X3)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_90])])).
% 4.58/1.02 tff(f1577,plain,(
% 4.58/1.02 ( ! [X2 : bool,X0 : fun(bool,bool),X1 : bool] : (fFalse != X1 | ~pp(aa(bool,bool,X0,X2)) | the(bool,X0) = X2 | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK27(bool,X0,X1)) ) | (~spl53_8 | ~spl53_90)),
% 4.58/1.02 inference(superposition,[],[f1487,f785])).
% 4.58/1.02 tff(f1487,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (sK27(X0,X2,X3) != X3 | ~pp(aa(X0,bool,X2,X1)) | the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X3))) ) | ~spl53_90),
% 4.58/1.02 inference(avatar_component_clause,[],[f1486])).
% 4.58/1.02 tff(f5624,plain,(
% 4.58/1.02 spl53_303 | ~spl53_8 | ~spl53_89),
% 4.58/1.02 inference(avatar_split_clause,[],[f1558,f1482,f784,f5622])).
% 4.58/1.02 tff(f5622,plain,(
% 4.58/1.02 spl53_303 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,X1,fFalse)) | pp(aa(bool,bool,X1,the(bool,X1))) | ~pp(aa(bool,bool,X1,X0)) | fTrue = sK24(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_303])])).
% 4.58/1.02 tff(f1558,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,X1,fFalse)) | pp(aa(bool,bool,X1,the(bool,X1))) | ~pp(aa(bool,bool,X1,X0)) | fTrue = sK24(bool,X0,X1)) ) | (~spl53_8 | ~spl53_89)),
% 4.58/1.02 inference(superposition,[],[f1483,f785])).
% 4.58/1.02 tff(f5608,plain,(
% 4.58/1.02 spl53_302 | ~spl53_8 | ~spl53_87),
% 4.58/1.02 inference(avatar_split_clause,[],[f1525,f1473,f784,f5606])).
% 4.58/1.02 tff(f5606,plain,(
% 4.58/1.02 spl53_302 <=> ! [X0 : fun(bool,bool),X1 : bool] : (pp(aa(bool,bool,X0,fFalse)) | pp(aa(bool,bool,X0,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK5(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_302])])).
% 4.58/1.02 tff(f1525,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool),X1 : bool] : (pp(aa(bool,bool,X0,fFalse)) | pp(aa(bool,bool,X0,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK5(bool,X0,X1)) ) | (~spl53_8 | ~spl53_87)),
% 4.58/1.02 inference(superposition,[],[f1474,f785])).
% 4.58/1.02 tff(f5604,plain,(
% 4.58/1.02 spl53_301 | ~spl53_58 | ~spl53_69),
% 4.58/1.02 inference(avatar_split_clause,[],[f1138,f1114,f1048,f5602])).
% 4.58/1.02 tff(f5602,plain,(
% 4.58/1.02 spl53_301 <=> ! [X0 : bool] : (aa(bool,fun(bool,bool),fimplies,X0) = combk(bool,bool,fFalse) | ~pp(X0) | pp(sK11(bool,aa(bool,fun(bool,bool),fimplies,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_301])])).
% 4.58/1.02 tff(f1138,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (aa(bool,fun(bool,bool),fimplies,X0) = combk(bool,bool,fFalse) | ~pp(X0) | pp(sK11(bool,aa(bool,fun(bool,bool),fimplies,X0)))) ) | (~spl53_58 | ~spl53_69)),
% 4.58/1.02 inference(resolution,[],[f1115,f1049])).
% 4.58/1.02 tff(f5600,plain,(
% 4.58/1.02 spl53_300 | ~spl53_57 | ~spl53_69),
% 4.58/1.02 inference(avatar_split_clause,[],[f1137,f1114,f1044,f5598])).
% 4.58/1.02 tff(f5598,plain,(
% 4.58/1.02 spl53_300 <=> ! [X0 : bool] : (aa(bool,fun(bool,bool),fdisj,X0) = combk(bool,bool,fFalse) | pp(X0) | pp(sK11(bool,aa(bool,fun(bool,bool),fdisj,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_300])])).
% 4.58/1.02 tff(f1137,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (aa(bool,fun(bool,bool),fdisj,X0) = combk(bool,bool,fFalse) | pp(X0) | pp(sK11(bool,aa(bool,fun(bool,bool),fdisj,X0)))) ) | (~spl53_57 | ~spl53_69)),
% 4.58/1.02 inference(resolution,[],[f1115,f1045])).
% 4.58/1.02 tff(f5596,plain,(
% 4.58/1.02 spl53_299 | ~spl53_58 | ~spl53_68),
% 4.58/1.02 inference(avatar_split_clause,[],[f1124,f1110,f1048,f5594])).
% 4.58/1.02 tff(f5594,plain,(
% 4.58/1.02 spl53_299 <=> ! [X0 : bool] : (aa(bool,fun(bool,bool),fimplies,X0) = combk(bool,bool,fFalse) | ~pp(X0) | pp(sK10(bool,aa(bool,fun(bool,bool),fimplies,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_299])])).
% 4.58/1.02 tff(f1124,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (aa(bool,fun(bool,bool),fimplies,X0) = combk(bool,bool,fFalse) | ~pp(X0) | pp(sK10(bool,aa(bool,fun(bool,bool),fimplies,X0)))) ) | (~spl53_58 | ~spl53_68)),
% 4.58/1.02 inference(resolution,[],[f1111,f1049])).
% 4.58/1.02 tff(f5592,plain,(
% 4.58/1.02 spl53_298 | ~spl53_57 | ~spl53_68),
% 4.58/1.02 inference(avatar_split_clause,[],[f1123,f1110,f1044,f5590])).
% 4.58/1.02 tff(f5590,plain,(
% 4.58/1.02 spl53_298 <=> ! [X0 : bool] : (aa(bool,fun(bool,bool),fdisj,X0) = combk(bool,bool,fFalse) | pp(X0) | pp(sK10(bool,aa(bool,fun(bool,bool),fdisj,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_298])])).
% 4.58/1.02 tff(f1123,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (aa(bool,fun(bool,bool),fdisj,X0) = combk(bool,bool,fFalse) | pp(X0) | pp(sK10(bool,aa(bool,fun(bool,bool),fdisj,X0)))) ) | (~spl53_57 | ~spl53_68)),
% 4.58/1.02 inference(resolution,[],[f1111,f1045])).
% 4.58/1.02 tff(f5568,plain,(
% 4.58/1.02 spl53_297 | ~spl53_92 | ~spl53_138),
% 4.58/1.02 inference(avatar_split_clause,[],[f2287,f2263,f1494,f5566])).
% 4.58/1.02 tff(f5566,plain,(
% 4.58/1.02 spl53_297 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X1,fun(X0,X0)),X4 : X0,X5 : fun(X1,bool),X2 : X0] : (~sP3(X0,X1,X2,X3,X4,X5) | ~pp(aa(X1,bool,sK48(X0,X1,X2,X3,X4,X5),sK47(X0,X1,X2,X3,X4,X5))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_297])])).
% 4.58/1.02 tff(f2287,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : fun(X1,fun(X0,X0)),X4 : X0,X5 : fun(X1,bool)] : (~sP3(X0,X1,X2,X3,X4,X5) | ~pp(aa(X1,bool,sK48(X0,X1,X2,X3,X4,X5),sK47(X0,X1,X2,X3,X4,X5)))) ) | (~spl53_92 | ~spl53_138)),
% 4.58/1.02 inference(resolution,[],[f2264,f1495])).
% 4.58/1.02 tff(f5488,plain,(
% 4.58/1.02 spl53_296 | ~spl53_15 | ~spl53_278),
% 4.58/1.02 inference(avatar_split_clause,[],[f5385,f5071,f815,f5486])).
% 4.58/1.02 tff(f5486,plain,(
% 4.58/1.02 spl53_296 <=> ! [X0 : bool] : (the(bool,fNot) = X0 | pp(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_296])])).
% 4.58/1.02 tff(f5071,plain,(
% 4.58/1.02 spl53_278 <=> ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | the(bool,fNot) = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_278])])).
% 4.58/1.02 tff(f5385,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (the(bool,fNot) = X0 | pp(X0)) ) | (~spl53_15 | ~spl53_278)),
% 4.58/1.02 inference(resolution,[],[f5072,f816])).
% 4.58/1.02 tff(f5072,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | the(bool,fNot) = X0) ) | ~spl53_278),
% 4.58/1.02 inference(avatar_component_clause,[],[f5071])).
% 4.58/1.02 tff(f5455,plain,(
% 4.58/1.02 spl53_295 | ~spl53_135 | ~spl53_137),
% 4.58/1.02 inference(avatar_split_clause,[],[f2281,f2259,f2238,f5453])).
% 4.58/1.02 tff(f5453,plain,(
% 4.58/1.02 spl53_295 <=> ! [X0 : $tType,X1 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),aa(X0,fun(X0,bool),fequal(X0),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_295])])).
% 4.58/1.02 tff(f2281,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),aa(X0,fun(X0,bool),fequal(X0),X1)))) ) | (~spl53_135 | ~spl53_137)),
% 4.58/1.02 inference(superposition,[],[f2260,f2239])).
% 4.58/1.02 tff(f5434,plain,(
% 4.58/1.02 ~spl53_293 | spl53_294 | ~spl53_27 | ~spl53_34 | ~spl53_60 | ~spl53_68 | ~spl53_115),
% 4.58/1.02 inference(avatar_split_clause,[],[f1914,f1808,f1110,f1057,f912,f871,f5432,f5428])).
% 4.58/1.02 tff(f5428,plain,(
% 4.58/1.02 spl53_293 <=> pp(the(bool,combk(bool,bool,fFalse)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_293])])).
% 4.58/1.02 tff(f5432,plain,(
% 4.58/1.02 spl53_294 <=> ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,X1))) | ~finite_finite1(bool,X1) | finite_finite1(bool,sK22(bool,finite_fold1(bool,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_294])])).
% 4.58/1.02 tff(f1914,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (pp(the(bool,finite_fold1Set(bool,X0,X1))) | ~pp(the(bool,combk(bool,bool,fFalse))) | finite_finite1(bool,sK22(bool,finite_fold1(bool,X0))) | ~finite_finite1(bool,X1)) ) | (~spl53_27 | ~spl53_34 | ~spl53_60 | ~spl53_68 | ~spl53_115)),
% 4.58/1.02 inference(forward_demodulation,[],[f1913,f1058])).
% 4.58/1.02 tff(f1913,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,combk(bool,bool,fFalse))) | pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1)) | finite_finite1(bool,sK22(bool,finite_fold1(bool,X0))) | ~finite_finite1(bool,X1)) ) | (~spl53_27 | ~spl53_34 | ~spl53_60 | ~spl53_68 | ~spl53_115)),
% 4.58/1.02 inference(forward_demodulation,[],[f1909,f1133])).
% 4.58/1.02 tff(f1133,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,combk(bool,X0,fFalse))) ) | (~spl53_27 | ~spl53_34 | ~spl53_68)),
% 4.58/1.02 inference(forward_demodulation,[],[f1125,f913])).
% 4.58/1.02 tff(f1125,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = finite_fold1Set(X0,X1,bot_bot(fun(X0,bool)))) ) | (~spl53_27 | ~spl53_68)),
% 4.58/1.02 inference(resolution,[],[f1111,f872])).
% 4.58/1.02 tff(f1909,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (~pp(the(bool,finite_fold1Set(bool,X0,combk(bool,bool,fFalse)))) | pp(aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1)) | finite_finite1(bool,sK22(bool,finite_fold1(bool,X0))) | ~finite_finite1(bool,X1)) ) | (~spl53_60 | ~spl53_115)),
% 4.58/1.02 inference(superposition,[],[f1809,f1058])).
% 4.58/1.02 tff(f5426,plain,(
% 4.58/1.02 spl53_292 | ~spl53_62 | ~spl53_93),
% 4.58/1.02 inference(avatar_split_clause,[],[f1600,f1541,f1065,f5424])).
% 4.58/1.02 tff(f5424,plain,(
% 4.58/1.02 spl53_292 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | ~finite_finite1(X0,X1) | sK20(X0,X2,X1) = sK33(X0,sK20(X0,X2,X1),X1,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_292])])).
% 4.58/1.02 tff(f1600,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | ~finite_finite1(X0,X1) | sK20(X0,X2,X1) = sK33(X0,sK20(X0,X2,X1),X1,X2)) ) | (~spl53_62 | ~spl53_93)),
% 4.58/1.02 inference(resolution,[],[f1542,f1066])).
% 4.58/1.02 tff(f5422,plain,(
% 4.58/1.02 spl53_291 | ~spl53_49 | ~spl53_69),
% 4.58/1.02 inference(avatar_split_clause,[],[f1135,f1114,f992,f5420])).
% 4.58/1.02 tff(f5420,plain,(
% 4.58/1.02 spl53_291 <=> ! [X0 : bool] : (aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) | pp(sK11(bool,aa(bool,fun(bool,bool),fconj,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_291])])).
% 4.58/1.02 tff(f1135,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) | pp(sK11(bool,aa(bool,fun(bool,bool),fconj,X0)))) ) | (~spl53_49 | ~spl53_69)),
% 4.58/1.02 inference(resolution,[],[f1115,f993])).
% 4.58/1.02 tff(f5418,plain,(
% 4.58/1.02 spl53_290 | ~spl53_49 | ~spl53_68),
% 4.58/1.02 inference(avatar_split_clause,[],[f1121,f1110,f992,f5416])).
% 4.58/1.02 tff(f5416,plain,(
% 4.58/1.02 spl53_290 <=> ! [X0 : bool] : (aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) | pp(sK10(bool,aa(bool,fun(bool,bool),fconj,X0))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_290])])).
% 4.58/1.02 tff(f1121,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) | pp(sK10(bool,aa(bool,fun(bool,bool),fconj,X0)))) ) | (~spl53_49 | ~spl53_68)),
% 4.58/1.02 inference(resolution,[],[f1111,f993])).
% 4.58/1.02 tff(f5384,plain,(
% 4.58/1.02 spl53_289 | ~spl53_16 | ~spl53_277),
% 4.58/1.02 inference(avatar_split_clause,[],[f5076,f5068,f819,f5382])).
% 4.58/1.02 tff(f5382,plain,(
% 4.58/1.02 spl53_289 <=> ! [X0 : bool] : (pp(X0) | ~pp(sK27(bool,fNot,X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_289])])).
% 4.58/1.02 tff(f5068,plain,(
% 4.58/1.02 spl53_277 <=> ! [X1 : bool] : (pp(aa(bool,bool,fNot,sK27(bool,fNot,X1))) | pp(X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_277])])).
% 4.58/1.02 tff(f5076,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (pp(X0) | ~pp(sK27(bool,fNot,X0))) ) | (~spl53_16 | ~spl53_277)),
% 4.58/1.02 inference(resolution,[],[f5069,f820])).
% 4.58/1.02 tff(f5069,plain,(
% 4.58/1.02 ( ! [X1 : bool] : (pp(aa(bool,bool,fNot,sK27(bool,fNot,X1))) | pp(X1)) ) | ~spl53_277),
% 4.58/1.02 inference(avatar_component_clause,[],[f5068])).
% 4.58/1.02 tff(f5220,plain,(
% 4.58/1.02 spl53_288 | ~spl53_92 | ~spl53_131),
% 4.58/1.02 inference(avatar_split_clause,[],[f2207,f2174,f1494,f5218])).
% 4.58/1.02 tff(f5218,plain,(
% 4.58/1.02 spl53_288 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (~pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3)) | ~pp(aa(X0,bool,sK32(X0,X3,X2,X1),sK31(X0,X3,X2,X1))))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_288])])).
% 4.58/1.02 tff(f2207,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,fun(X0,X0))] : (~pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3)) | ~pp(aa(X0,bool,sK32(X0,X3,X2,X1),sK31(X0,X3,X2,X1)))) ) | (~spl53_92 | ~spl53_131)),
% 4.58/1.02 inference(resolution,[],[f2175,f1495])).
% 4.58/1.02 tff(f5216,plain,(
% 4.58/1.02 spl53_287 | ~spl53_8 | ~spl53_95),
% 4.58/1.02 inference(avatar_split_clause,[],[f1648,f1618,f784,f5214])).
% 4.58/1.02 tff(f5214,plain,(
% 4.58/1.02 spl53_287 <=> ! [X0 : $tType,X2 : fun(bool,X0),X1 : fun(bool,X0)] : (aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) | X1 = X2 | fTrue = sK30(X0,bool,X1,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_287])])).
% 4.58/1.02 tff(f1648,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(bool,X0),X1 : fun(bool,X0)] : (aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) | X1 = X2 | fTrue = sK30(X0,bool,X1,X2)) ) | (~spl53_8 | ~spl53_95)),
% 4.58/1.02 inference(superposition,[],[f1619,f785])).
% 4.58/1.02 tff(f5212,plain,(
% 4.58/1.02 spl53_286 | ~spl53_15 | ~spl53_266),
% 4.58/1.02 inference(avatar_split_clause,[],[f4798,f4767,f815,f5210])).
% 4.58/1.02 tff(f5210,plain,(
% 4.58/1.02 spl53_286 <=> ! [X0 : bool] : (~pp(sK5(bool,fNot,X0)) | pp(X0))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_286])])).
% 4.58/1.02 tff(f4798,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (~pp(sK5(bool,fNot,X0)) | pp(X0)) ) | (~spl53_15 | ~spl53_266)),
% 4.58/1.02 inference(resolution,[],[f4768,f816])).
% 4.58/1.02 tff(f5208,plain,(
% 4.58/1.02 spl53_285 | ~spl53_54 | ~spl53_86),
% 4.58/1.02 inference(avatar_split_clause,[],[f1471,f1467,f1026,f5206])).
% 4.58/1.02 tff(f5206,plain,(
% 4.58/1.02 spl53_285 <=> ! [X1 : $tType,X0 : $tType,X4 : fun(X1,bool),X3 : fun(X1,fun(X0,X0)),X2 : X0] : (sP3(X0,X1,X2,X3,sK34(X1,X0,X2,X3,X4),X4) | combk(bool,X1,fFalse) = X4 | ~finite_finite1(X1,X4))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_285])])).
% 4.58/1.02 tff(f1026,plain,(
% 4.58/1.02 spl53_54 <=> ! [X1 : $tType,X0 : $tType,X4 : fun(X0,bool),X3 : fun(X0,fun(X1,X1)),X2 : X1] : (finite_fold_graph(X0,X1,X3,X2,X4,sK34(X0,X1,X2,X3,X4)) | ~finite_finite1(X0,X4))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_54])])).
% 4.58/1.02 tff(f1467,plain,(
% 4.58/1.02 spl53_86 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1)),X2 : X1] : (combk(bool,X0,fFalse) = X3 | sP3(X1,X0,X4,X5,X2,X3) | ~finite_fold_graph(X0,X1,X5,X4,X3,X2))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_86])])).
% 4.58/1.02 tff(f1471,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : fun(X1,fun(X0,X0)),X4 : fun(X1,bool)] : (sP3(X0,X1,X2,X3,sK34(X1,X0,X2,X3,X4),X4) | combk(bool,X1,fFalse) = X4 | ~finite_finite1(X1,X4)) ) | (~spl53_54 | ~spl53_86)),
% 4.58/1.02 inference(resolution,[],[f1468,f1027])).
% 4.58/1.02 tff(f1027,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1)),X4 : fun(X0,bool)] : (finite_fold_graph(X0,X1,X3,X2,X4,sK34(X0,X1,X2,X3,X4)) | ~finite_finite1(X0,X4)) ) | ~spl53_54),
% 4.58/1.02 inference(avatar_component_clause,[],[f1026])).
% 4.58/1.02 tff(f1468,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (~finite_fold_graph(X0,X1,X5,X4,X3,X2) | sP3(X1,X0,X4,X5,X2,X3) | combk(bool,X0,fFalse) = X3) ) | ~spl53_86),
% 4.58/1.02 inference(avatar_component_clause,[],[f1467])).
% 4.58/1.02 tff(f5204,plain,(
% 4.58/1.02 spl53_284 | ~spl53_8 | ~spl53_83),
% 4.58/1.02 inference(avatar_split_clause,[],[f1451,f1408,f784,f5202])).
% 4.58/1.02 tff(f5202,plain,(
% 4.58/1.02 spl53_284 <=> ! [X1 : $tType,X2 : X1,X0 : bool] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X2),combk(bool,X1,X0))) | fTrue = X0)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_284])])).
% 4.58/1.02 tff(f1408,plain,(
% 4.58/1.02 spl53_83 <=> ! [X0 : $tType,X1 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),combk(bool,X0,fFalse)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_83])])).
% 4.58/1.02 tff(f1451,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X2 : X1,X0 : bool] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X2),combk(bool,X1,X0))) | fTrue = X0) ) | (~spl53_8 | ~spl53_83)),
% 4.58/1.02 inference(superposition,[],[f1409,f785])).
% 4.58/1.02 tff(f1409,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),combk(bool,X0,fFalse)))) ) | ~spl53_83),
% 4.58/1.02 inference(avatar_component_clause,[],[f1408])).
% 4.58/1.02 tff(f5200,plain,(
% 4.58/1.02 spl53_283 | ~spl53_8 | ~spl53_82),
% 4.58/1.02 inference(avatar_split_clause,[],[f1446,f1404,f784,f5198])).
% 4.58/1.02 tff(f5198,plain,(
% 4.58/1.02 spl53_283 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (fFalse != X0 | pp(aa(bool,bool,X1,the(bool,X1))) | ~pp(aa(bool,bool,X1,X0)) | fTrue = sK24(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_283])])).
% 4.58/1.02 tff(f1404,plain,(
% 4.58/1.02 spl53_82 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (pp(aa(X0,bool,X2,the(X0,X2))) | sK24(X0,X1,X2) != X1 | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_82])])).
% 4.58/1.02 tff(f1446,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (fFalse != X0 | pp(aa(bool,bool,X1,the(bool,X1))) | ~pp(aa(bool,bool,X1,X0)) | fTrue = sK24(bool,X0,X1)) ) | (~spl53_8 | ~spl53_82)),
% 4.58/1.02 inference(superposition,[],[f1405,f785])).
% 4.58/1.02 tff(f1405,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (sK24(X0,X1,X2) != X1 | pp(aa(X0,bool,X2,the(X0,X2))) | ~pp(aa(X0,bool,X2,X1))) ) | ~spl53_82),
% 4.58/1.02 inference(avatar_component_clause,[],[f1404])).
% 4.58/1.02 tff(f5196,plain,(
% 4.58/1.02 spl53_282 | ~spl53_8 | ~spl53_81),
% 4.58/1.02 inference(avatar_split_clause,[],[f1430,f1400,f784,f5194])).
% 4.58/1.02 tff(f5194,plain,(
% 4.58/1.02 spl53_282 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,X1,fFalse)) | the(bool,X1) = X0 | ~pp(aa(bool,bool,X1,X0)) | fTrue = sK23(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_282])])).
% 4.58/1.02 tff(f1430,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (pp(aa(bool,bool,X1,fFalse)) | the(bool,X1) = X0 | ~pp(aa(bool,bool,X1,X0)) | fTrue = sK23(bool,X0,X1)) ) | (~spl53_8 | ~spl53_81)),
% 4.58/1.02 inference(superposition,[],[f1401,f785])).
% 4.58/1.02 tff(f5192,plain,(
% 4.58/1.02 spl53_281 | ~spl53_8 | ~spl53_80),
% 4.58/1.02 inference(avatar_split_clause,[],[f1415,f1396,f784,f5190])).
% 4.58/1.02 tff(f5190,plain,(
% 4.58/1.02 spl53_281 <=> ! [X0 : fun(bool,bool),X1 : bool] : (fFalse != X1 | pp(aa(bool,bool,X0,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK5(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_281])])).
% 4.58/1.02 tff(f1396,plain,(
% 4.58/1.02 spl53_80 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X1))) | sK5(X0,X1,X2) != X2 | ~pp(aa(X0,bool,X1,X2)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_80])])).
% 4.58/1.02 tff(f1415,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,bool),X1 : bool] : (fFalse != X1 | pp(aa(bool,bool,X0,the(bool,X0))) | ~pp(aa(bool,bool,X0,X1)) | fTrue = sK5(bool,X0,X1)) ) | (~spl53_8 | ~spl53_80)),
% 4.58/1.02 inference(superposition,[],[f1397,f785])).
% 4.58/1.02 tff(f1397,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (sK5(X0,X1,X2) != X2 | pp(aa(X0,bool,X1,the(X0,X1))) | ~pp(aa(X0,bool,X1,X2))) ) | ~spl53_80),
% 4.58/1.02 inference(avatar_component_clause,[],[f1396])).
% 4.58/1.02 tff(f5188,plain,(
% 4.58/1.02 spl53_280 | ~spl53_54 | ~spl53_71),
% 4.58/1.02 inference(avatar_split_clause,[],[f1158,f1153,f1026,f5186])).
% 4.58/1.02 tff(f5186,plain,(
% 4.58/1.02 spl53_280 <=> ! [X1 : $tType,X0 : $tType,X4 : fun(X0,bool),X3 : fun(X0,fun(X1,X1)),X2 : X1] : (sK34(X0,X1,X2,X3,X4) = X2 | sP3(X1,X0,X2,X3,sK34(X0,X1,X2,X3,X4),X4) | ~finite_finite1(X0,X4))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_280])])).
% 4.58/1.02 tff(f1158,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1)),X4 : fun(X0,bool)] : (sK34(X0,X1,X2,X3,X4) = X2 | sP3(X1,X0,X2,X3,sK34(X0,X1,X2,X3,X4),X4) | ~finite_finite1(X0,X4)) ) | (~spl53_54 | ~spl53_71)),
% 4.58/1.02 inference(resolution,[],[f1154,f1027])).
% 4.58/1.02 tff(f5113,plain,(
% 4.58/1.02 spl53_279 | ~spl53_122 | ~spl53_140),
% 4.58/1.02 inference(avatar_split_clause,[],[f2311,f2271,f1987,f5111])).
% 4.58/1.02 tff(f5111,plain,(
% 4.58/1.02 spl53_279 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~pp(aa(X0,bool,sK9(X0,X1),X2)) | combk(bool,X0,fFalse) = X1)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_279])])).
% 4.58/1.02 tff(f1987,plain,(
% 4.58/1.02 spl53_122 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : X0] : (pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1)) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_122])])).
% 4.58/1.02 tff(f2311,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~pp(aa(X0,bool,sK9(X0,X1),X2)) | combk(bool,X0,fFalse) = X1) ) | (~spl53_122 | ~spl53_140)),
% 4.58/1.02 inference(superposition,[],[f1988,f2272])).
% 4.58/1.02 tff(f1988,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1)) | ~pp(aa(X0,bool,X2,X1))) ) | ~spl53_122),
% 4.58/1.02 inference(avatar_component_clause,[],[f1987])).
% 4.58/1.02 tff(f5073,plain,(
% 4.58/1.02 spl53_277 | spl53_278 | ~spl53_15 | ~spl53_100),
% 4.58/1.02 inference(avatar_split_clause,[],[f1685,f1678,f815,f5071,f5068])).
% 4.58/1.02 tff(f1685,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,fNot,X0)) | pp(aa(bool,bool,fNot,sK27(bool,fNot,X1))) | the(bool,fNot) = X0 | pp(X1)) ) | (~spl53_15 | ~spl53_100)),
% 4.58/1.02 inference(resolution,[],[f1679,f816])).
% 4.58/1.02 tff(f5066,plain,(
% 4.58/1.02 spl53_276 | ~spl53_20 | ~spl53_95),
% 4.58/1.02 inference(avatar_split_clause,[],[f1650,f1618,f840,f5064])).
% 4.58/1.02 tff(f5064,plain,(
% 4.58/1.02 spl53_276 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,X1),X2 : X1] : (aa(X0,X1,X3,sK30(X1,X0,combk(X1,X0,X2),X3)) != X2 | combk(X1,X0,X2) = X3)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_276])])).
% 4.58/1.02 tff(f1650,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,X1)] : (aa(X0,X1,X3,sK30(X1,X0,combk(X1,X0,X2),X3)) != X2 | combk(X1,X0,X2) = X3) ) | (~spl53_20 | ~spl53_95)),
% 4.58/1.02 inference(superposition,[],[f1619,f841])).
% 4.58/1.02 tff(f5062,plain,(
% 4.58/1.02 spl53_275 | ~spl53_20 | ~spl53_95),
% 4.58/1.02 inference(avatar_split_clause,[],[f1638,f1618,f840,f5060])).
% 4.58/1.02 tff(f5060,plain,(
% 4.58/1.02 spl53_275 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,X1),X2 : X1] : (aa(X0,X1,X3,sK30(X1,X0,X3,combk(X1,X0,X2))) != X2 | combk(X1,X0,X2) = X3)),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_275])])).
% 4.58/1.02 tff(f1638,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,X1)] : (aa(X0,X1,X3,sK30(X1,X0,X3,combk(X1,X0,X2))) != X2 | combk(X1,X0,X2) = X3) ) | (~spl53_20 | ~spl53_95)),
% 4.58/1.02 inference(superposition,[],[f1619,f841])).
% 4.58/1.02 tff(f5037,plain,(
% 4.58/1.02 spl53_274 | ~spl53_8 | ~spl53_73),
% 4.58/1.02 inference(avatar_split_clause,[],[f1172,f1164,f784,f5035])).
% 4.58/1.02 tff(f5035,plain,(
% 4.58/1.02 spl53_274 <=> ! [X0 : fun(bool,fun(bool,bool)),X1 : bool] : (fFalse = X1 | fTrue = aa(fun(bool,bool),bool,finite_fold1(bool,X0),aa(bool,fun(bool,bool),fequal(bool),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_274])])).
% 4.58/1.02 tff(f1172,plain,(
% 4.58/1.02 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : bool] : (fFalse = X1 | fTrue = aa(fun(bool,bool),bool,finite_fold1(bool,X0),aa(bool,fun(bool,bool),fequal(bool),X1))) ) | (~spl53_8 | ~spl53_73)),
% 4.58/1.02 inference(superposition,[],[f1165,f785])).
% 4.58/1.02 tff(f5033,plain,(
% 4.58/1.02 spl53_273 | ~spl53_9 | ~spl53_35),
% 4.58/1.02 inference(avatar_split_clause,[],[f946,f920,f788,f5031])).
% 4.58/1.02 tff(f5031,plain,(
% 4.58/1.02 spl53_273 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : X2] : (bot_bot(fun(X0,X1)) = aa(X2,fun(X0,X1),bot_bot(fun(X2,fun(X0,X1))),X3) | ~bot(X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_273])])).
% 4.58/1.02 tff(f788,plain,(
% 4.58/1.02 spl53_9 <=> ! [X1 : $tType,X0 : $tType] : (bot(fun(X0,X1)) | ~bot(X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_9])])).
% 4.58/1.02 tff(f920,plain,(
% 4.58/1.02 spl53_35 <=> ! [X1 : $tType,X0 : $tType,X2 : X0] : (bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) | ~bot(X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_35])])).
% 4.58/1.02 tff(f946,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2] : (bot_bot(fun(X0,X1)) = aa(X2,fun(X0,X1),bot_bot(fun(X2,fun(X0,X1))),X3) | ~bot(X1)) ) | (~spl53_9 | ~spl53_35)),
% 4.58/1.02 inference(resolution,[],[f921,f789])).
% 4.58/1.02 tff(f789,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType] : (bot(fun(X0,X1)) | ~bot(X1)) ) | ~spl53_9),
% 4.58/1.02 inference(avatar_component_clause,[],[f788])).
% 4.58/1.02 tff(f921,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X0 : $tType,X2 : X0] : (~bot(X1) | bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2)) ) | ~spl53_35),
% 4.58/1.02 inference(avatar_component_clause,[],[f920])).
% 4.58/1.02 tff(f4999,plain,(
% 4.58/1.02 ~spl53_272 | ~spl53_16 | ~spl53_267),
% 4.58/1.02 inference(avatar_split_clause,[],[f4831,f4770,f819,f4996])).
% 4.58/1.02 tff(f4831,plain,(
% 4.58/1.02 ~pp(the(bool,fNot)) | (~spl53_16 | ~spl53_267)),
% 4.58/1.02 inference(resolution,[],[f4772,f820])).
% 4.58/1.02 tff(f4988,plain,(
% 4.58/1.02 spl53_271 | ~spl53_92 | ~spl53_124),
% 4.58/1.02 inference(avatar_split_clause,[],[f2014,f1995,f1494,f4986])).
% 4.58/1.02 tff(f4986,plain,(
% 4.58/1.02 spl53_271 <=> ! [X2 : $tType,X4 : fun(X2,bool),X0 : X2,X3 : fun(X2,bool),X1 : X2] : (X0 = X1 | ~sP1(X2,X0,X3,X1,X4) | ~pp(aa(X2,bool,sK35(X2,X0,X3,X1,X4),X0)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_271])])).
% 4.58/1.02 tff(f1995,plain,(
% 4.58/1.02 spl53_124 <=> ! [X1 : $tType,X4 : fun(X1,bool),X0 : X1,X3 : X1,X2 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),sK35(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP1(X1,X0,X2,X3,X4))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_124])])).
% 4.58/1.02 tff(f2014,plain,(
% 4.58/1.02 ( ! [X2 : $tType,X3 : fun(X2,bool),X0 : X2,X1 : X2,X4 : fun(X2,bool)] : (X0 = X1 | ~sP1(X2,X0,X3,X1,X4) | ~pp(aa(X2,bool,sK35(X2,X0,X3,X1,X4),X0))) ) | (~spl53_92 | ~spl53_124)),
% 4.58/1.02 inference(resolution,[],[f1996,f1495])).
% 4.58/1.02 tff(f1996,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),sK35(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP1(X1,X0,X2,X3,X4)) ) | ~spl53_124),
% 4.58/1.02 inference(avatar_component_clause,[],[f1995])).
% 4.58/1.02 tff(f4984,plain,(
% 4.58/1.02 spl53_270 | ~spl53_92 | ~spl53_123),
% 4.58/1.02 inference(avatar_split_clause,[],[f2006,f1991,f1494,f4982])).
% 4.58/1.02 tff(f4982,plain,(
% 4.58/1.02 spl53_270 <=> ! [X2 : $tType,X4 : fun(X2,bool),X0 : X2,X3 : fun(X2,bool),X1 : X2] : (X0 = X1 | ~sP1(X2,X0,X3,X1,X4) | ~pp(aa(X2,bool,sK35(X2,X0,X3,X1,X4),X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_270])])).
% 4.58/1.02 tff(f1991,plain,(
% 4.58/1.02 spl53_123 <=> ! [X1 : $tType,X4 : fun(X1,bool),X0 : X1,X3 : X1,X2 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),sK35(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP1(X1,X0,X2,X3,X4))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_123])])).
% 4.58/1.02 tff(f2006,plain,(
% 4.58/1.02 ( ! [X2 : $tType,X3 : fun(X2,bool),X0 : X2,X1 : X2,X4 : fun(X2,bool)] : (X0 = X1 | ~sP1(X2,X0,X3,X1,X4) | ~pp(aa(X2,bool,sK35(X2,X0,X3,X1,X4),X1))) ) | (~spl53_92 | ~spl53_123)),
% 4.58/1.02 inference(resolution,[],[f1992,f1495])).
% 4.58/1.02 tff(f1992,plain,(
% 4.58/1.02 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),sK35(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP1(X1,X0,X2,X3,X4)) ) | ~spl53_123),
% 4.58/1.02 inference(avatar_component_clause,[],[f1991])).
% 4.58/1.02 tff(f4980,plain,(
% 4.58/1.02 spl53_269 | ~spl53_8 | ~spl53_70),
% 4.58/1.02 inference(avatar_split_clause,[],[f1156,f1149,f784,f4978])).
% 4.58/1.02 tff(f4978,plain,(
% 4.58/1.02 spl53_269 <=> ! [X0 : bool,X1 : fun(bool,bool)] : (fFalse != X0 | the(bool,X1) = X0 | ~pp(aa(bool,bool,X1,X0)) | fTrue = sK23(bool,X0,X1))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_269])])).
% 4.58/1.02 tff(f1149,plain,(
% 4.58/1.02 spl53_70 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (the(X0,X2) = X1 | sK23(X0,X1,X2) != X1 | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.02 introduced(avatar_definition,[new_symbols(naming,[spl53_70])])).
% 4.58/1.02 tff(f1156,plain,(
% 4.58/1.02 ( ! [X0 : bool,X1 : fun(bool,bool)] : (fFalse != X0 | the(bool,X1) = X0 | ~pp(aa(bool,bool,X1,X0)) | fTrue = sK23(bool,X0,X1)) ) | (~spl53_8 | ~spl53_70)),
% 4.58/1.02 inference(superposition,[],[f1150,f785])).
% 4.58/1.02 tff(f1150,plain,(
% 4.58/1.02 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (sK23(X0,X1,X2) != X1 | the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X1))) ) | ~spl53_70),
% 4.58/1.02 inference(avatar_component_clause,[],[f1149])).
% 4.58/1.02 tff(f4828,plain,(
% 4.58/1.02 spl53_268 | spl53_267 | ~spl53_16 | ~spl53_89),
% 4.58/1.02 inference(avatar_split_clause,[],[f1544,f1482,f819,f4770,f4826])).
% 4.58/1.02 tff(f1544,plain,(
% 4.58/1.02 ( ! [X0 : bool] : (pp(aa(bool,bool,fNot,the(bool,fNot))) | ~pp(aa(bool,bool,fNot,X0)) | ~pp(sK24(bool,X0,fNot))) ) | (~spl53_16 | ~spl53_89)),
% 4.58/1.02 inference(resolution,[],[f1483,f820])).
% 4.58/1.03 tff(f4773,plain,(
% 4.58/1.03 spl53_266 | spl53_267 | ~spl53_16 | ~spl53_87),
% 4.58/1.03 inference(avatar_split_clause,[],[f1511,f1473,f819,f4770,f4767])).
% 4.58/1.03 tff(f1511,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (pp(aa(bool,bool,fNot,the(bool,fNot))) | ~pp(aa(bool,bool,fNot,X0)) | ~pp(sK5(bool,fNot,X0))) ) | (~spl53_16 | ~spl53_87)),
% 4.58/1.03 inference(resolution,[],[f1474,f820])).
% 4.58/1.03 tff(f4765,plain,(
% 4.58/1.03 spl53_265 | ~spl53_8 | ~spl53_69),
% 4.58/1.03 inference(avatar_split_clause,[],[f1143,f1114,f784,f4763])).
% 4.58/1.03 tff(f4763,plain,(
% 4.58/1.03 spl53_265 <=> ! [X0 : fun(bool,bool)] : (pp(aa(bool,bool,X0,fFalse)) | combk(bool,bool,fFalse) = X0 | fTrue = sK11(bool,X0))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_265])])).
% 4.58/1.03 tff(f1143,plain,(
% 4.58/1.03 ( ! [X0 : fun(bool,bool)] : (pp(aa(bool,bool,X0,fFalse)) | combk(bool,bool,fFalse) = X0 | fTrue = sK11(bool,X0)) ) | (~spl53_8 | ~spl53_69)),
% 4.58/1.03 inference(superposition,[],[f1115,f785])).
% 4.58/1.03 tff(f4741,plain,(
% 4.58/1.03 spl53_264 | ~spl53_228 | ~spl53_263),
% 4.58/1.03 inference(avatar_split_clause,[],[f4737,f4734,f4018,f4739])).
% 4.58/1.03 tff(f4739,plain,(
% 4.58/1.03 spl53_264 <=> ! [X0 : fun(bool,bool)] : (fNot = X0 | pp(aa(bool,bool,X0,fFalse)) | fTrue = sK10(bool,X0))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_264])])).
% 4.58/1.03 tff(f4018,plain,(
% 4.58/1.03 spl53_228 <=> fNot = combk(bool,bool,fFalse)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_228])])).
% 4.58/1.03 tff(f4734,plain,(
% 4.58/1.03 spl53_263 <=> ! [X0 : fun(bool,bool)] : (pp(aa(bool,bool,X0,fFalse)) | combk(bool,bool,fFalse) = X0 | fTrue = sK10(bool,X0))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_263])])).
% 4.58/1.03 tff(f4737,plain,(
% 4.58/1.03 ( ! [X0 : fun(bool,bool)] : (fNot = X0 | pp(aa(bool,bool,X0,fFalse)) | fTrue = sK10(bool,X0)) ) | (~spl53_228 | ~spl53_263)),
% 4.58/1.03 inference(forward_demodulation,[],[f4735,f4020])).
% 4.58/1.03 tff(f4020,plain,(
% 4.58/1.03 fNot = combk(bool,bool,fFalse) | ~spl53_228),
% 4.58/1.03 inference(avatar_component_clause,[],[f4018])).
% 4.58/1.03 tff(f4735,plain,(
% 4.58/1.03 ( ! [X0 : fun(bool,bool)] : (pp(aa(bool,bool,X0,fFalse)) | combk(bool,bool,fFalse) = X0 | fTrue = sK10(bool,X0)) ) | ~spl53_263),
% 4.58/1.03 inference(avatar_component_clause,[],[f4734])).
% 4.58/1.03 tff(f4736,plain,(
% 4.58/1.03 spl53_263 | ~spl53_8 | ~spl53_68),
% 4.58/1.03 inference(avatar_split_clause,[],[f1129,f1110,f784,f4734])).
% 4.58/1.03 tff(f1129,plain,(
% 4.58/1.03 ( ! [X0 : fun(bool,bool)] : (pp(aa(bool,bool,X0,fFalse)) | combk(bool,bool,fFalse) = X0 | fTrue = sK10(bool,X0)) ) | (~spl53_8 | ~spl53_68)),
% 4.58/1.03 inference(superposition,[],[f1111,f785])).
% 4.58/1.03 tff(f4732,plain,(
% 4.58/1.03 spl53_262 | ~spl53_8 | ~spl53_60),
% 4.58/1.03 inference(avatar_split_clause,[],[f1100,f1057,f784,f4730])).
% 4.58/1.03 tff(f4730,plain,(
% 4.58/1.03 spl53_262 <=> ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (fFalse = the(bool,finite_fold1Set(bool,X0,X1)) | fTrue = aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_262])])).
% 4.58/1.03 tff(f1100,plain,(
% 4.58/1.03 ( ! [X0 : fun(bool,fun(bool,bool)),X1 : fun(bool,bool)] : (fFalse = the(bool,finite_fold1Set(bool,X0,X1)) | fTrue = aa(fun(bool,bool),bool,finite_fold1(bool,X0),X1)) ) | (~spl53_8 | ~spl53_60)),
% 4.58/1.03 inference(superposition,[],[f1058,f785])).
% 4.58/1.03 tff(f4668,plain,(
% 4.58/1.03 spl53_261 | ~spl53_84 | spl53_229),
% 4.58/1.03 inference(avatar_split_clause,[],[f4044,f4038,f1448,f4666])).
% 4.58/1.03 tff(f4038,plain,(
% 4.58/1.03 spl53_229 <=> pp(sK11(bool,fNot))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_229])])).
% 4.58/1.03 tff(f4044,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (sK11(bool,fNot) = X0 | fTrue = X0) ) | (~spl53_84 | spl53_229)),
% 4.58/1.03 inference(resolution,[],[f4040,f1449])).
% 4.58/1.03 tff(f4040,plain,(
% 4.58/1.03 ~pp(sK11(bool,fNot)) | spl53_229),
% 4.58/1.03 inference(avatar_component_clause,[],[f4038])).
% 4.58/1.03 tff(f4654,plain,(
% 4.58/1.03 spl53_260 | ~spl53_92 | ~spl53_121),
% 4.58/1.03 inference(avatar_split_clause,[],[f1973,f1947,f1494,f4652])).
% 4.58/1.03 tff(f4652,plain,(
% 4.58/1.03 spl53_260 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | ~pp(aa(X0,bool,sK9(X0,X1),sK8(X0,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_260])])).
% 4.58/1.03 tff(f1973,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | ~pp(aa(X0,bool,sK9(X0,X1),sK8(X0,X1)))) ) | (~spl53_92 | ~spl53_121)),
% 4.58/1.03 inference(resolution,[],[f1948,f1495])).
% 4.58/1.03 tff(f4650,plain,(
% 4.58/1.03 spl53_259 | ~spl53_8 | ~spl53_54),
% 4.58/1.03 inference(avatar_split_clause,[],[f1035,f1026,f784,f4648])).
% 4.58/1.03 tff(f4648,plain,(
% 4.58/1.03 spl53_259 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : fun(X0,fun(bool,bool)),X1 : bool] : (finite_fold_graph(X0,bool,X2,X1,X3,fFalse) | ~finite_finite1(X0,X3) | fTrue = sK34(X0,bool,X1,X2,X3))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_259])])).
% 4.58/1.03 tff(f1035,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(bool,bool)),X3 : fun(X0,bool),X1 : bool] : (finite_fold_graph(X0,bool,X2,X1,X3,fFalse) | ~finite_finite1(X0,X3) | fTrue = sK34(X0,bool,X1,X2,X3)) ) | (~spl53_8 | ~spl53_54)),
% 4.58/1.03 inference(superposition,[],[f1027,f785])).
% 4.58/1.03 tff(f4632,plain,(
% 4.58/1.03 spl53_258 | ~spl53_50 | ~spl53_76),
% 4.58/1.03 inference(avatar_split_clause,[],[f1194,f1180,f996,f4630])).
% 4.58/1.03 tff(f4630,plain,(
% 4.58/1.03 spl53_258 <=> ! [X0 : $tType,X4 : fun(X0,fun(state,bool)),X3 : com,X2 : fun(X0,fun(state,bool)),X1 : hoare_28830079triple(X0)] : (hoare_1841697145triple(X0,X2,X3,X4) != X1 | sK16(X0,X1) = X4)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_258])])).
% 4.58/1.03 tff(f996,plain,(
% 4.58/1.03 spl53_50 <=> ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : hoare_1841697145triple(X0,sK14(X0,X1),sK15(X0,X1),sK16(X0,X1)) = X1),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_50])])).
% 4.58/1.03 tff(f1180,plain,(
% 4.58/1.03 spl53_76 <=> ! [X0 : $tType,X2 : com,X6 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X5 : com,X1 : fun(X0,fun(state,bool))] : (X1 = X4 | hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_76])])).
% 4.58/1.03 tff(f1194,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : hoare_28830079triple(X0),X4 : fun(X0,fun(state,bool))] : (hoare_1841697145triple(X0,X2,X3,X4) != X1 | sK16(X0,X1) = X4) ) | (~spl53_50 | ~spl53_76)),
% 4.58/1.03 inference(superposition,[],[f1181,f997])).
% 4.58/1.03 tff(f997,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : (hoare_1841697145triple(X0,sK14(X0,X1),sK15(X0,X1),sK16(X0,X1)) = X1) ) | ~spl53_50),
% 4.58/1.03 inference(avatar_component_clause,[],[f996])).
% 4.58/1.03 tff(f1181,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : com] : (hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4) | X1 = X4) ) | ~spl53_76),
% 4.58/1.03 inference(avatar_component_clause,[],[f1180])).
% 4.58/1.03 tff(f4628,plain,(
% 4.58/1.03 spl53_257 | ~spl53_50 | ~spl53_75),
% 4.58/1.03 inference(avatar_split_clause,[],[f1191,f1176,f996,f4626])).
% 4.58/1.03 tff(f4626,plain,(
% 4.58/1.03 spl53_257 <=> ! [X0 : $tType,X4 : fun(X0,fun(state,bool)),X3 : com,X2 : fun(X0,fun(state,bool)),X1 : hoare_28830079triple(X0)] : (hoare_1841697145triple(X0,X2,X3,X4) != X1 | sK14(X0,X1) = X2)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_257])])).
% 4.58/1.03 tff(f1176,plain,(
% 4.58/1.03 spl53_75 <=> ! [X0 : $tType,X5 : com,X4 : fun(X0,fun(state,bool)),X2 : com,X6 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool))] : (X3 = X6 | hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_75])])).
% 4.58/1.03 tff(f1191,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : hoare_28830079triple(X0),X4 : fun(X0,fun(state,bool))] : (hoare_1841697145triple(X0,X2,X3,X4) != X1 | sK14(X0,X1) = X2) ) | (~spl53_50 | ~spl53_75)),
% 4.58/1.03 inference(superposition,[],[f1177,f997])).
% 4.58/1.03 tff(f1177,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : com] : (hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4) | X3 = X6) ) | ~spl53_75),
% 4.58/1.03 inference(avatar_component_clause,[],[f1176])).
% 4.58/1.03 tff(f4624,plain,(
% 4.58/1.03 spl53_256 | ~spl53_42 | ~spl53_54),
% 4.58/1.03 inference(avatar_split_clause,[],[f1034,f1026,f959,f4622])).
% 4.58/1.03 tff(f4622,plain,(
% 4.58/1.03 spl53_256 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,fun(X1,X1)),X2 : X1] : (~finite_finite1(X0,combk(bool,X0,fFalse)) | sK34(X0,X1,X2,X3,combk(bool,X0,fFalse)) = X2)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_256])])).
% 4.58/1.03 tff(f959,plain,(
% 4.58/1.03 spl53_42 <=> ! [X1 : $tType,X0 : $tType,X4 : fun(X0,fun(X1,X1)),X3 : X1,X2 : X1] : (~finite_fold_graph(X0,X1,X4,X3,combk(bool,X0,fFalse),X2) | X2 = X3)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_42])])).
% 4.58/1.03 tff(f1034,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : (~finite_finite1(X0,combk(bool,X0,fFalse)) | sK34(X0,X1,X2,X3,combk(bool,X0,fFalse)) = X2) ) | (~spl53_42 | ~spl53_54)),
% 4.58/1.03 inference(resolution,[],[f1027,f960])).
% 4.58/1.03 tff(f960,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X1,X4 : fun(X0,fun(X1,X1))] : (~finite_fold_graph(X0,X1,X4,X3,combk(bool,X0,fFalse),X2) | X2 = X3) ) | ~spl53_42),
% 4.58/1.03 inference(avatar_component_clause,[],[f959])).
% 4.58/1.03 tff(f4619,plain,(
% 4.58/1.03 spl53_255 | ~spl53_8 | ~spl53_53),
% 4.58/1.03 inference(avatar_split_clause,[],[f1022,f1019,f784,f4617])).
% 4.58/1.03 tff(f4617,plain,(
% 4.58/1.03 spl53_255 <=> ! [X1 : $tType,X0 : bool,X3 : X1,X2 : fun(X1,bool)] : (combk(bool,X1,X0) != X2 | ~pp(aa(X1,bool,X2,X3)) | fTrue = X0)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_255])])).
% 4.58/1.03 tff(f1019,plain,(
% 4.58/1.03 spl53_53 <=> ! [X0 : $tType,X1 : fun(X0,bool),X3 : X0] : (combk(bool,X0,fFalse) != X1 | ~pp(aa(X0,bool,X1,X3)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_53])])).
% 4.58/1.03 tff(f1022,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : bool] : (combk(bool,X1,X0) != X2 | ~pp(aa(X1,bool,X2,X3)) | fTrue = X0) ) | (~spl53_8 | ~spl53_53)),
% 4.58/1.03 inference(superposition,[],[f1020,f785])).
% 4.58/1.03 tff(f1020,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X3 : X0,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) != X1 | ~pp(aa(X0,bool,X1,X3))) ) | ~spl53_53),
% 4.58/1.03 inference(avatar_component_clause,[],[f1019])).
% 4.58/1.03 tff(f4360,plain,(
% 4.58/1.03 ~spl53_3 | ~spl53_5 | spl53_242),
% 4.58/1.03 inference(avatar_split_clause,[],[f4321,f4263,f772,f762])).
% 4.58/1.03 tff(f762,plain,(
% 4.58/1.03 spl53_3 <=> finite_finite(bool)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_3])])).
% 4.58/1.03 tff(f4263,plain,(
% 4.58/1.03 spl53_242 <=> finite_finite1(bool,fNot)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_242])])).
% 4.58/1.03 tff(f4321,plain,(
% 4.58/1.03 ~finite_finite(bool) | (~spl53_5 | spl53_242)),
% 4.58/1.03 inference(resolution,[],[f4264,f773])).
% 4.58/1.03 tff(f4264,plain,(
% 4.58/1.03 ~finite_finite1(bool,fNot) | spl53_242),
% 4.58/1.03 inference(avatar_component_clause,[],[f4263])).
% 4.58/1.03 tff(f4349,plain,(
% 4.58/1.03 spl53_254 | ~spl53_99 | ~spl53_140),
% 4.58/1.03 inference(avatar_split_clause,[],[f2309,f2271,f1666,f4347])).
% 4.58/1.03 tff(f4347,plain,(
% 4.58/1.03 spl53_254 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,sK8(X0,X1))) | combk(bool,X0,fFalse) = X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_254])])).
% 4.58/1.03 tff(f1666,plain,(
% 4.58/1.03 spl53_99 <=> ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X3))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_99])])).
% 4.58/1.03 tff(f2309,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,sK8(X0,X1))) | combk(bool,X0,fFalse) = X1) ) | (~spl53_99 | ~spl53_140)),
% 4.58/1.03 inference(superposition,[],[f1667,f2272])).
% 4.58/1.03 tff(f1667,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X3))) ) | ~spl53_99),
% 4.58/1.03 inference(avatar_component_clause,[],[f1666])).
% 4.58/1.03 tff(f4345,plain,(
% 4.58/1.03 spl53_253 | ~spl53_98 | ~spl53_140),
% 4.58/1.03 inference(avatar_split_clause,[],[f2308,f2271,f1662,f4343])).
% 4.58/1.03 tff(f4343,plain,(
% 4.58/1.03 spl53_253 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,sK9(X0,X1)) | combk(bool,X0,fFalse) = X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_253])])).
% 4.58/1.03 tff(f1662,plain,(
% 4.58/1.03 spl53_98 <=> ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)) | ~finite_finite1(X0,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_98])])).
% 4.58/1.03 tff(f2308,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,sK9(X0,X1)) | combk(bool,X0,fFalse) = X1) ) | (~spl53_98 | ~spl53_140)),
% 4.58/1.03 inference(superposition,[],[f1663,f2272])).
% 4.58/1.03 tff(f1663,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)) | ~finite_finite1(X0,X2)) ) | ~spl53_98),
% 4.58/1.03 inference(avatar_component_clause,[],[f1662])).
% 4.58/1.03 tff(f4341,plain,(
% 4.58/1.03 spl53_252 | ~spl53_97 | ~spl53_140),
% 4.58/1.03 inference(avatar_split_clause,[],[f2307,f2271,f1658,f4339])).
% 4.58/1.03 tff(f4339,plain,(
% 4.58/1.03 spl53_252 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (~finite_finite1(X0,X1) | finite_finite1(X0,sK9(X0,X1)) | combk(bool,X0,fFalse) = X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_252])])).
% 4.58/1.03 tff(f1658,plain,(
% 4.58/1.03 spl53_97 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_97])])).
% 4.58/1.03 tff(f2307,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (~finite_finite1(X0,X1) | finite_finite1(X0,sK9(X0,X1)) | combk(bool,X0,fFalse) = X1) ) | (~spl53_97 | ~spl53_140)),
% 4.58/1.03 inference(superposition,[],[f1659,f2272])).
% 4.58/1.03 tff(f1659,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) | finite_finite1(X0,X1)) ) | ~spl53_97),
% 4.58/1.03 inference(avatar_component_clause,[],[f1658])).
% 4.58/1.03 tff(f4337,plain,(
% 4.58/1.03 spl53_251 | ~spl53_98 | ~spl53_135),
% 4.58/1.03 inference(avatar_split_clause,[],[f2250,f2238,f1662,f4335])).
% 4.58/1.03 tff(f4335,plain,(
% 4.58/1.03 spl53_251 <=> ! [X0 : $tType,X1 : X0] : (finite_finite1(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) | ~finite_finite1(X0,combk(bool,X0,fFalse)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_251])])).
% 4.58/1.03 tff(f2250,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (finite_finite1(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) | ~finite_finite1(X0,combk(bool,X0,fFalse))) ) | (~spl53_98 | ~spl53_135)),
% 4.58/1.03 inference(superposition,[],[f1663,f2239])).
% 4.58/1.03 tff(f4333,plain,(
% 4.58/1.03 spl53_250 | ~spl53_91 | ~spl53_113),
% 4.58/1.03 inference(avatar_split_clause,[],[f1871,f1800,f1490,f4331])).
% 4.58/1.03 tff(f4331,plain,(
% 4.58/1.03 spl53_250 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK13(X0,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_250])])).
% 4.58/1.03 tff(f1871,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK13(X0,X1)))) ) | (~spl53_91 | ~spl53_113)),
% 4.58/1.03 inference(resolution,[],[f1801,f1491])).
% 4.58/1.03 tff(f4329,plain,(
% 4.58/1.03 spl53_249 | ~spl53_91 | ~spl53_112),
% 4.58/1.03 inference(avatar_split_clause,[],[f1856,f1796,f1490,f4327])).
% 4.58/1.03 tff(f4327,plain,(
% 4.58/1.03 spl53_249 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK12(X0,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_249])])).
% 4.58/1.03 tff(f1856,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK12(X0,X1)))) ) | (~spl53_91 | ~spl53_112)),
% 4.58/1.03 inference(resolution,[],[f1797,f1491])).
% 4.58/1.03 tff(f4325,plain,(
% 4.58/1.03 spl53_248 | ~spl53_91 | ~spl53_111),
% 4.58/1.03 inference(avatar_split_clause,[],[f1841,f1792,f1490,f4323])).
% 4.58/1.03 tff(f4323,plain,(
% 4.58/1.03 spl53_248 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK4(X0,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_248])])).
% 4.58/1.03 tff(f1841,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK4(X0,X1)))) ) | (~spl53_91 | ~spl53_111)),
% 4.58/1.03 inference(resolution,[],[f1793,f1491])).
% 4.58/1.03 tff(f4320,plain,(
% 4.58/1.03 spl53_247 | ~spl53_16 | ~spl53_81),
% 4.58/1.03 inference(avatar_split_clause,[],[f1416,f1400,f819,f4318])).
% 4.58/1.03 tff(f4318,plain,(
% 4.58/1.03 spl53_247 <=> ! [X0 : bool] : (the(bool,fNot) = X0 | ~pp(aa(bool,bool,fNot,X0)) | ~pp(sK23(bool,X0,fNot)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_247])])).
% 4.58/1.03 tff(f1416,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (the(bool,fNot) = X0 | ~pp(aa(bool,bool,fNot,X0)) | ~pp(sK23(bool,X0,fNot))) ) | (~spl53_16 | ~spl53_81)),
% 4.58/1.03 inference(resolution,[],[f1401,f820])).
% 4.58/1.03 tff(f4316,plain,(
% 4.58/1.03 spl53_246 | ~spl53_48 | ~spl53_68),
% 4.58/1.03 inference(avatar_split_clause,[],[f1122,f1110,f988,f4314])).
% 4.58/1.03 tff(f4314,plain,(
% 4.58/1.03 spl53_246 <=> ! [X0 : bool] : (aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) | pp(X0))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_246])])).
% 4.58/1.03 tff(f1122,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) | pp(X0)) ) | (~spl53_48 | ~spl53_68)),
% 4.58/1.03 inference(resolution,[],[f1111,f989])).
% 4.58/1.03 tff(f4312,plain,(
% 4.58/1.03 spl53_245 | ~spl53_38 | ~spl53_60),
% 4.58/1.03 inference(avatar_split_clause,[],[f1101,f1057,f933,f4310])).
% 4.58/1.03 tff(f4310,plain,(
% 4.58/1.03 spl53_245 <=> ! [X0 : fun(bool,fun(bool,bool))] : (pp(the(bool,finite_fold1Set(bool,X0,sK18(bool,finite_fold1(bool,X0))))) | ~sP0(bool,finite_fold1(bool,X0)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_245])])).
% 4.58/1.03 tff(f1101,plain,(
% 4.58/1.03 ( ! [X0 : fun(bool,fun(bool,bool))] : (pp(the(bool,finite_fold1Set(bool,X0,sK18(bool,finite_fold1(bool,X0))))) | ~sP0(bool,finite_fold1(bool,X0))) ) | (~spl53_38 | ~spl53_60)),
% 4.58/1.03 inference(superposition,[],[f934,f1058])).
% 4.58/1.03 tff(f4308,plain,(
% 4.58/1.03 spl53_244 | ~spl53_8 | ~spl53_42),
% 4.58/1.03 inference(avatar_split_clause,[],[f965,f959,f784,f4306])).
% 4.58/1.03 tff(f4306,plain,(
% 4.58/1.03 spl53_244 <=> ! [X1 : $tType,X2 : $tType,X3 : fun(X1,fun(X2,X2)),X4 : X2,X0 : bool,X5 : X2] : (~finite_fold_graph(X1,X2,X3,X4,combk(bool,X1,X0),X5) | X4 = X5 | fTrue = X0)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_244])])).
% 4.58/1.03 tff(f965,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : $tType,X3 : fun(X1,fun(X2,X2)),X0 : bool,X4 : X2,X5 : X2] : (~finite_fold_graph(X1,X2,X3,X4,combk(bool,X1,X0),X5) | X4 = X5 | fTrue = X0) ) | (~spl53_8 | ~spl53_42)),
% 4.58/1.03 inference(superposition,[],[f960,f785])).
% 4.58/1.03 tff(f4304,plain,(
% 4.58/1.03 spl53_243 | ~spl53_8 | ~spl53_41),
% 4.58/1.03 inference(avatar_split_clause,[],[f964,f950,f784,f4302])).
% 4.58/1.03 tff(f4302,plain,(
% 4.58/1.03 spl53_243 <=> ! [X1 : $tType,X2 : fun(fun(X1,bool),bool),X0 : bool] : (sK18(X1,X2) != combk(bool,X1,X0) | ~sP0(X1,X2) | fTrue = X0)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_243])])).
% 4.58/1.03 tff(f950,plain,(
% 4.58/1.03 spl53_41 <=> ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (combk(bool,X0,fFalse) != sK18(X0,X1) | ~sP0(X0,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_41])])).
% 4.58/1.03 tff(f964,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(fun(X1,bool),bool),X0 : bool] : (sK18(X1,X2) != combk(bool,X1,X0) | ~sP0(X1,X2) | fTrue = X0) ) | (~spl53_8 | ~spl53_41)),
% 4.58/1.03 inference(superposition,[],[f951,f785])).
% 4.58/1.03 tff(f951,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (combk(bool,X0,fFalse) != sK18(X0,X1) | ~sP0(X0,X1)) ) | ~spl53_41),
% 4.58/1.03 inference(avatar_component_clause,[],[f950])).
% 4.58/1.03 tff(f4266,plain,(
% 4.58/1.03 spl53_242 | ~spl53_37 | ~spl53_228),
% 4.58/1.03 inference(avatar_split_clause,[],[f4187,f4018,f929,f4263])).
% 4.58/1.03 tff(f929,plain,(
% 4.58/1.03 spl53_37 <=> ! [X0 : $tType] : finite_finite1(X0,combk(bool,X0,fFalse))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_37])])).
% 4.58/1.03 tff(f4187,plain,(
% 4.58/1.03 finite_finite1(bool,fNot) | (~spl53_37 | ~spl53_228)),
% 4.58/1.03 inference(superposition,[],[f930,f4020])).
% 4.58/1.03 tff(f930,plain,(
% 4.58/1.03 ( ! [X0 : $tType] : (finite_finite1(X0,combk(bool,X0,fFalse))) ) | ~spl53_37),
% 4.58/1.03 inference(avatar_component_clause,[],[f929])).
% 4.58/1.03 tff(f4261,plain,(
% 4.58/1.03 spl53_241 | ~spl53_114 | ~spl53_135),
% 4.58/1.03 inference(avatar_split_clause,[],[f2248,f2238,f1804,f4259])).
% 4.58/1.03 tff(f4259,plain,(
% 4.58/1.03 spl53_241 <=> ! [X0 : $tType,X1 : X0] : combk(bool,X0,fFalse) != aa(X0,fun(X0,bool),fequal(X0),X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_241])])).
% 4.58/1.03 tff(f1804,plain,(
% 4.58/1.03 spl53_114 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_114])])).
% 4.58/1.03 tff(f2248,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (combk(bool,X0,fFalse) != aa(X0,fun(X0,bool),fequal(X0),X1)) ) | (~spl53_114 | ~spl53_135)),
% 4.58/1.03 inference(superposition,[],[f1805,f2239])).
% 4.58/1.03 tff(f1805,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) ) | ~spl53_114),
% 4.58/1.03 inference(avatar_component_clause,[],[f1804])).
% 4.58/1.03 tff(f4257,plain,(
% 4.58/1.03 spl53_240 | ~spl53_60 | ~spl53_73),
% 4.58/1.03 inference(avatar_split_clause,[],[f1171,f1164,f1057,f4255])).
% 4.58/1.03 tff(f4255,plain,(
% 4.58/1.03 spl53_240 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : the(X0,finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2))) = X2),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_240])])).
% 4.58/1.03 tff(f1171,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : (the(X0,finite_fold1Set(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X2))) = X2) ) | (~spl53_60 | ~spl53_73)),
% 4.58/1.03 inference(superposition,[],[f1165,f1058])).
% 4.58/1.03 tff(f4253,plain,(
% 4.58/1.03 spl53_239 | ~spl53_8 | ~spl53_26),
% 4.58/1.03 inference(avatar_split_clause,[],[f894,f867,f784,f4251])).
% 4.58/1.03 tff(f4251,plain,(
% 4.58/1.03 spl53_239 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = the(bool,aa(bool,fun(bool,bool),fequal(bool),X0)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_239])])).
% 4.58/1.03 tff(f867,plain,(
% 4.58/1.03 spl53_26 <=> ! [X0 : $tType,X1 : X0] : the(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_26])])).
% 4.58/1.03 tff(f894,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (fFalse = X0 | fTrue = the(bool,aa(bool,fun(bool,bool),fequal(bool),X0))) ) | (~spl53_8 | ~spl53_26)),
% 4.58/1.03 inference(superposition,[],[f868,f785])).
% 4.58/1.03 tff(f868,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (the(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) ) | ~spl53_26),
% 4.58/1.03 inference(avatar_component_clause,[],[f867])).
% 4.58/1.03 tff(f4229,plain,(
% 4.58/1.03 spl53_238 | ~spl53_27 | ~spl53_34 | ~spl53_68),
% 4.58/1.03 inference(avatar_split_clause,[],[f1133,f1110,f912,f871,f4227])).
% 4.58/1.03 tff(f4225,plain,(
% 4.58/1.03 spl53_237 | ~spl53_62 | ~spl53_66),
% 4.58/1.03 inference(avatar_split_clause,[],[f1117,f1083,f1065,f4223])).
% 4.58/1.03 tff(f4223,plain,(
% 4.58/1.03 spl53_237 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : sK33(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X1),X2) = X1),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_237])])).
% 4.58/1.03 tff(f1083,plain,(
% 4.58/1.03 spl53_66 <=> ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(X0,fun(X0,bool),fequal(X0),X2)),X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_66])])).
% 4.58/1.03 tff(f1117,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (sK33(X0,X1,aa(X0,fun(X0,bool),fequal(X0),X1),X2) = X1) ) | (~spl53_62 | ~spl53_66)),
% 4.58/1.03 inference(resolution,[],[f1084,f1066])).
% 4.58/1.03 tff(f1084,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(X0,fun(X0,bool),fequal(X0),X2)),X2))) ) | ~spl53_66),
% 4.58/1.03 inference(avatar_component_clause,[],[f1083])).
% 4.58/1.03 tff(f4173,plain,(
% 4.58/1.03 spl53_236 | ~spl53_84 | spl53_227),
% 4.58/1.03 inference(avatar_split_clause,[],[f4024,f4014,f1448,f4171])).
% 4.58/1.03 tff(f4014,plain,(
% 4.58/1.03 spl53_227 <=> pp(sK10(bool,fNot))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_227])])).
% 4.58/1.03 tff(f4024,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (sK10(bool,fNot) = X0 | fTrue = X0) ) | (~spl53_84 | spl53_227)),
% 4.58/1.03 inference(resolution,[],[f4016,f1449])).
% 4.58/1.03 tff(f4016,plain,(
% 4.58/1.03 ~pp(sK10(bool,fNot)) | spl53_227),
% 4.58/1.03 inference(avatar_component_clause,[],[f4014])).
% 4.58/1.03 tff(f4081,plain,(
% 4.58/1.03 spl53_235 | ~spl53_92 | ~spl53_94),
% 4.58/1.03 inference(avatar_split_clause,[],[f1621,f1614,f1494,f4079])).
% 4.58/1.03 tff(f4079,plain,(
% 4.58/1.03 spl53_235 <=> ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (~sP0(X0,X1) | ~pp(aa(X0,bool,sK18(X0,X1),sK17(X0,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_235])])).
% 4.58/1.03 tff(f1621,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (~sP0(X0,X1) | ~pp(aa(X0,bool,sK18(X0,X1),sK17(X0,X1)))) ) | (~spl53_92 | ~spl53_94)),
% 4.58/1.03 inference(resolution,[],[f1615,f1495])).
% 4.58/1.03 tff(f4077,plain,(
% 4.58/1.03 spl53_234 | ~spl53_20 | ~spl53_68),
% 4.58/1.03 inference(avatar_split_clause,[],[f1132,f1110,f840,f4075])).
% 4.58/1.03 tff(f4075,plain,(
% 4.58/1.03 spl53_234 <=> ! [X0 : $tType,X1 : bool] : (pp(X1) | combk(bool,X0,fFalse) = combk(bool,X0,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_234])])).
% 4.58/1.03 tff(f1132,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : bool] : (pp(X1) | combk(bool,X0,fFalse) = combk(bool,X0,X1)) ) | (~spl53_20 | ~spl53_68)),
% 4.58/1.03 inference(superposition,[],[f1111,f841])).
% 4.58/1.03 tff(f4073,plain,(
% 4.58/1.03 spl53_233 | ~spl53_50 | ~spl53_55),
% 4.58/1.03 inference(avatar_split_clause,[],[f1036,f1031,f996,f4071])).
% 4.58/1.03 tff(f4071,plain,(
% 4.58/1.03 spl53_233 <=> ! [X0 : $tType,X4 : fun(X0,fun(state,bool)),X3 : com,X2 : fun(X0,fun(state,bool)),X1 : hoare_28830079triple(X0)] : (hoare_1841697145triple(X0,X2,X3,X4) != X1 | sK15(X0,X1) = X3)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_233])])).
% 4.58/1.03 tff(f1031,plain,(
% 4.58/1.03 spl53_55 <=> ! [X0 : $tType,X5 : com,X3 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X6 : fun(X0,fun(state,bool)),X2 : com,X1 : fun(X0,fun(state,bool))] : (X2 = X5 | hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_55])])).
% 4.58/1.03 tff(f1036,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : hoare_28830079triple(X0),X4 : fun(X0,fun(state,bool))] : (hoare_1841697145triple(X0,X2,X3,X4) != X1 | sK15(X0,X1) = X3) ) | (~spl53_50 | ~spl53_55)),
% 4.58/1.03 inference(superposition,[],[f1032,f997])).
% 4.58/1.03 tff(f1032,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : com] : (hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4) | X2 = X5) ) | ~spl53_55),
% 4.58/1.03 inference(avatar_component_clause,[],[f1031])).
% 4.58/1.03 tff(f4064,plain,(
% 4.58/1.03 spl53_232 | ~spl53_27 | ~spl53_34 | ~spl53_68 | ~spl53_231),
% 4.58/1.03 inference(avatar_split_clause,[],[f4060,f4057,f1110,f912,f871,f4062])).
% 4.58/1.03 tff(f4062,plain,(
% 4.58/1.03 spl53_232 <=> ! [X0 : $tType] : ~sP0(X0,combk(bool,fun(X0,bool),fFalse))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_232])])).
% 4.58/1.03 tff(f4057,plain,(
% 4.58/1.03 spl53_231 <=> ! [X0 : $tType,X1 : fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)))] : ~sP0(X0,finite_fold1Set(fun(X0,bool),X1,combk(bool,fun(X0,bool),fFalse)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_231])])).
% 4.58/1.03 tff(f4060,plain,(
% 4.58/1.03 ( ! [X0 : $tType] : (~sP0(X0,combk(bool,fun(X0,bool),fFalse))) ) | (~spl53_27 | ~spl53_34 | ~spl53_68 | ~spl53_231)),
% 4.58/1.03 inference(forward_demodulation,[],[f4058,f1133])).
% 4.58/1.03 tff(f4058,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)))] : (~sP0(X0,finite_fold1Set(fun(X0,bool),X1,combk(bool,fun(X0,bool),fFalse)))) ) | ~spl53_231),
% 4.58/1.03 inference(avatar_component_clause,[],[f4057])).
% 4.58/1.03 tff(f4059,plain,(
% 4.58/1.03 spl53_231 | ~spl53_27 | ~spl53_34 | ~spl53_38),
% 4.58/1.03 inference(avatar_split_clause,[],[f957,f933,f912,f871,f4057])).
% 4.58/1.03 tff(f957,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)))] : (~sP0(X0,finite_fold1Set(fun(X0,bool),X1,combk(bool,fun(X0,bool),fFalse)))) ) | (~spl53_27 | ~spl53_34 | ~spl53_38)),
% 4.58/1.03 inference(forward_demodulation,[],[f953,f913])).
% 4.58/1.03 tff(f953,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)))] : (~sP0(X0,finite_fold1Set(fun(X0,bool),X1,bot_bot(fun(fun(X0,bool),bool))))) ) | (~spl53_27 | ~spl53_38)),
% 4.58/1.03 inference(resolution,[],[f934,f872])).
% 4.58/1.03 tff(f4055,plain,(
% 4.58/1.03 spl53_230 | ~spl53_8 | ~spl53_20),
% 4.58/1.03 inference(avatar_split_clause,[],[f855,f840,f784,f4053])).
% 4.58/1.03 tff(f4053,plain,(
% 4.58/1.03 spl53_230 <=> ! [X0 : $tType,X2 : X0,X1 : bool] : (fFalse = X1 | fTrue = aa(X0,bool,combk(bool,X0,X1),X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_230])])).
% 4.58/1.03 tff(f855,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : bool] : (fFalse = X1 | fTrue = aa(X0,bool,combk(bool,X0,X1),X2)) ) | (~spl53_8 | ~spl53_20)),
% 4.58/1.03 inference(superposition,[],[f841,f785])).
% 4.58/1.03 tff(f4041,plain,(
% 4.58/1.03 ~spl53_229 | spl53_228 | ~spl53_16 | ~spl53_69),
% 4.58/1.03 inference(avatar_split_clause,[],[f1134,f1114,f819,f4018,f4038])).
% 4.58/1.03 tff(f1134,plain,(
% 4.58/1.03 fNot = combk(bool,bool,fFalse) | ~pp(sK11(bool,fNot)) | (~spl53_16 | ~spl53_69)),
% 4.58/1.03 inference(resolution,[],[f1115,f820])).
% 4.58/1.03 tff(f4021,plain,(
% 4.58/1.03 ~spl53_227 | spl53_228 | ~spl53_16 | ~spl53_68),
% 4.58/1.03 inference(avatar_split_clause,[],[f1120,f1110,f819,f4018,f4014])).
% 4.58/1.03 tff(f1120,plain,(
% 4.58/1.03 fNot = combk(bool,bool,fFalse) | ~pp(sK10(bool,fNot)) | (~spl53_16 | ~spl53_68)),
% 4.58/1.03 inference(resolution,[],[f1111,f820])).
% 4.58/1.03 tff(f4010,plain,(
% 4.58/1.03 spl53_226 | ~spl53_27 | ~spl53_34),
% 4.58/1.03 inference(avatar_split_clause,[],[f915,f912,f871,f4008])).
% 4.58/1.03 tff(f4008,plain,(
% 4.58/1.03 spl53_226 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : ~pp(aa(X0,bool,finite_fold1Set(X0,X1,combk(bool,X0,fFalse)),X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_226])])).
% 4.58/1.03 tff(f915,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : (~pp(aa(X0,bool,finite_fold1Set(X0,X1,combk(bool,X0,fFalse)),X2))) ) | (~spl53_27 | ~spl53_34)),
% 4.58/1.03 inference(superposition,[],[f872,f913])).
% 4.58/1.03 tff(f3955,plain,(
% 4.58/1.03 spl53_225 | ~spl53_14 | ~spl53_139 | ~spl53_224),
% 4.58/1.03 inference(avatar_split_clause,[],[f3951,f3947,f2267,f811,f3953])).
% 4.58/1.03 tff(f3953,plain,(
% 4.58/1.03 spl53_225 <=> ! [X0 : $tType,X3 : bool,X2 : X0,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),fequal(X0),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),fequal(X0),X1)))) = X1 | pp(X3))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_225])])).
% 4.58/1.03 tff(f3947,plain,(
% 4.58/1.03 spl53_224 <=> ! [X0 : $tType,X3 : bool,X2 : X0,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X1 | pp(X3))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_224])])).
% 4.58/1.03 tff(f3951,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : bool,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),fequal(X0),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),fequal(X0),X1)))) = X1 | pp(X3)) ) | (~spl53_14 | ~spl53_139 | ~spl53_224)),
% 4.58/1.03 inference(forward_demodulation,[],[f3950,f2300])).
% 4.58/1.03 tff(f3950,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : bool,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),fequal(X0),X1)))) = X1 | pp(X3)) ) | (~spl53_14 | ~spl53_139 | ~spl53_224)),
% 4.58/1.03 inference(forward_demodulation,[],[f3948,f2300])).
% 4.58/1.03 tff(f3948,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : bool,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X1 | pp(X3)) ) | ~spl53_224),
% 4.58/1.03 inference(avatar_component_clause,[],[f3947])).
% 4.58/1.03 tff(f3949,plain,(
% 4.58/1.03 spl53_224),
% 4.58/1.03 inference(avatar_split_clause,[],[f562,f3947])).
% 4.58/1.03 tff(f562,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : bool,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X1 | pp(X3)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f288])).
% 4.58/1.03 tff(f288,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : bool] : ((the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X1 | pp(X3)) & (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X2 | ~pp(X3)))),
% 4.58/1.03 inference(ennf_transformation,[],[f208])).
% 4.58/1.03 tff(f208,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : bool] : ((~pp(X3) => the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X1) & (pp(X3) => the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X2))),
% 4.58/1.03 inference(rectify,[],[f56])).
% 4.58/1.03 tff(f56,axiom,(
% 4.58/1.03 ! [X1 : $tType,X31 : X1,X26 : X1,X16 : bool] : ((~pp(X16) => the(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fconj),aa(fun(X1,bool),fun(X1,bool),combb(bool,bool,X1,aa(bool,fun(bool,bool),fimplies,X16)),aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X26)))),aa(fun(X1,bool),fun(X1,bool),combb(bool,bool,X1,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X16))),aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X31)))) = X31) & (pp(X16) => the(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fconj),aa(fun(X1,bool),fun(X1,bool),combb(bool,bool,X1,aa(bool,fun(bool,bool),fimplies,X16)),aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X26)))),aa(fun(X1,bool),fun(X1,bool),combb(bool,bool,X1,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X16))),aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X31)))) = X26))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_If__def)).
% 4.58/1.03 tff(f3909,plain,(
% 4.58/1.03 spl53_223 | ~spl53_14 | ~spl53_139 | ~spl53_222),
% 4.58/1.03 inference(avatar_split_clause,[],[f3904,f3900,f2267,f811,f3907])).
% 4.58/1.03 tff(f3907,plain,(
% 4.58/1.03 spl53_223 <=> ! [X0 : $tType,X3 : bool,X2 : X0,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),fequal(X0),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),fequal(X0),X1)))) = X2 | ~pp(X3))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_223])])).
% 4.58/1.03 tff(f3900,plain,(
% 4.58/1.03 spl53_222 <=> ! [X0 : $tType,X3 : bool,X2 : X0,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X2 | ~pp(X3))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_222])])).
% 4.58/1.03 tff(f3904,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : bool,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),fequal(X0),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),fequal(X0),X1)))) = X2 | ~pp(X3)) ) | (~spl53_14 | ~spl53_139 | ~spl53_222)),
% 4.58/1.03 inference(forward_demodulation,[],[f3903,f2300])).
% 4.58/1.03 tff(f3903,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : bool,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),fequal(X0),X1)))) = X2 | ~pp(X3)) ) | (~spl53_14 | ~spl53_139 | ~spl53_222)),
% 4.58/1.03 inference(forward_demodulation,[],[f3901,f2300])).
% 4.58/1.03 tff(f3901,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : bool,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X2 | ~pp(X3)) ) | ~spl53_222),
% 4.58/1.03 inference(avatar_component_clause,[],[f3900])).
% 4.58/1.03 tff(f3902,plain,(
% 4.58/1.03 spl53_222),
% 4.58/1.03 inference(avatar_split_clause,[],[f561,f3900])).
% 4.58/1.03 tff(f561,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : bool,X1 : X0] : (the(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,X3)),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,aa(bool,fun(bool,bool),fimplies,aa(bool,bool,fNot,X3))),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))) = X2 | ~pp(X3)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f288])).
% 4.58/1.03 tff(f3880,plain,(
% 4.58/1.03 spl53_221),
% 4.58/1.03 inference(avatar_split_clause,[],[f740,f3878])).
% 4.58/1.03 tff(f3878,plain,(
% 4.58/1.03 spl53_221 <=> ! [X0 : $tType,X5 : bool,X4 : fun(hoare_28830079triple(X0),bool),X3 : fun(X0,fun(state,bool)),X2 : com,X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1))) | hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,aa(bool,fun(X0,fun(state,bool)),aa(fun(X0,fun(bool,fun(state,bool))),fun(bool,fun(X0,fun(state,bool))),combc(X0,bool,fun(state,bool)),aa(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X0,combc(state,bool,bool)),aa(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0,combb(bool,fun(bool,bool),state,fconj)),X3))),X5),X2,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_221])])).
% 4.58/1.03 tff(f740,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X5 : bool] : (~hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1))) | hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,aa(bool,fun(X0,fun(state,bool)),aa(fun(X0,fun(bool,fun(state,bool))),fun(bool,fun(X0,fun(state,bool))),combc(X0,bool,fun(state,bool)),aa(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X0,combc(state,bool,bool)),aa(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0,combb(bool,fun(bool,bool),state,fconj)),X3))),X5),X2,X1)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f739,f685])).
% 4.58/1.03 tff(f685,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f463,f456])).
% 4.58/1.03 tff(f456,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (collect(X0,X1) = X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f138])).
% 4.58/1.03 tff(f138,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : collect(X0,X1) = X1),
% 4.58/1.03 inference(rectify,[],[f78])).
% 4.58/1.03 tff(f78,axiom,(
% 4.58/1.03 ! [X1 : $tType,X16 : fun(X1,bool)] : collect(X1,X16) = X16),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def)).
% 4.58/1.03 tff(f463,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(X0,fun(X0,bool),fequal(X0),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f145])).
% 4.58/1.03 tff(f145,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(X0,fun(X0,bool),fequal(X0),X1))),
% 4.58/1.03 inference(rectify,[],[f6])).
% 4.58/1.03 tff(f6,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1] : collect(X1,aa(X1,fun(X1,bool),fequal(X1),X18)) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),bot_bot(fun(X1,bool)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_singleton__conv2)).
% 4.58/1.03 tff(f739,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X5 : bool] : (hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,aa(bool,fun(X0,fun(state,bool)),aa(fun(X0,fun(bool,fun(state,bool))),fun(bool,fun(X0,fun(state,bool))),combc(X0,bool,fun(state,bool)),aa(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X0,combc(state,bool,bool)),aa(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0,combb(bool,fun(bool,bool),state,fconj)),X3))),X5),X2,X1))) | ~hoare_992312373derivs(X0,X4,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f629,f685])).
% 4.58/1.03 tff(f629,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X5 : bool] : (hoare_992312373derivs(X0,X4,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,aa(bool,fun(X0,fun(state,bool)),aa(fun(X0,fun(bool,fun(state,bool))),fun(bool,fun(X0,fun(state,bool))),combc(X0,bool,fun(state,bool)),aa(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X0,combc(state,bool,bool)),aa(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0,combb(bool,fun(bool,bool),state,fconj)),X3))),X5),X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X4,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f316])).
% 4.58/1.03 tff(f316,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X5 : bool] : (hoare_992312373derivs(X0,X4,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,aa(bool,fun(X0,fun(state,bool)),aa(fun(X0,fun(bool,fun(state,bool))),fun(bool,fun(X0,fun(state,bool))),combc(X0,bool,fun(state,bool)),aa(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X0,combc(state,bool,bool)),aa(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0,combb(bool,fun(bool,bool),state,fconj)),X3))),X5),X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | (~hoare_992312373derivs(X0,X4,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) & pp(X5)))),
% 4.58/1.03 inference(ennf_transformation,[],[f243])).
% 4.58/1.03 tff(f243,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X5 : bool] : ((pp(X5) => hoare_992312373derivs(X0,X4,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool))))) => hoare_992312373derivs(X0,X4,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,aa(bool,fun(X0,fun(state,bool)),aa(fun(X0,fun(bool,fun(state,bool))),fun(bool,fun(X0,fun(state,bool))),combc(X0,bool,fun(state,bool)),aa(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X0,combc(state,bool,bool)),aa(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0,combb(bool,fun(bool,bool),state,fconj)),X3))),X5),X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(rectify,[],[f5])).
% 4.58/1.03 tff(f5,axiom,(
% 4.58/1.03 ! [X1 : $tType,X14 : fun(X1,fun(state,bool)),X15 : com,X16 : fun(X1,fun(state,bool)),X10 : fun(hoare_28830079triple(X1),bool),X17 : bool] : ((pp(X17) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,X15,X14)),bot_bot(fun(hoare_28830079triple(X1),bool))))) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,aa(bool,fun(X1,fun(state,bool)),aa(fun(X1,fun(bool,fun(state,bool))),fun(bool,fun(X1,fun(state,bool))),combc(X1,bool,fun(state,bool)),aa(fun(X1,fun(state,fun(bool,bool))),fun(X1,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X1,combc(state,bool,bool)),aa(fun(X1,fun(state,bool)),fun(X1,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X1,combb(bool,fun(bool,bool),state,fconj)),X16))),X17),X15,X14)),bot_bot(fun(hoare_28830079triple(X1),bool)))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_constant)).
% 4.58/1.03 tff(f3874,plain,(
% 4.58/1.03 spl53_220 | ~spl53_14 | ~spl53_139 | ~spl53_219),
% 4.58/1.03 inference(avatar_split_clause,[],[f3870,f3867,f2267,f811,f3872])).
% 4.58/1.03 tff(f3872,plain,(
% 4.58/1.03 spl53_220 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),aa(X0,fun(X0,bool),fequal(X0),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_220])])).
% 4.58/1.03 tff(f3867,plain,(
% 4.58/1.03 spl53_219 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_219])])).
% 4.58/1.03 tff(f3870,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),aa(X0,fun(X0,bool),fequal(X0),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))) ) | (~spl53_14 | ~spl53_139 | ~spl53_219)),
% 4.58/1.03 inference(forward_demodulation,[],[f3868,f2300])).
% 4.58/1.03 tff(f3868,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))) ) | ~spl53_219),
% 4.58/1.03 inference(avatar_component_clause,[],[f3867])).
% 4.58/1.03 tff(f3869,plain,(
% 4.58/1.03 spl53_219),
% 4.58/1.03 inference(avatar_split_clause,[],[f509,f3867])).
% 4.58/1.03 tff(f509,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f180])).
% 4.58/1.03 tff(f180,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))),
% 4.58/1.03 inference(rectify,[],[f31])).
% 4.58/1.03 tff(f31,axiom,(
% 4.58/1.03 ! [X1 : $tType,X28 : fun(X1,bool),X18 : X1] : aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X28) = collect(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fdisj),aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X18))),aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X28)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_insert__compr)).
% 4.58/1.03 tff(f3847,plain,(
% 4.58/1.03 spl53_218),
% 4.58/1.03 inference(avatar_split_clause,[],[f741,f3845])).
% 4.58/1.03 tff(f3845,plain,(
% 4.58/1.03 spl53_218 <=> ! [X0 : $tType,X3 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X5 : bool,X2 : com,X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,aa(bool,fun(X0,fun(state,bool)),aa(fun(X0,fun(bool,fun(state,bool))),fun(bool,fun(X0,fun(state,bool))),combc(X0,bool,fun(state,bool)),aa(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X0,combc(state,bool,bool)),aa(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0,combb(bool,fun(bool,bool),state,fconj)),X3))),X5),X2,X1))) | pp(X5))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_218])])).
% 4.58/1.03 tff(f741,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X5 : bool] : (hoare_992312373derivs(X0,X4,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,aa(bool,fun(X0,fun(state,bool)),aa(fun(X0,fun(bool,fun(state,bool))),fun(bool,fun(X0,fun(state,bool))),combc(X0,bool,fun(state,bool)),aa(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X0,combc(state,bool,bool)),aa(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0,combb(bool,fun(bool,bool),state,fconj)),X3))),X5),X2,X1))) | pp(X5)) )),
% 4.58/1.03 inference(forward_demodulation,[],[f628,f685])).
% 4.58/1.03 tff(f628,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X4 : fun(hoare_28830079triple(X0),bool),X5 : bool] : (hoare_992312373derivs(X0,X4,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,aa(bool,fun(X0,fun(state,bool)),aa(fun(X0,fun(bool,fun(state,bool))),fun(bool,fun(X0,fun(state,bool))),combc(X0,bool,fun(state,bool)),aa(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(bool,fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X0,combc(state,bool,bool)),aa(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0,combb(bool,fun(bool,bool),state,fconj)),X3))),X5),X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | pp(X5)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f316])).
% 4.58/1.03 tff(f3840,plain,(
% 4.58/1.03 spl53_217 | ~spl53_14 | ~spl53_139 | ~spl53_215),
% 4.58/1.03 inference(avatar_split_clause,[],[f3832,f3829,f2267,f811,f3838])).
% 4.58/1.03 tff(f3838,plain,(
% 4.58/1.03 spl53_217 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fimplies),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,fNot),aa(X0,fun(X0,bool),fequal(X0),X2)))),X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_217])])).
% 4.58/1.03 tff(f3829,plain,(
% 4.58/1.03 spl53_215 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fimplies),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,fNot),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_215])])).
% 4.58/1.03 tff(f3832,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fimplies),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,fNot),aa(X0,fun(X0,bool),fequal(X0),X2)))),X1))) ) | (~spl53_14 | ~spl53_139 | ~spl53_215)),
% 4.58/1.03 inference(forward_demodulation,[],[f3830,f2300])).
% 4.58/1.03 tff(f3830,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fimplies),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,fNot),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),X1))) ) | ~spl53_215),
% 4.58/1.03 inference(avatar_component_clause,[],[f3829])).
% 4.58/1.03 tff(f3836,plain,(
% 4.58/1.03 spl53_216 | ~spl53_8 | ~spl53_63),
% 4.58/1.03 inference(avatar_split_clause,[],[f1108,f1069,f784,f3834])).
% 4.58/1.03 tff(f3834,plain,(
% 4.58/1.03 spl53_216 <=> ! [X1 : $tType,X2 : fun(hoare_28830079triple(X1),bool),X0 : bool] : (hoare_992312373derivs(X1,X2,combk(bool,hoare_28830079triple(X1),X0)) | fTrue = X0)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_216])])).
% 4.58/1.03 tff(f1069,plain,(
% 4.58/1.03 spl53_63 <=> ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : hoare_992312373derivs(X0,X1,combk(bool,hoare_28830079triple(X0),fFalse))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_63])])).
% 4.58/1.03 tff(f1108,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(hoare_28830079triple(X1),bool),X0 : bool] : (hoare_992312373derivs(X1,X2,combk(bool,hoare_28830079triple(X1),X0)) | fTrue = X0) ) | (~spl53_8 | ~spl53_63)),
% 4.58/1.03 inference(superposition,[],[f1070,f785])).
% 4.58/1.03 tff(f1070,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,combk(bool,hoare_28830079triple(X0),fFalse))) ) | ~spl53_63),
% 4.58/1.03 inference(avatar_component_clause,[],[f1069])).
% 4.58/1.03 tff(f3831,plain,(
% 4.58/1.03 spl53_215),
% 4.58/1.03 inference(avatar_split_clause,[],[f693,f3829])).
% 4.58/1.03 tff(f693,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fimplies),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,fNot),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f508,f456])).
% 4.58/1.03 tff(f508,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),collect(X0,X1)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fimplies),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,fNot),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f179])).
% 4.58/1.03 tff(f179,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),collect(X0,X1)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fimplies),aa(fun(X0,bool),fun(X0,bool),combb(bool,bool,X0,fNot),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))),X1))),
% 4.58/1.03 inference(rectify,[],[f30])).
% 4.58/1.03 tff(f30,axiom,(
% 4.58/1.03 ! [X1 : $tType,X16 : fun(X1,bool),X18 : X1] : aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),collect(X1,X16)) = collect(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fimplies),aa(fun(X1,bool),fun(X1,bool),combb(bool,bool,X1,fNot),aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X18)))),X16))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_insert__Collect)).
% 4.58/1.03 tff(f3815,plain,(
% 4.58/1.03 spl53_214 | ~spl53_34 | ~spl53_135 | ~spl53_213),
% 4.58/1.03 inference(avatar_split_clause,[],[f3811,f3807,f2238,f912,f3813])).
% 4.58/1.03 tff(f3813,plain,(
% 4.58/1.03 spl53_214 <=> ! [X0 : $tType,X1 : X0] : the(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),combb(fun(X0,bool),bool,X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),aa(X0,fun(X0,bool),fequal(X0),X1))),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),combk(bool,X0,fFalse)))) = X1),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_214])])).
% 4.58/1.03 tff(f3807,plain,(
% 4.58/1.03 spl53_213 <=> ! [X0 : $tType,X1 : X0] : the(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),combb(fun(X0,bool),bool,X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool))))) = X1),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_213])])).
% 4.58/1.03 tff(f3811,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (the(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),combb(fun(X0,bool),bool,X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),aa(X0,fun(X0,bool),fequal(X0),X1))),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),combk(bool,X0,fFalse)))) = X1) ) | (~spl53_34 | ~spl53_135 | ~spl53_213)),
% 4.58/1.03 inference(forward_demodulation,[],[f3810,f2239])).
% 4.58/1.03 tff(f3810,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (the(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),combb(fun(X0,bool),bool,X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),combk(bool,X0,fFalse)))),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),combk(bool,X0,fFalse)))) = X1) ) | (~spl53_34 | ~spl53_213)),
% 4.58/1.03 inference(forward_demodulation,[],[f3808,f913])).
% 4.58/1.03 tff(f3808,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (the(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),combb(fun(X0,bool),bool,X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool))))) = X1) ) | ~spl53_213),
% 4.58/1.03 inference(avatar_component_clause,[],[f3807])).
% 4.58/1.03 tff(f3809,plain,(
% 4.58/1.03 spl53_213),
% 4.58/1.03 inference(avatar_split_clause,[],[f648,f3807])).
% 4.58/1.03 tff(f648,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (the(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),combb(fun(X0,bool),bool,X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool))))) = X1) )),
% 4.58/1.03 inference(definition_unfolding,[],[f461,f465])).
% 4.58/1.03 tff(f465,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (the_elem(X0,X1) = the(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),combb(fun(X0,bool),bool,X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool)))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f147])).
% 4.58/1.03 tff(f147,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : the_elem(X0,X1) = the(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),combb(fun(X0,bool),bool,X0,aa(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool)))))),
% 4.58/1.03 inference(rectify,[],[f53])).
% 4.58/1.03 tff(f53,axiom,(
% 4.58/1.03 ! [X1 : $tType,X46 : fun(X1,bool)] : the_elem(X1,X46) = the(X1,aa(fun(X1,fun(X1,bool)),fun(X1,bool),combb(fun(X1,bool),bool,X1,aa(fun(X1,bool),fun(fun(X1,bool),bool),fequal(fun(X1,bool)),X46)),aa(fun(X1,bool),fun(X1,fun(X1,bool)),aa(fun(X1,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X1,fun(X1,bool))),combc(X1,fun(X1,bool),fun(X1,bool)),insert(X1)),bot_bot(fun(X1,bool)))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_the__elem__def)).
% 4.58/1.03 tff(f461,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (the_elem(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f143])).
% 4.58/1.03 tff(f143,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0] : the_elem(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = X1),
% 4.58/1.03 inference(rectify,[],[f42])).
% 4.58/1.03 tff(f42,axiom,(
% 4.58/1.03 ! [X1 : $tType,X26 : X1] : the_elem(X1,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),bot_bot(fun(X1,bool)))) = X26),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_the__elem__eq)).
% 4.58/1.03 tff(f3803,plain,(
% 4.58/1.03 spl53_212),
% 4.58/1.03 inference(avatar_split_clause,[],[f601,f3801])).
% 4.58/1.03 tff(f3801,plain,(
% 4.58/1.03 spl53_212 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) | ~sP1(X0,X4,X1,X2,X3) | X2 = X4 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_212])])).
% 4.58/1.03 tff(f601,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) | ~sP1(X0,X4,X1,X2,X3) | X2 = X4 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f414])).
% 4.58/1.03 tff(f414,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : (((aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) | ~sP1(X0,X4,X1,X2,X3) | (X1 != X3 & X2 = X4)) & ((sP1(X0,X4,X1,X2,X3) & (X1 = X3 | X2 != X4)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3)))),
% 4.58/1.03 inference(flattening,[],[f413])).
% 4.58/1.03 tff(f413,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : (((aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) | (~sP1(X0,X4,X1,X2,X3) | (X1 != X3 & X2 = X4))) & ((sP1(X0,X4,X1,X2,X3) & (X1 = X3 | X2 != X4)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3)))),
% 4.58/1.03 inference(nnf_transformation,[],[f326])).
% 4.58/1.03 tff(f326,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : ((aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) <=> (sP1(X0,X4,X1,X2,X3) & (X1 = X3 | X2 != X4))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3)))),
% 4.58/1.03 inference(definition_folding,[],[f307,f325])).
% 4.58/1.03 tff(f325,plain,(
% 4.58/1.03 ! [X4 : X0,X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : (sP1(X0,X4,X1,X2,X3) <=> (? [X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X5) = X3) | X2 = X4))),
% 4.58/1.03 introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])).
% 4.58/1.03 tff(f307,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : ((aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) <=> ((? [X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X5) = X3) | X2 = X4) & (X1 = X3 | X2 != X4))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3)))),
% 4.58/1.03 inference(flattening,[],[f306])).
% 4.58/1.03 tff(f306,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : (((aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) <=> ((? [X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X5) = X3) | X2 = X4) & (X1 = X3 | X2 != X4))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3)))),
% 4.58/1.03 inference(ennf_transformation,[],[f231])).
% 4.58/1.03 tff(f231,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3)) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) => (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) <=> ((X2 != X4 => ? [X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X5) = X3)) & (X2 = X4 => X1 = X3)))))),
% 4.58/1.03 inference(rectify,[],[f26])).
% 4.58/1.03 tff(f26,axiom,(
% 4.58/1.03 ! [X1 : $tType,X28 : fun(X1,bool),X27 : X1,X25 : fun(X1,bool),X18 : X1] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),X25)) => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X27),X28)) => (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X27),X28) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X25) <=> ((X18 != X27 => ? [X30 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),X30)) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X30) = X28 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X27),X30)) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X27),X30) = X25)) & (X18 = X27 => X25 = X28)))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_insert__eq__iff)).
% 4.58/1.03 tff(f3785,plain,(
% 4.58/1.03 spl53_211 | ~spl53_14 | ~spl53_139 | ~spl53_210),
% 4.58/1.03 inference(avatar_split_clause,[],[f3781,f3778,f2267,f811,f3783])).
% 4.58/1.03 tff(f3783,plain,(
% 4.58/1.03 spl53_211 <=> ! [X0 : $tType,X4 : fun(X0,fun(state,bool)),X3 : fun(hoare_28830079triple(X0),bool),X2 : com,X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),fequal(state),sK39(X0,X1,X2,X3,X4))),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,sK38(X0,X1,X2,X3,X4)))))) | hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_211])])).
% 4.58/1.03 tff(f3778,plain,(
% 4.58/1.03 spl53_210 <=> ! [X0 : $tType,X4 : fun(X0,fun(state,bool)),X3 : fun(hoare_28830079triple(X0),bool),X2 : com,X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),sK39(X0,X1,X2,X3,X4))),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,sK38(X0,X1,X2,X3,X4)))))) | hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_210])])).
% 4.58/1.03 tff(f3781,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),fequal(state),sK39(X0,X1,X2,X3,X4))),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,sK38(X0,X1,X2,X3,X4)))))) | hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))) ) | (~spl53_14 | ~spl53_139 | ~spl53_210)),
% 4.58/1.03 inference(forward_demodulation,[],[f3779,f2300])).
% 4.58/1.03 tff(f3779,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),sK39(X0,X1,X2,X3,X4))),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,sK38(X0,X1,X2,X3,X4)))))) | hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))) ) | ~spl53_210),
% 4.58/1.03 inference(avatar_component_clause,[],[f3778])).
% 4.58/1.03 tff(f3780,plain,(
% 4.58/1.03 spl53_210),
% 4.58/1.03 inference(avatar_split_clause,[],[f719,f3778])).
% 4.58/1.03 tff(f719,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),sK39(X0,X1,X2,X3,X4))),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,sK38(X0,X1,X2,X3,X4)))))) | hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f718,f685])).
% 4.58/1.03 tff(f718,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),sK39(X0,X1,X2,X3,X4))),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,sK38(X0,X1,X2,X3,X4))))),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f607,f685])).
% 4.58/1.03 tff(f607,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),sK39(X0,X1,X2,X3,X4))),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,sK38(X0,X1,X2,X3,X4))))),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f418])).
% 4.58/1.03 tff(f418,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | (~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),sK39(X0,X1,X2,X3,X4))),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,sK38(X0,X1,X2,X3,X4))))),bot_bot(fun(hoare_28830079triple(X0),bool)))) & pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK38(X0,X1,X2,X3,X4)),sK39(X0,X1,X2,X3,X4)))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f310,f417])).
% 4.58/1.03 tff(f417,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool))] : (? [X5 : X0,X6 : state] : (~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),X6)),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,X5)))),bot_bot(fun(hoare_28830079triple(X0),bool)))) & pp(aa(state,bool,aa(X0,fun(state,bool),X4,X5),X6))) => (~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),sK39(X0,X1,X2,X3,X4))),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,sK38(X0,X1,X2,X3,X4))))),bot_bot(fun(hoare_28830079triple(X0),bool)))) & pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK38(X0,X1,X2,X3,X4)),sK39(X0,X1,X2,X3,X4)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f310,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ? [X5 : X0,X6 : state] : (~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),X6)),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,X5)))),bot_bot(fun(hoare_28830079triple(X0),bool)))) & pp(aa(state,bool,aa(X0,fun(state,bool),X4,X5),X6))))),
% 4.58/1.03 inference(ennf_transformation,[],[f233])).
% 4.58/1.03 tff(f233,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool))] : (! [X5 : X0,X6 : state] : (pp(aa(state,bool,aa(X0,fun(state,bool),X4,X5),X6)) => hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,combk(fun(state,bool),X0,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),X6)),X2,combk(fun(state,bool),X0,aa(X0,fun(state,bool),X1,X5)))),bot_bot(fun(hoare_28830079triple(X0),bool))))) => hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(rectify,[],[f8])).
% 4.58/1.03 tff(f8,axiom,(
% 4.58/1.03 ! [X1 : $tType,X14 : fun(X1,fun(state,bool)),X15 : com,X10 : fun(hoare_28830079triple(X1),bool),X16 : fun(X1,fun(state,bool))] : (! [X19 : X1,X20 : state] : (pp(aa(state,bool,aa(X1,fun(state,bool),X16,X19),X20)) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,combk(fun(state,bool),X1,aa(state,fun(state,bool),aa(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),X20)),X15,combk(fun(state,bool),X1,aa(X1,fun(state,bool),X14,X19)))),bot_bot(fun(hoare_28830079triple(X1),bool))))) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,X15,X14)),bot_bot(fun(hoare_28830079triple(X1),bool)))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_escape)).
% 4.58/1.03 tff(f3751,plain,(
% 4.58/1.03 spl53_209),
% 4.58/1.03 inference(avatar_split_clause,[],[f671,f3749])).
% 4.58/1.03 tff(f3749,plain,(
% 4.58/1.03 spl53_209 <=> ! [X0 : $tType,X4 : X0,X3 : fun(X0,bool),X2 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) | ~sP1(X0,X4,X3,X2,X3) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_209])])).
% 4.58/1.03 tff(f671,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) | ~sP1(X0,X4,X3,X2,X3) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3))) )),
% 4.58/1.03 inference(equality_resolution,[],[f602])).
% 4.58/1.03 tff(f602,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) | ~sP1(X0,X4,X1,X2,X3) | X1 != X3 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f414])).
% 4.58/1.03 tff(f3747,plain,(
% 4.58/1.03 spl53_208),
% 4.58/1.03 inference(avatar_split_clause,[],[f600,f3745])).
% 4.58/1.03 tff(f3745,plain,(
% 4.58/1.03 spl53_208 <=> ! [X0 : $tType,X4 : X0,X3 : fun(X0,bool),X2 : X0,X1 : fun(X0,bool)] : (sP1(X0,X4,X1,X2,X3) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_208])])).
% 4.58/1.03 tff(f600,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (sP1(X0,X4,X1,X2,X3) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X3) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f414])).
% 4.58/1.03 tff(f3729,plain,(
% 4.58/1.03 spl53_207),
% 4.58/1.03 inference(avatar_split_clause,[],[f566,f3727])).
% 4.58/1.03 tff(f3727,plain,(
% 4.58/1.03 spl53_207 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (X1 = X2 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_207])])).
% 4.58/1.03 tff(f566,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (X1 = X2 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f392])).
% 4.58/1.03 tff(f392,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : X0] : (((aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1) | X1 != X2) & (X1 = X2 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 4.58/1.03 inference(nnf_transformation,[],[f294])).
% 4.58/1.03 tff(f294,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : X0] : ((aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1) <=> X1 = X2) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 4.58/1.03 inference(flattening,[],[f293])).
% 4.58/1.03 tff(f293,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : X0] : (((aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1) <=> X1 = X2) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 4.58/1.03 inference(ennf_transformation,[],[f215])).
% 4.58/1.03 tff(f215,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) => (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1) <=> X1 = X2)))),
% 4.58/1.03 inference(rectify,[],[f27])).
% 4.58/1.03 tff(f27,axiom,(
% 4.58/1.03 ! [X1 : $tType,X28 : fun(X1,bool),X25 : fun(X1,bool),X26 : X1] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X26),X25)) => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X26),X28)) => (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),X25) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),X28) <=> X25 = X28)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_insert__ident)).
% 4.58/1.03 tff(f3636,plain,(
% 4.58/1.03 spl53_206),
% 4.58/1.03 inference(avatar_split_clause,[],[f699,f3634])).
% 4.58/1.03 tff(f3634,plain,(
% 4.58/1.03 spl53_206 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_206])])).
% 4.58/1.03 tff(f699,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2) | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f698,f685])).
% 4.58/1.03 tff(f698,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2) | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f513,f456])).
% 4.58/1.03 tff(f513,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2)) | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f265])).
% 4.58/1.03 tff(f265,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2)) | pp(aa(X0,bool,X2,X1))) & (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2)) | ~pp(aa(X0,bool,X2,X1))))),
% 4.58/1.03 inference(ennf_transformation,[],[f183])).
% 4.58/1.03 tff(f183,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : ((~pp(aa(X0,bool,X2,X1)) => bot_bot(fun(X0,bool)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2))) & (pp(aa(X0,bool,X2,X1)) => aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2))))),
% 4.58/1.03 inference(rectify,[],[f40])).
% 4.58/1.03 tff(f40,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1,X16 : fun(X1,bool)] : ((~pp(aa(X1,bool,X16,X18)) => bot_bot(fun(X1,bool)) = collect(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fconj),aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X18))),X16))) & (pp(aa(X1,bool,X16,X18)) => aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),bot_bot(fun(X1,bool))) = collect(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fconj),aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X18))),X16))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Collect__conv__if)).
% 4.58/1.03 tff(f3632,plain,(
% 4.58/1.03 spl53_205),
% 4.58/1.03 inference(avatar_split_clause,[],[f603,f3630])).
% 4.58/1.03 tff(f3630,plain,(
% 4.58/1.03 spl53_205 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,X0)),X3 : X0,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4)) | ~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_205])])).
% 4.58/1.03 tff(f603,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4)) | ~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f416])).
% 4.58/1.03 tff(f416,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0,X4 : fun(X0,fun(X0,X0))] : ((~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))) & finite_fold_graph(X0,X0,X4,sK36(X0,X1,X2,X3,X4),sK37(X0,X1,X2,X3,X4),X1) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))) | ~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f309,f415])).
% 4.58/1.03 tff(f415,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0,X4 : fun(X0,fun(X0,X0))] : (? [X5 : X0,X6 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X5),X6)) & finite_fold_graph(X0,X0,X4,X5,X6,X1) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X6)) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))) & finite_fold_graph(X0,X0,X4,sK36(X0,X1,X2,X3,X4),sK37(X0,X1,X2,X3,X4),X1) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f309,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0,X4 : fun(X0,fun(X0,X0))] : (? [X5 : X0,X6 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X5),X6)) & finite_fold_graph(X0,X0,X4,X5,X6,X1) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X6)) | ~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1)))),
% 4.58/1.03 inference(flattening,[],[f308])).
% 4.58/1.03 tff(f308,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0,X4 : fun(X0,fun(X0,X0))] : (? [X5 : X0,X6 : fun(X0,bool)] : ((~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X5),X6)) & finite_fold_graph(X0,X0,X4,X5,X6,X1)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X6)) | ~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1)))),
% 4.58/1.03 inference(ennf_transformation,[],[f232])).
% 4.58/1.03 tff(f232,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0,X4 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1)) => ~! [X5 : X0,X6 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X6) => (finite_fold_graph(X0,X0,X4,X5,X6,X1) => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X5),X6)))))),
% 4.58/1.03 inference(rectify,[],[f92])).
% 4.58/1.03 tff(f92,axiom,(
% 4.58/1.03 ! [X1 : $tType,X26 : X1,X46 : fun(X1,bool),X18 : X1,X53 : fun(X1,fun(X1,X1))] : (pp(aa(X1,bool,finite_fold1Set(X1,X53,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X46)),X26)) => ~! [X57 : X1,X58 : fun(X1,bool)] : (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X46) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X57),X58) => (finite_fold_graph(X1,X1,X53,X57,X58,X26) => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X57),X58)))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_insert__fold1SetE)).
% 4.58/1.03 tff(f3628,plain,(
% 4.58/1.03 spl53_204),
% 4.58/1.03 inference(avatar_split_clause,[],[f560,f3626])).
% 4.58/1.03 tff(f3626,plain,(
% 4.58/1.03 spl53_204 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : fun(X0,bool)] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_204])])).
% 4.58/1.03 tff(f560,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f207])).
% 4.58/1.03 tff(f207,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : X0] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X1))),
% 4.58/1.03 inference(rectify,[],[f29])).
% 4.58/1.03 tff(f29,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X31 : X1,X26 : X1] : aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X31),X25)) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X31),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),X25))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_insert__commute)).
% 4.58/1.03 tff(f3624,plain,(
% 4.58/1.03 spl53_203 | ~spl53_50 | ~spl53_78),
% 4.58/1.03 inference(avatar_split_clause,[],[f1384,f1188,f996,f3622])).
% 4.58/1.03 tff(f3622,plain,(
% 4.58/1.03 spl53_203 <=> ! [X2 : $tType,X0 : $tType,X3 : fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X2))),X1 : hoare_28830079triple(X0)] : hoare_376461865e_case(X0,X2,X3,X1) = hoare_678420151le_rec(X0,X2,X3,X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_203])])).
% 4.58/1.03 tff(f1188,plain,(
% 4.58/1.03 spl53_78 <=> ! [X1 : $tType,X0 : $tType,X5 : fun(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0))),X4 : fun(X1,fun(state,bool)),X3 : com,X2 : fun(X1,fun(state,bool))] : hoare_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2)) = hoare_678420151le_rec(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_78])])).
% 4.58/1.03 tff(f1384,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : $tType,X3 : fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X2))),X1 : hoare_28830079triple(X0)] : (hoare_376461865e_case(X0,X2,X3,X1) = hoare_678420151le_rec(X0,X2,X3,X1)) ) | (~spl53_50 | ~spl53_78)),
% 4.58/1.03 inference(superposition,[],[f1189,f997])).
% 4.58/1.03 tff(f1189,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(state,bool)),X3 : com,X4 : fun(X1,fun(state,bool)),X5 : fun(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)))] : (hoare_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2)) = hoare_678420151le_rec(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))) ) | ~spl53_78),
% 4.58/1.03 inference(avatar_component_clause,[],[f1188])).
% 4.58/1.03 tff(f3608,plain,(
% 4.58/1.03 spl53_202),
% 4.58/1.03 inference(avatar_split_clause,[],[f669,f3606])).
% 4.58/1.03 tff(f3606,plain,(
% 4.58/1.03 spl53_202 <=> ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (sP1(X1,X0,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),X5),X3,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X5)) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X5)) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_202])])).
% 4.58/1.03 tff(f669,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (sP1(X1,X0,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),X5),X3,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X5)) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X5)) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5))) )),
% 4.58/1.03 inference(equality_resolution,[],[f668])).
% 4.58/1.03 tff(f668,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X3 : X1,X0 : X1,X4 : fun(X1,bool),X5 : fun(X1,bool)] : (sP1(X1,X0,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),X5),X3,X4) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X5)) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5)) | aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X5) != X4) )),
% 4.58/1.03 inference(equality_resolution,[],[f598])).
% 4.58/1.03 tff(f598,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool),X5 : fun(X1,bool)] : (sP1(X1,X0,X2,X3,X4) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X5)) | aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),X5) != X2 | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5)) | aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X5) != X4) )),
% 4.58/1.03 inference(cnf_transformation,[],[f412])).
% 4.58/1.03 tff(f412,plain,(
% 4.58/1.03 ! [X0 : X1,X1 : $tType,X2 : fun(X1,bool),X3 : X1,X4 : fun(X1,bool)] : ((sP1(X1,X0,X2,X3,X4) | (! [X5 : fun(X1,bool)] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X5)) | aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),X5) != X2 | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5)) | aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X5) != X4) & X0 != X3)) & ((~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),sK35(X1,X0,X2,X3,X4))) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),sK35(X1,X0,X2,X3,X4)) = X2 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),sK35(X1,X0,X2,X3,X4))) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),sK35(X1,X0,X2,X3,X4)) = X4) | X0 = X3 | ~sP1(X1,X0,X2,X3,X4)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f410,f411])).
% 4.58/1.03 tff(f411,plain,(
% 4.58/1.03 ! [X1 : $tType,X0 : X1,X2 : fun(X1,bool),X3 : X1,X4 : fun(X1,bool)] : (? [X6 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X6)) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),X6) = X2 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X6)) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X6) = X4) => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),sK35(X1,X0,X2,X3,X4))) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),sK35(X1,X0,X2,X3,X4)) = X2 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),sK35(X1,X0,X2,X3,X4))) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),sK35(X1,X0,X2,X3,X4)) = X4))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f410,plain,(
% 4.58/1.03 ! [X0 : X1,X1 : $tType,X2 : fun(X1,bool),X3 : X1,X4 : fun(X1,bool)] : ((sP1(X1,X0,X2,X3,X4) | (! [X5 : fun(X1,bool)] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X5)) | aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),X5) != X2 | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5)) | aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X5) != X4) & X0 != X3)) & (? [X6 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X6)) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),X6) = X2 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X6)) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X6) = X4) | X0 = X3 | ~sP1(X1,X0,X2,X3,X4)))),
% 4.58/1.03 inference(rectify,[],[f409])).
% 4.58/1.03 tff(f409,plain,(
% 4.58/1.03 ! [X4 : X0,X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : ((sP1(X0,X4,X1,X2,X3) | (! [X5 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) != X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X5) != X3) & X2 != X4)) & (? [X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X5) = X3) | X2 = X4 | ~sP1(X0,X4,X1,X2,X3)))),
% 4.58/1.03 inference(flattening,[],[f408])).
% 4.58/1.03 tff(f408,plain,(
% 4.58/1.03 ! [X4 : X0,X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : ((sP1(X0,X4,X1,X2,X3) | (! [X5 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) != X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X5) != X3) & X2 != X4)) & ((? [X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X5) = X3) | X2 = X4) | ~sP1(X0,X4,X1,X2,X3)))),
% 4.58/1.03 inference(nnf_transformation,[],[f325])).
% 4.58/1.03 tff(f3602,plain,(
% 4.58/1.03 spl53_201),
% 4.58/1.03 inference(avatar_split_clause,[],[f697,f3600])).
% 4.58/1.03 tff(f3600,plain,(
% 4.58/1.03 spl53_201 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2) | pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_201])])).
% 4.58/1.03 tff(f697,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2) | pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f514,f456])).
% 4.58/1.03 tff(f514,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (bot_bot(fun(X0,bool)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),X2)) | pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f265])).
% 4.58/1.03 tff(f3594,plain,(
% 4.58/1.03 spl53_200),
% 4.58/1.03 inference(avatar_split_clause,[],[f724,f3592])).
% 4.58/1.03 tff(f3592,plain,(
% 4.58/1.03 spl53_200 <=> ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool)),X3 : fun(hoare_28830079triple(X0),bool),X10 : X0,X2 : com,X7 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))) | hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK42(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK41(X0,X1,X2,X3,X4))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_200])])).
% 4.58/1.03 tff(f724,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X10 : X0,X1 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool)),X7 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))) | hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK42(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK41(X0,X1,X2,X3,X4)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f723,f685])).
% 4.58/1.03 tff(f723,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X10 : X0,X1 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool)),X7 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK42(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK41(X0,X1,X2,X3,X4))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f609,f685])).
% 4.58/1.03 tff(f609,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X10 : X0,X1 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool)),X7 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK42(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK41(X0,X1,X2,X3,X4))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f421])).
% 4.58/1.03 tff(f421,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | (! [X7 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool))] : ((~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK40(X0,X1,X2,X3,X4)),sK42(X0,X1,X2,X3,X4,X7,X8))) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK42(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK41(X0,X1,X2,X3,X4))))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)),bot_bot(fun(hoare_28830079triple(X0),bool))))) & pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK40(X0,X1,X2,X3,X4)),sK41(X0,X1,X2,X3,X4)))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42])],[f311,f420,f419])).
% 4.58/1.03 tff(f419,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool))] : (? [X5 : X0,X6 : state] : (! [X7 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool))] : (? [X9 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X9)) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),X9)) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),X6)))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)),bot_bot(fun(hoare_28830079triple(X0),bool))))) & pp(aa(state,bool,aa(X0,fun(state,bool),X4,X5),X6))) => (! [X8 : fun(X0,fun(state,bool)),X7 : fun(X0,fun(state,bool))] : (? [X9 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK40(X0,X1,X2,X3,X4)),X9)) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),X9)) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK41(X0,X1,X2,X3,X4))))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)),bot_bot(fun(hoare_28830079triple(X0),bool))))) & pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK40(X0,X1,X2,X3,X4)),sK41(X0,X1,X2,X3,X4)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f420,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool)),X7 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool))] : (? [X9 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK40(X0,X1,X2,X3,X4)),X9)) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),X9)) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK41(X0,X1,X2,X3,X4))))) => (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK40(X0,X1,X2,X3,X4)),sK42(X0,X1,X2,X3,X4,X7,X8))) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK42(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK41(X0,X1,X2,X3,X4))))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f311,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ? [X5 : X0,X6 : state] : (! [X7 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool))] : (? [X9 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X9)) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),X9)) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),X6)))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)),bot_bot(fun(hoare_28830079triple(X0),bool))))) & pp(aa(state,bool,aa(X0,fun(state,bool),X4,X5),X6))))),
% 4.58/1.03 inference(ennf_transformation,[],[f234])).
% 4.58/1.03 tff(f234,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool))] : (! [X5 : X0,X6 : state] : (pp(aa(state,bool,aa(X0,fun(state,bool),X4,X5),X6)) => ? [X7 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool))] : (! [X9 : state] : (! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),X6)) => pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),X9))) => pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X9))) & hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)),bot_bot(fun(hoare_28830079triple(X0),bool)))))) => hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(rectify,[],[f64])).
% 4.58/1.03 tff(f64,axiom,(
% 4.58/1.03 ! [X1 : $tType,X14 : fun(X1,fun(state,bool)),X15 : com,X10 : fun(hoare_28830079triple(X1),bool),X16 : fun(X1,fun(state,bool))] : (! [X19 : X1,X20 : state] : (pp(aa(state,bool,aa(X1,fun(state,bool),X16,X19),X20)) => ? [X50 : fun(X1,fun(state,bool)),X51 : fun(X1,fun(state,bool))] : (! [X23 : state] : (! [X24 : X1] : (pp(aa(state,bool,aa(X1,fun(state,bool),X50,X24),X20)) => pp(aa(state,bool,aa(X1,fun(state,bool),X51,X24),X23))) => pp(aa(state,bool,aa(X1,fun(state,bool),X14,X19),X23))) & hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X50,X15,X51)),bot_bot(fun(hoare_28830079triple(X1),bool)))))) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,X15,X14)),bot_bot(fun(hoare_28830079triple(X1),bool)))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_conseq)).
% 4.58/1.03 tff(f3586,plain,(
% 4.58/1.03 spl53_199),
% 4.58/1.03 inference(avatar_split_clause,[],[f748,f3584])).
% 4.58/1.03 tff(f3584,plain,(
% 4.58/1.03 spl53_199 <=> ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool)),X10 : X0,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),sK52(X0,X1,X2,X3,X5))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),sK51(X0,X1,X2,X3,X5))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_199])])).
% 4.58/1.03 tff(f748,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X10 : X0,X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),sK52(X0,X1,X2,X3,X5))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),sK51(X0,X1,X2,X3,X5)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f747,f685])).
% 4.58/1.03 tff(f747,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X10 : X0,X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),sK52(X0,X1,X2,X3,X5))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),sK51(X0,X1,X2,X3,X5))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f642,f685])).
% 4.58/1.03 tff(f642,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X10 : X0,X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),sK52(X0,X1,X2,X3,X5))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),sK51(X0,X1,X2,X3,X5))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f438])).
% 4.58/1.03 tff(f438,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X4 : com,X5 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ((~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK50(X0,X1,X2,X3,X5)),sK52(X0,X1,X2,X3,X5))) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),sK52(X0,X1,X2,X3,X5))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),sK51(X0,X1,X2,X3,X5))))) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK50(X0,X1,X2,X3,X5)),sK51(X0,X1,X2,X3,X5)))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52])],[f322,f437,f436])).
% 4.58/1.03 tff(f436,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X5 : fun(X0,fun(state,bool))] : (? [X7 : X0,X8 : state] : (? [X9 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,X7),X9)) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),X9)) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),X8)))) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,X7),X8))) => (? [X9 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK50(X0,X1,X2,X3,X5)),X9)) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),X9)) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),sK51(X0,X1,X2,X3,X5))))) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK50(X0,X1,X2,X3,X5)),sK51(X0,X1,X2,X3,X5)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f437,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X5 : fun(X0,fun(state,bool))] : (? [X9 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK50(X0,X1,X2,X3,X5)),X9)) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),X9)) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),sK51(X0,X1,X2,X3,X5))))) => (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK50(X0,X1,X2,X3,X5)),sK52(X0,X1,X2,X3,X5))) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),sK52(X0,X1,X2,X3,X5))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),sK51(X0,X1,X2,X3,X5))))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f322,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X4 : com,X5 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ? [X7 : X0,X8 : state] : (? [X9 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,X7),X9)) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),X9)) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),X8)))) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,X7),X8))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(flattening,[],[f321])).
% 4.58/1.03 tff(f321,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X4 : com,X5 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool)] : ((hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ? [X7 : X0,X8 : state] : (? [X9 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,X7),X9)) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),X9)) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),X8)))) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,X7),X8)))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(ennf_transformation,[],[f247])).
% 4.58/1.03 tff(f247,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X4 : com,X5 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool)))) => (! [X7 : X0,X8 : state] : (pp(aa(state,bool,aa(X0,fun(state,bool),X2,X7),X8)) => ! [X9 : state] : (! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X5,X10),X8)) => pp(aa(state,bool,aa(X0,fun(state,bool),X3,X10),X9))) => pp(aa(state,bool,aa(X0,fun(state,bool),X1,X7),X9)))) => hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1)),bot_bot(fun(hoare_28830079triple(X0),bool))))))),
% 4.58/1.03 inference(rectify,[],[f11])).
% 4.58/1.03 tff(f11,axiom,(
% 4.58/1.03 ! [X1 : $tType,X14 : fun(X1,fun(state,bool)),X16 : fun(X1,fun(state,bool)),X21 : fun(X1,fun(state,bool)),X15 : com,X22 : fun(X1,fun(state,bool)),X10 : fun(hoare_28830079triple(X1),bool)] : (hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X22,X15,X21)),bot_bot(fun(hoare_28830079triple(X1),bool)))) => (! [X19 : X1,X20 : state] : (pp(aa(state,bool,aa(X1,fun(state,bool),X16,X19),X20)) => ! [X23 : state] : (! [X24 : X1] : (pp(aa(state,bool,aa(X1,fun(state,bool),X22,X24),X20)) => pp(aa(state,bool,aa(X1,fun(state,bool),X21,X24),X23))) => pp(aa(state,bool,aa(X1,fun(state,bool),X14,X19),X23)))) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,X15,X14)),bot_bot(fun(hoare_28830079triple(X1),bool))))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_conseq12)).
% 4.58/1.03 tff(f3534,plain,(
% 4.58/1.03 spl53_198),
% 4.58/1.03 inference(avatar_split_clause,[],[f696,f3532])).
% 4.58/1.03 tff(f3532,plain,(
% 4.58/1.03 spl53_198 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_198])])).
% 4.58/1.03 tff(f696,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2) | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f695,f685])).
% 4.58/1.03 tff(f695,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2) | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f511,f456])).
% 4.58/1.03 tff(f511,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2)) | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f264])).
% 4.58/1.03 tff(f264,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2)) | pp(aa(X0,bool,X2,X1))) & (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2)) | ~pp(aa(X0,bool,X2,X1))))),
% 4.58/1.03 inference(ennf_transformation,[],[f182])).
% 4.58/1.03 tff(f182,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : ((~pp(aa(X0,bool,X2,X1)) => bot_bot(fun(X0,bool)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2))) & (pp(aa(X0,bool,X2,X1)) => aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2))))),
% 4.58/1.03 inference(rectify,[],[f41])).
% 4.58/1.03 tff(f41,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1,X16 : fun(X1,bool)] : ((~pp(aa(X1,bool,X16,X18)) => bot_bot(fun(X1,bool)) = collect(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fconj),aa(X1,fun(X1,bool),fequal(X1),X18))),X16))) & (pp(aa(X1,bool,X16,X18)) => aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),bot_bot(fun(X1,bool))) = collect(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fconj),aa(X1,fun(X1,bool),fequal(X1),X18))),X16))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Collect__conv__if2)).
% 4.58/1.03 tff(f3504,plain,(
% 4.58/1.03 spl53_197),
% 4.58/1.03 inference(avatar_split_clause,[],[f729,f3502])).
% 4.58/1.03 tff(f3502,plain,(
% 4.58/1.03 spl53_197 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : X0,X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(X0,fun(X0,bool),fequal(X0),X1)) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(X0,fun(X0,bool),fequal(X0),X3)) | sP2(X0,X3,X2,X4,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_197])])).
% 4.58/1.03 tff(f729,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(X0,fun(X0,bool),fequal(X0),X1)) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(X0,fun(X0,bool),fequal(X0),X3)) | sP2(X0,X3,X2,X4,X1)) )),
% 4.58/1.03 inference(forward_demodulation,[],[f728,f685])).
% 4.58/1.03 tff(f728,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(X0,fun(X0,bool),fequal(X0),X1)) | sP2(X0,X3,X2,X4,X1)) )),
% 4.58/1.03 inference(forward_demodulation,[],[f617,f685])).
% 4.58/1.03 tff(f617,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (sP2(X0,X3,X2,X4,X1) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f425])).
% 4.58/1.03 tff(f425,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) | ~sP2(X0,X3,X2,X4,X1)) & (sP2(X0,X3,X2,X4,X1) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))),
% 4.58/1.03 inference(nnf_transformation,[],[f328])).
% 4.58/1.03 tff(f328,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) <=> sP2(X0,X3,X2,X4,X1))),
% 4.58/1.03 inference(definition_folding,[],[f235,f327])).
% 4.58/1.03 tff(f327,plain,(
% 4.58/1.03 ! [X3 : X0,X2 : X0,X0 : $tType,X4 : X0,X1 : X0] : (sP2(X0,X3,X2,X4,X1) <=> ((X2 = X3 & X1 = X4) | (X1 = X3 & X2 = X4)))),
% 4.58/1.03 introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])])).
% 4.58/1.03 tff(f235,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) <=> ((X2 = X3 & X1 = X4) | (X1 = X3 & X2 = X4)))),
% 4.58/1.03 inference(rectify,[],[f36])).
% 4.58/1.03 tff(f36,axiom,(
% 4.58/1.03 ! [X1 : $tType,X34 : X1,X15 : X1,X27 : X1,X18 : X1] : (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X27),bot_bot(fun(X1,bool)))) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X15),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),bot_bot(fun(X1,bool)))) <=> ((X15 = X27 & X18 = X34) | (X27 = X34 & X15 = X18)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_doubleton__eq__iff)).
% 4.58/1.03 tff(f3500,plain,(
% 4.58/1.03 spl53_196),
% 4.58/1.03 inference(avatar_split_clause,[],[f727,f3498])).
% 4.58/1.03 tff(f3498,plain,(
% 4.58/1.03 spl53_196 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : X0,X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(X0,fun(X0,bool),fequal(X0),X1)) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(X0,fun(X0,bool),fequal(X0),X3)) | ~sP2(X0,X3,X2,X4,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_196])])).
% 4.58/1.03 tff(f727,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(X0,fun(X0,bool),fequal(X0),X1)) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(X0,fun(X0,bool),fequal(X0),X3)) | ~sP2(X0,X3,X2,X4,X1)) )),
% 4.58/1.03 inference(forward_demodulation,[],[f726,f685])).
% 4.58/1.03 tff(f726,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(X0,fun(X0,bool),fequal(X0),X1)) | ~sP2(X0,X3,X2,X4,X1)) )),
% 4.58/1.03 inference(forward_demodulation,[],[f618,f685])).
% 4.58/1.03 tff(f618,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) | ~sP2(X0,X3,X2,X4,X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f425])).
% 4.58/1.03 tff(f3438,plain,(
% 4.58/1.03 spl53_195 | ~spl53_34 | ~spl53_194),
% 4.58/1.03 inference(avatar_split_clause,[],[f3409,f3406,f912,f3436])).
% 4.58/1.03 tff(f3436,plain,(
% 4.58/1.03 spl53_195 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2) | pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_195])])).
% 4.58/1.03 tff(f3406,plain,(
% 4.58/1.03 spl53_194 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2) | pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_194])])).
% 4.58/1.03 tff(f3409,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2) | pp(aa(X0,bool,X2,X1))) ) | (~spl53_34 | ~spl53_194)),
% 4.58/1.03 inference(forward_demodulation,[],[f3407,f913])).
% 4.58/1.03 tff(f3407,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2) | pp(aa(X0,bool,X2,X1))) ) | ~spl53_194),
% 4.58/1.03 inference(avatar_component_clause,[],[f3406])).
% 4.58/1.03 tff(f3408,plain,(
% 4.58/1.03 spl53_194),
% 4.58/1.03 inference(avatar_split_clause,[],[f694,f3406])).
% 4.58/1.03 tff(f694,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2) | pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f512,f456])).
% 4.58/1.03 tff(f512,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (bot_bot(fun(X0,bool)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),aa(X0,fun(X0,bool),fequal(X0),X1))),X2)) | pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f264])).
% 4.58/1.03 tff(f3404,plain,(
% 4.58/1.03 spl53_193),
% 4.58/1.03 inference(avatar_split_clause,[],[f507,f3402])).
% 4.58/1.03 tff(f507,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f178])).
% 4.58/1.03 tff(f178,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))),
% 4.58/1.03 inference(rectify,[],[f12])).
% 4.58/1.03 tff(f12,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X26 : X1] : aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),X25) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),X25))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_insert__absorb2)).
% 4.58/1.03 tff(f3346,plain,(
% 4.58/1.03 spl53_192 | ~spl53_13 | ~spl53_96),
% 4.58/1.03 inference(avatar_split_clause,[],[f1787,f1634,f807,f3344])).
% 4.58/1.03 tff(f3344,plain,(
% 4.58/1.03 spl53_192 <=> ! [X0 : bool] : (fTrue = aa(bool,bool,fNot,X0) | fTrue = X0)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_192])])).
% 4.58/1.03 tff(f1634,plain,(
% 4.58/1.03 spl53_96 <=> ! [X0 : bool] : (fTrue = aa(bool,bool,fNot,X0) | pp(X0))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_96])])).
% 4.58/1.03 tff(f1787,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (fTrue = aa(bool,bool,fNot,X0) | fTrue = X0) ) | (~spl53_13 | ~spl53_96)),
% 4.58/1.03 inference(resolution,[],[f1635,f808])).
% 4.58/1.03 tff(f1635,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (pp(X0) | fTrue = aa(bool,bool,fNot,X0)) ) | ~spl53_96),
% 4.58/1.03 inference(avatar_component_clause,[],[f1634])).
% 4.58/1.03 tff(f3313,plain,(
% 4.58/1.03 spl53_191),
% 4.58/1.03 inference(avatar_split_clause,[],[f722,f3311])).
% 4.58/1.03 tff(f3311,plain,(
% 4.58/1.03 spl53_191 <=> ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool)),X3 : fun(hoare_28830079triple(X0),bool),X2 : com,X7 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))) | hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK40(X0,X1,X2,X3,X4)),sK42(X0,X1,X2,X3,X4,X7,X8))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_191])])).
% 4.58/1.03 tff(f722,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool)),X7 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))) | hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK40(X0,X1,X2,X3,X4)),sK42(X0,X1,X2,X3,X4,X7,X8)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f721,f685])).
% 4.58/1.03 tff(f721,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool)),X7 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK40(X0,X1,X2,X3,X4)),sK42(X0,X1,X2,X3,X4,X7,X8))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f610,f685])).
% 4.58/1.03 tff(f610,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X8 : fun(X0,fun(state,bool)),X7 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK40(X0,X1,X2,X3,X4)),sK42(X0,X1,X2,X3,X4,X7,X8))) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f421])).
% 4.58/1.03 tff(f3309,plain,(
% 4.58/1.03 spl53_190),
% 4.58/1.03 inference(avatar_split_clause,[],[f678,f3307])).
% 4.58/1.03 tff(f3307,plain,(
% 4.58/1.03 spl53_190 <=> ! [X3 : $tType,X2 : $tType,X7 : fun(X3,bool),X8 : X2,X0 : X2,X6 : X3,X1 : fun(X3,fun(X2,X2))] : (sP3(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X6),X7)) | ~finite_fold_graph(X3,X2,X1,X0,X7,X8) | pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),X6),X7)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_190])])).
% 4.58/1.03 tff(f678,plain,(
% 4.58/1.03 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X8 : X2,X6 : X3,X7 : fun(X3,bool)] : (sP3(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X6),X7)) | ~finite_fold_graph(X3,X2,X1,X0,X7,X8) | pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),X6),X7))) )),
% 4.58/1.03 inference(equality_resolution,[],[f677])).
% 4.58/1.03 tff(f677,plain,(
% 4.58/1.03 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X8 : X2,X6 : X3,X7 : fun(X3,bool),X5 : fun(X3,bool)] : (sP3(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),X5) | ~finite_fold_graph(X3,X2,X1,X0,X7,X8) | pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),X6),X7)) | aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X6),X7) != X5) )),
% 4.58/1.03 inference(equality_resolution,[],[f634])).
% 4.58/1.03 tff(f634,plain,(
% 4.58/1.03 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X8 : X2,X6 : X3,X7 : fun(X3,bool),X4 : X2,X5 : fun(X3,bool)] : (sP3(X2,X3,X0,X1,X4,X5) | ~finite_fold_graph(X3,X2,X1,X0,X7,X8) | pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),X6),X7)) | aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8) != X4 | aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X6),X7) != X5) )),
% 4.58/1.03 inference(cnf_transformation,[],[f433])).
% 4.58/1.03 tff(f433,plain,(
% 4.58/1.03 ! [X0 : X2,X1 : fun(X3,fun(X2,X2)),X2 : $tType,X3 : $tType,X4 : X2,X5 : fun(X3,bool)] : ((sP3(X2,X3,X0,X1,X4,X5) | ! [X6 : X3,X7 : fun(X3,bool),X8 : X2] : (~finite_fold_graph(X3,X2,X1,X0,X7,X8) | pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),X6),X7)) | aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8) != X4 | aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X6),X7) != X5)) & ((finite_fold_graph(X3,X2,X1,X0,sK48(X2,X3,X0,X1,X4,X5),sK49(X2,X3,X0,X1,X4,X5)) & ~pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),sK47(X2,X3,X0,X1,X4,X5)),sK48(X2,X3,X0,X1,X4,X5))) & aa(X2,X2,aa(X3,fun(X2,X2),X1,sK47(X2,X3,X0,X1,X4,X5)),sK49(X2,X3,X0,X1,X4,X5)) = X4 & aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),sK47(X2,X3,X0,X1,X4,X5)),sK48(X2,X3,X0,X1,X4,X5)) = X5) | ~sP3(X2,X3,X0,X1,X4,X5)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49])],[f431,f432])).
% 4.58/1.03 tff(f432,plain,(
% 4.58/1.03 ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (? [X9 : X3,X10 : fun(X3,bool),X11 : X2] : (finite_fold_graph(X3,X2,X1,X0,X10,X11) & ~pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),X9),X10)) & aa(X2,X2,aa(X3,fun(X2,X2),X1,X9),X11) = X4 & aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X9),X10) = X5) => (finite_fold_graph(X3,X2,X1,X0,sK48(X2,X3,X0,X1,X4,X5),sK49(X2,X3,X0,X1,X4,X5)) & ~pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),sK47(X2,X3,X0,X1,X4,X5)),sK48(X2,X3,X0,X1,X4,X5))) & aa(X2,X2,aa(X3,fun(X2,X2),X1,sK47(X2,X3,X0,X1,X4,X5)),sK49(X2,X3,X0,X1,X4,X5)) = X4 & aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),sK47(X2,X3,X0,X1,X4,X5)),sK48(X2,X3,X0,X1,X4,X5)) = X5))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f431,plain,(
% 4.58/1.03 ! [X0 : X2,X1 : fun(X3,fun(X2,X2)),X2 : $tType,X3 : $tType,X4 : X2,X5 : fun(X3,bool)] : ((sP3(X2,X3,X0,X1,X4,X5) | ! [X6 : X3,X7 : fun(X3,bool),X8 : X2] : (~finite_fold_graph(X3,X2,X1,X0,X7,X8) | pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),X6),X7)) | aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8) != X4 | aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X6),X7) != X5)) & (? [X9 : X3,X10 : fun(X3,bool),X11 : X2] : (finite_fold_graph(X3,X2,X1,X0,X10,X11) & ~pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),X9),X10)) & aa(X2,X2,aa(X3,fun(X2,X2),X1,X9),X11) = X4 & aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X9),X10) = X5) | ~sP3(X2,X3,X0,X1,X4,X5)))),
% 4.58/1.03 inference(rectify,[],[f430])).
% 4.58/1.03 tff(f430,plain,(
% 4.58/1.03 ! [X4 : X1,X5 : fun(X0,fun(X1,X1)),X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool)] : ((sP3(X1,X0,X4,X5,X2,X3) | ! [X6 : X0,X7 : fun(X0,bool),X8 : X1] : (~finite_fold_graph(X0,X1,X5,X4,X7,X8) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X7)) | aa(X1,X1,aa(X0,fun(X1,X1),X5,X6),X8) != X2 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X6),X7) != X3)) & (? [X6 : X0,X7 : fun(X0,bool),X8 : X1] : (finite_fold_graph(X0,X1,X5,X4,X7,X8) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X7)) & aa(X1,X1,aa(X0,fun(X1,X1),X5,X6),X8) = X2 & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X6),X7) = X3) | ~sP3(X1,X0,X4,X5,X2,X3)))),
% 4.58/1.03 inference(nnf_transformation,[],[f329])).
% 4.58/1.03 tff(f329,plain,(
% 4.58/1.03 ! [X4 : X1,X5 : fun(X0,fun(X1,X1)),X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool)] : (sP3(X1,X0,X4,X5,X2,X3) <=> ? [X6 : X0,X7 : fun(X0,bool),X8 : X1] : (finite_fold_graph(X0,X1,X5,X4,X7,X8) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X7)) & aa(X1,X1,aa(X0,fun(X1,X1),X5,X6),X8) = X2 & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X6),X7) = X3))),
% 4.58/1.03 introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])])).
% 4.58/1.03 tff(f3305,plain,(
% 4.58/1.03 spl53_189),
% 4.58/1.03 inference(avatar_split_clause,[],[f639,f3303])).
% 4.58/1.03 tff(f3303,plain,(
% 4.58/1.03 spl53_189 <=> ! [X1 : $tType,X0 : $tType,X5 : fun(X0,bool),X3 : X1,X4 : fun(X0,fun(X1,X1)),X6 : X0,X2 : X1] : (finite_fold_graph(X0,X1,X4,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X6),X5),aa(X1,X1,aa(X0,fun(X1,X1),X4,X6),X2)) | ~finite_fold_graph(X0,X1,X4,X3,X5,X2) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X5)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_189])])).
% 4.58/1.03 tff(f639,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X1,X6 : X0,X4 : fun(X0,fun(X1,X1)),X5 : fun(X0,bool)] : (finite_fold_graph(X0,X1,X4,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X6),X5),aa(X1,X1,aa(X0,fun(X1,X1),X4,X6),X2)) | ~finite_fold_graph(X0,X1,X4,X3,X5,X2) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X5))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f318])).
% 4.58/1.03 tff(f318,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X1,X4 : fun(X0,fun(X1,X1)),X5 : fun(X0,bool),X6 : X0] : (finite_fold_graph(X0,X1,X4,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X6),X5),aa(X1,X1,aa(X0,fun(X1,X1),X4,X6),X2)) | ~finite_fold_graph(X0,X1,X4,X3,X5,X2) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X5)))),
% 4.58/1.03 inference(flattening,[],[f317])).
% 4.58/1.03 tff(f317,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X1,X4 : fun(X0,fun(X1,X1)),X5 : fun(X0,bool),X6 : X0] : ((finite_fold_graph(X0,X1,X4,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X6),X5),aa(X1,X1,aa(X0,fun(X1,X1),X4,X6),X2)) | ~finite_fold_graph(X0,X1,X4,X3,X5,X2)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X5)))),
% 4.58/1.03 inference(ennf_transformation,[],[f245])).
% 4.58/1.03 tff(f245,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X1,X4 : fun(X0,fun(X1,X1)),X5 : fun(X0,bool),X6 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X5)) => (finite_fold_graph(X0,X1,X4,X3,X5,X2) => finite_fold_graph(X0,X1,X4,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X6),X5),aa(X1,X1,aa(X0,fun(X1,X1),X4,X6),X2))))),
% 4.58/1.03 inference(rectify,[],[f86])).
% 4.58/1.03 tff(f86,axiom,(
% 4.58/1.03 ! [X1 : $tType,X2 : $tType,X31 : X2,X56 : X2,X53 : fun(X1,fun(X2,X2)),X25 : fun(X1,bool),X26 : X1] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X26),X25)) => (finite_fold_graph(X1,X2,X53,X56,X25,X31) => finite_fold_graph(X1,X2,X53,X56,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),X25),aa(X2,X2,aa(X1,fun(X2,X2),X53,X26),X31))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_fold__graph_OinsertI)).
% 4.58/1.03 tff(f3273,plain,(
% 4.58/1.03 spl53_188),
% 4.58/1.03 inference(avatar_split_clause,[],[f750,f3271])).
% 4.58/1.03 tff(f3271,plain,(
% 4.58/1.03 spl53_188 <=> ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK50(X0,X1,X2,X3,X5)),sK51(X0,X1,X2,X3,X5))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_188])])).
% 4.58/1.03 tff(f750,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK50(X0,X1,X2,X3,X5)),sK51(X0,X1,X2,X3,X5)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f749,f685])).
% 4.58/1.03 tff(f749,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK50(X0,X1,X2,X3,X5)),sK51(X0,X1,X2,X3,X5))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f641,f685])).
% 4.58/1.03 tff(f641,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK50(X0,X1,X2,X3,X5)),sK51(X0,X1,X2,X3,X5))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f438])).
% 4.58/1.03 tff(f3269,plain,(
% 4.58/1.03 spl53_187),
% 4.58/1.03 inference(avatar_split_clause,[],[f746,f3267])).
% 4.58/1.03 tff(f3267,plain,(
% 4.58/1.03 spl53_187 <=> ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK50(X0,X1,X2,X3,X5)),sK52(X0,X1,X2,X3,X5))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_187])])).
% 4.58/1.03 tff(f746,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK50(X0,X1,X2,X3,X5)),sK52(X0,X1,X2,X3,X5)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f745,f685])).
% 4.58/1.03 tff(f745,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK50(X0,X1,X2,X3,X5)),sK52(X0,X1,X2,X3,X5))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f643,f685])).
% 4.58/1.03 tff(f643,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X2,X4,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK50(X0,X1,X2,X3,X5)),sK52(X0,X1,X2,X3,X5))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f438])).
% 4.58/1.03 tff(f3234,plain,(
% 4.58/1.03 spl53_186),
% 4.58/1.03 inference(avatar_split_clause,[],[f744,f3232])).
% 4.58/1.03 tff(f744,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3))) | ~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,semi(X4,X2),X1)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f743,f685])).
% 4.58/1.03 tff(f743,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1))) | hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,semi(X4,X2),X1))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f742,f685])).
% 4.58/1.03 tff(f742,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X6,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,semi(X4,X2),X1))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f640,f685])).
% 4.58/1.03 tff(f640,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool),X4 : com,X5 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,semi(X4,X2),X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f320])).
% 4.58/1.03 tff(f320,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(X0,fun(state,bool)),X4 : com,X5 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,semi(X4,X2),X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(flattening,[],[f319])).
% 4.58/1.03 tff(f319,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(X0,fun(state,bool)),X4 : com,X5 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool)] : ((hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,semi(X4,X2),X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | ~hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(ennf_transformation,[],[f246])).
% 4.58/1.03 tff(f246,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(X0,fun(state,bool)),X4 : com,X5 : fun(X0,fun(state,bool)),X6 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,X4,X3)),bot_bot(fun(hoare_28830079triple(X0),bool)))) => (hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X3,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) => hoare_992312373derivs(X0,X6,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X5,semi(X4,X2),X1)),bot_bot(fun(hoare_28830079triple(X0),bool))))))),
% 4.58/1.03 inference(rectify,[],[f48])).
% 4.58/1.03 tff(f48,axiom,(
% 4.58/1.03 ! [X1 : $tType,X36 : fun(X1,fun(state,bool)),X34 : com,X14 : fun(X1,fun(state,bool)),X15 : com,X16 : fun(X1,fun(state,bool)),X10 : fun(hoare_28830079triple(X1),bool)] : (hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,X15,X14)),bot_bot(fun(hoare_28830079triple(X1),bool)))) => (hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X14,X34,X36)),bot_bot(fun(hoare_28830079triple(X1),bool)))) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,semi(X15,X34),X36)),bot_bot(fun(hoare_28830079triple(X1),bool))))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Comp)).
% 4.58/1.03 tff(f3230,plain,(
% 4.58/1.03 spl53_185),
% 4.58/1.03 inference(avatar_split_clause,[],[f570,f3228])).
% 4.58/1.03 tff(f3228,plain,(
% 4.58/1.03 spl53_185 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | X2 = X3 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_185])])).
% 4.58/1.03 tff(f570,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | X2 = X3 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f299])).
% 4.58/1.03 tff(f299,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | X2 = X3 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))))),
% 4.58/1.03 inference(flattening,[],[f298])).
% 4.58/1.03 tff(f298,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : X0] : ((pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | X2 = X3) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))))),
% 4.58/1.03 inference(ennf_transformation,[],[f218])).
% 4.58/1.03 tff(f218,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) => (X2 != X3 => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))))),
% 4.58/1.03 inference(rectify,[],[f14])).
% 4.58/1.03 tff(f14,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X27 : X1,X18 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X27),X25))) => (X18 != X27 => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),X25))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_insertE)).
% 4.58/1.03 tff(f3204,plain,(
% 4.58/1.03 spl53_184),
% 4.58/1.03 inference(avatar_split_clause,[],[f605,f3202])).
% 4.58/1.03 tff(f3202,plain,(
% 4.58/1.03 spl53_184 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,X0)),X3 : X0,X2 : fun(X0,bool),X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))) | ~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_184])])).
% 4.58/1.03 tff(f605,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))) | ~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f416])).
% 4.58/1.03 tff(f3144,plain,(
% 4.58/1.03 spl53_183),
% 4.58/1.03 inference(avatar_split_clause,[],[f738,f3142])).
% 4.58/1.03 tff(f738,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK45(X0,X1,X2)),sK46(X0,X1,X2)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f737,f685])).
% 4.58/1.03 tff(f737,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK45(X0,X1,X2)),sK46(X0,X1,X2))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f626,f685])).
% 4.58/1.03 tff(f626,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK45(X0,X1,X2)),sK46(X0,X1,X2))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f429])).
% 4.58/1.03 tff(f429,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK45(X0,X1,X2)),sK46(X0,X1,X2))) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK45(X0,X1,X2)),sK46(X0,X1,X2)))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK45,sK46])],[f315,f428])).
% 4.58/1.03 tff(f428,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool))] : (? [X6 : X0,X7 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,X6),X7)) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,X6),X7))) => (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK45(X0,X1,X2)),sK46(X0,X1,X2))) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,sK45(X0,X1,X2)),sK46(X0,X1,X2)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f315,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ? [X6 : X0,X7 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,X6),X7)) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,X6),X7))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(flattening,[],[f314])).
% 4.58/1.03 tff(f314,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : ((hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ? [X6 : X0,X7 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,X6),X7)) & pp(aa(state,bool,aa(X0,fun(state,bool),X2,X6),X7)))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(ennf_transformation,[],[f242])).
% 4.58/1.03 tff(f242,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))) => (! [X6 : X0,X7 : state] : (pp(aa(state,bool,aa(X0,fun(state,bool),X2,X6),X7)) => pp(aa(state,bool,aa(X0,fun(state,bool),X1,X6),X7))) => hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1)),bot_bot(fun(hoare_28830079triple(X0),bool))))))),
% 4.58/1.03 inference(rectify,[],[f9])).
% 4.58/1.03 tff(f9,axiom,(
% 4.58/1.03 ! [X1 : $tType,X14 : fun(X1,fun(state,bool)),X21 : fun(X1,fun(state,bool)),X15 : com,X16 : fun(X1,fun(state,bool)),X10 : fun(hoare_28830079triple(X1),bool)] : (hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,X15,X21)),bot_bot(fun(hoare_28830079triple(X1),bool)))) => (! [X19 : X1,X20 : state] : (pp(aa(state,bool,aa(X1,fun(state,bool),X21,X19),X20)) => pp(aa(state,bool,aa(X1,fun(state,bool),X14,X19),X20))) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,X15,X14)),bot_bot(fun(hoare_28830079triple(X1),bool))))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_conseq2)).
% 4.58/1.03 tff(f3140,plain,(
% 4.58/1.03 spl53_182),
% 4.58/1.03 inference(avatar_split_clause,[],[f736,f3138])).
% 4.58/1.03 tff(f3138,plain,(
% 4.58/1.03 spl53_182 <=> ! [X0 : $tType,X5 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool)),X3 : com,X2 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK45(X0,X1,X2)),sK46(X0,X1,X2))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_182])])).
% 4.58/1.03 tff(f736,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK45(X0,X1,X2)),sK46(X0,X1,X2)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f735,f685])).
% 4.58/1.03 tff(f735,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK45(X0,X1,X2)),sK46(X0,X1,X2))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f627,f685])).
% 4.58/1.03 tff(f627,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK45(X0,X1,X2)),sK46(X0,X1,X2))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f429])).
% 4.58/1.03 tff(f3136,plain,(
% 4.58/1.03 spl53_24 | ~spl53_181 | ~spl53_170),
% 4.58/1.03 inference(avatar_split_clause,[],[f2950,f2800,f3133,f858])).
% 4.58/1.03 tff(f3133,plain,(
% 4.58/1.03 spl53_181 <=> fTrue = bot_bot(bool)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_181])])).
% 4.58/1.03 tff(f2800,plain,(
% 4.58/1.03 spl53_170 <=> ! [X0 : bool] : (bot_bot(bool) = X0 | fTrue = X0)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_170])])).
% 4.58/1.03 tff(f2950,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (fTrue != bot_bot(bool) | fTrue = X0) ) | ~spl53_170),
% 4.58/1.03 inference(equality_factoring,[],[f2801])).
% 4.58/1.03 tff(f2801,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (bot_bot(bool) = X0 | fTrue = X0) ) | ~spl53_170),
% 4.58/1.03 inference(avatar_component_clause,[],[f2800])).
% 4.58/1.03 tff(f3131,plain,(
% 4.58/1.03 spl53_180),
% 4.58/1.03 inference(avatar_split_clause,[],[f734,f3129])).
% 4.58/1.03 tff(f734,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2))) | pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK43(X0,X1,X4)),sK44(X0,X1,X4)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f733,f685])).
% 4.58/1.03 tff(f733,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2))) | pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK43(X0,X1,X4)),sK44(X0,X1,X4))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f624,f685])).
% 4.58/1.03 tff(f624,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK43(X0,X1,X4)),sK44(X0,X1,X4))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f427])).
% 4.58/1.03 tff(f427,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | (~pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK43(X0,X1,X4)),sK44(X0,X1,X4))) & pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK43(X0,X1,X4)),sK44(X0,X1,X4)))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44])],[f313,f426])).
% 4.58/1.03 tff(f426,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (? [X6 : X0,X7 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X4,X6),X7)) & pp(aa(state,bool,aa(X0,fun(state,bool),X1,X6),X7))) => (~pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK43(X0,X1,X4)),sK44(X0,X1,X4))) & pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK43(X0,X1,X4)),sK44(X0,X1,X4)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f313,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ? [X6 : X0,X7 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X4,X6),X7)) & pp(aa(state,bool,aa(X0,fun(state,bool),X1,X6),X7))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(flattening,[],[f312])).
% 4.58/1.03 tff(f312,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : ((hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ? [X6 : X0,X7 : state] : (~pp(aa(state,bool,aa(X0,fun(state,bool),X4,X6),X7)) & pp(aa(state,bool,aa(X0,fun(state,bool),X1,X6),X7)))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(ennf_transformation,[],[f241])).
% 4.58/1.03 tff(f241,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))) => (! [X6 : X0,X7 : state] : (pp(aa(state,bool,aa(X0,fun(state,bool),X1,X6),X7)) => pp(aa(state,bool,aa(X0,fun(state,bool),X4,X6),X7))) => hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool))))))),
% 4.58/1.03 inference(rectify,[],[f10])).
% 4.58/1.03 tff(f10,axiom,(
% 4.58/1.03 ! [X1 : $tType,X16 : fun(X1,fun(state,bool)),X14 : fun(X1,fun(state,bool)),X15 : com,X22 : fun(X1,fun(state,bool)),X10 : fun(hoare_28830079triple(X1),bool)] : (hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X22,X15,X14)),bot_bot(fun(hoare_28830079triple(X1),bool)))) => (! [X19 : X1,X20 : state] : (pp(aa(state,bool,aa(X1,fun(state,bool),X16,X19),X20)) => pp(aa(state,bool,aa(X1,fun(state,bool),X22,X19),X20))) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,X15,X14)),bot_bot(fun(hoare_28830079triple(X1),bool))))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_conseq1)).
% 4.58/1.03 tff(f3127,plain,(
% 4.58/1.03 spl53_179),
% 4.58/1.03 inference(avatar_split_clause,[],[f732,f3125])).
% 4.58/1.03 tff(f3125,plain,(
% 4.58/1.03 spl53_179 <=> ! [X0 : $tType,X5 : fun(hoare_28830079triple(X0),bool),X4 : fun(X0,fun(state,bool)),X3 : com,X2 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool))] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK43(X0,X1,X4)),sK44(X0,X1,X4))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_179])])).
% 4.58/1.03 tff(f732,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2))) | hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK43(X0,X1,X4)),sK44(X0,X1,X4)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f731,f685])).
% 4.58/1.03 tff(f731,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK43(X0,X1,X4)),sK44(X0,X1,X4))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f625,f685])).
% 4.58/1.03 tff(f625,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(state,bool)),X3 : com,X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK43(X0,X1,X4)),sK44(X0,X1,X4))) | ~hoare_992312373derivs(X0,X5,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X3,X2)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f427])).
% 4.58/1.03 tff(f3075,plain,(
% 4.58/1.03 spl53_178 | ~spl53_34 | ~spl53_176),
% 4.58/1.03 inference(avatar_split_clause,[],[f3067,f3064,f912,f3073])).
% 4.58/1.03 tff(f3073,plain,(
% 4.58/1.03 spl53_178 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK21(X0,X1)),sK22(X0,X1)))) | ~finite_finite1(X0,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_178])])).
% 4.58/1.03 tff(f3064,plain,(
% 4.58/1.03 spl53_176 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK21(X0,X1)),sK22(X0,X1)))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_176])])).
% 4.58/1.03 tff(f3067,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK21(X0,X1)),sK22(X0,X1)))) | ~finite_finite1(X0,X2)) ) | (~spl53_34 | ~spl53_176)),
% 4.58/1.03 inference(forward_demodulation,[],[f3065,f913])).
% 4.58/1.03 tff(f3065,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK21(X0,X1)),sK22(X0,X1)))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | ~spl53_176),
% 4.58/1.03 inference(avatar_component_clause,[],[f3064])).
% 4.58/1.03 tff(f3071,plain,(
% 4.58/1.03 spl53_177),
% 4.58/1.03 inference(avatar_split_clause,[],[f568,f3069])).
% 4.58/1.03 tff(f3069,plain,(
% 4.58/1.03 spl53_177 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_177])])).
% 4.58/1.03 tff(f568,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f295])).
% 4.58/1.03 tff(f295,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 4.58/1.03 inference(ennf_transformation,[],[f216])).
% 4.58/1.03 tff(f216,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))))),
% 4.58/1.03 inference(rectify,[],[f25])).
% 4.58/1.03 tff(f25,axiom,(
% 4.58/1.03 ! [X1 : $tType,X27 : X1,X28 : fun(X1,bool),X18 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),X28)) => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X27),X28))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_insertI2)).
% 4.58/1.03 tff(f3066,plain,(
% 4.58/1.03 spl53_176),
% 4.58/1.03 inference(avatar_split_clause,[],[f528,f3064])).
% 4.58/1.03 tff(f528,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK21(X0,X1)),sK22(X0,X1)))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f372])).
% 4.58/1.03 tff(f372,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK21(X0,X1)),sK22(X0,X1)))) & pp(aa(fun(X0,bool),bool,X1,sK22(X0,X1))) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK21(X0,X1)),sK22(X0,X1))) & finite_finite1(X0,sK22(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f272,f371])).
% 4.58/1.03 tff(f371,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (? [X3 : X0,X4 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4))) & pp(aa(fun(X0,bool),bool,X1,X4)) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X4)) & finite_finite1(X0,X4)) => (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK21(X0,X1)),sK22(X0,X1)))) & pp(aa(fun(X0,bool),bool,X1,sK22(X0,X1))) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK21(X0,X1)),sK22(X0,X1))) & finite_finite1(X0,sK22(X0,X1))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f272,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ? [X3 : X0,X4 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4))) & pp(aa(fun(X0,bool),bool,X1,X4)) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X4)) & finite_finite1(X0,X4)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(flattening,[],[f271])).
% 4.58/1.03 tff(f271,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (((pp(aa(fun(X0,bool),bool,X1,X2)) | ? [X3 : X0,X4 : fun(X0,bool)] : (((~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4))) & pp(aa(fun(X0,bool),bool,X1,X4))) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))) & finite_finite1(X0,X4))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))) | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(ennf_transformation,[],[f189])).
% 4.58/1.03 tff(f189,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (finite_finite1(X0,X2) => (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) => (! [X3 : X0,X4 : fun(X0,bool)] : (finite_finite1(X0,X4) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X4)) => (pp(aa(fun(X0,bool),bool,X1,X4)) => pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4)))))) => pp(aa(fun(X0,bool),bool,X1,X2)))))),
% 4.58/1.03 inference(rectify,[],[f95])).
% 4.58/1.03 tff(f95,axiom,(
% 4.58/1.03 ! [X1 : $tType,X16 : fun(fun(X1,bool),bool),X54 : fun(X1,bool)] : (finite_finite1(X1,X54) => (pp(aa(fun(X1,bool),bool,X16,bot_bot(fun(X1,bool)))) => (! [X48 : X1,X62 : fun(X1,bool)] : (finite_finite1(X1,X62) => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X48),X62)) => (pp(aa(fun(X1,bool),bool,X16,X62)) => pp(aa(fun(X1,bool),bool,X16,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X48),X62)))))) => pp(aa(fun(X1,bool),bool,X16,X54)))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_finite__induct)).
% 4.58/1.03 tff(f3035,plain,(
% 4.58/1.03 spl53_175 | ~spl53_34 | ~spl53_173),
% 4.58/1.03 inference(avatar_split_clause,[],[f2831,f2828,f912,f3033])).
% 4.58/1.03 tff(f2828,plain,(
% 4.58/1.03 spl53_173 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_173])])).
% 4.58/1.03 tff(f2831,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),combk(bool,X0,fFalse)) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),combk(bool,X0,fFalse)) | X1 = X2) ) | (~spl53_34 | ~spl53_173)),
% 4.58/1.03 inference(forward_demodulation,[],[f2829,f913])).
% 4.58/1.03 tff(f2829,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) ) | ~spl53_173),
% 4.58/1.03 inference(avatar_component_clause,[],[f2828])).
% 4.58/1.03 tff(f2835,plain,(
% 4.58/1.03 spl53_174),
% 4.58/1.03 inference(avatar_split_clause,[],[f664,f2833])).
% 4.58/1.03 tff(f2833,plain,(
% 4.58/1.03 spl53_174 <=> ! [X0 : $tType,X5 : fun(X0,bool),X4 : X0,X6 : X0,X3 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)),X6)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) | ~finite_fold_graph(X0,X0,X3,X4,X5,X6))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_174])])).
% 4.58/1.03 tff(f664,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X6 : X0,X4 : X0,X5 : fun(X0,bool)] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)),X6)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) | ~finite_fold_graph(X0,X0,X3,X4,X5,X6)) )),
% 4.58/1.03 inference(equality_resolution,[],[f663])).
% 4.58/1.03 tff(f663,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X6 : X0,X4 : X0,X5 : fun(X0,bool)] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X6)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) | ~finite_fold_graph(X0,X0,X3,X4,X5,X6) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) != X2) )),
% 4.58/1.03 inference(equality_resolution,[],[f581])).
% 4.58/1.03 tff(f581,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0,X6 : X0,X4 : X0,X5 : fun(X0,bool)] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) | ~finite_fold_graph(X0,X0,X3,X4,X5,X6) | X1 != X6 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) != X2) )),
% 4.58/1.03 inference(cnf_transformation,[],[f400])).
% 4.58/1.03 tff(f400,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0))] : ((pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)) | ! [X4 : X0,X5 : fun(X0,bool),X6 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) | ~finite_fold_graph(X0,X0,X3,X4,X5,X6) | X1 != X6 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) != X2)) & ((~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3))) & finite_fold_graph(X0,X0,X3,sK31(X0,X1,X2,X3),sK32(X0,X1,X2,X3),sK33(X0,X1,X2,X3)) & sK33(X0,X1,X2,X3) = X1 & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2) | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33])],[f398,f399])).
% 4.58/1.03 tff(f399,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0))] : (? [X7 : X0,X8 : fun(X0,bool),X9 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X7),X8)) & finite_fold_graph(X0,X0,X3,X7,X8,X9) & X1 = X9 & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X7),X8) = X2) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3))) & finite_fold_graph(X0,X0,X3,sK31(X0,X1,X2,X3),sK32(X0,X1,X2,X3),sK33(X0,X1,X2,X3)) & sK33(X0,X1,X2,X3) = X1 & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f398,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0))] : ((pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)) | ! [X4 : X0,X5 : fun(X0,bool),X6 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) | ~finite_fold_graph(X0,X0,X3,X4,X5,X6) | X1 != X6 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) != X2)) & (? [X7 : X0,X8 : fun(X0,bool),X9 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X7),X8)) & finite_fold_graph(X0,X0,X3,X7,X8,X9) & X1 = X9 & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X7),X8) = X2) | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1))))),
% 4.58/1.03 inference(rectify,[],[f397])).
% 4.58/1.03 tff(f397,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0))] : ((pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)) | ! [X4 : X0,X5 : fun(X0,bool),X6 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) | ~finite_fold_graph(X0,X0,X3,X4,X5,X6) | X1 != X6 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) != X2)) & (? [X4 : X0,X5 : fun(X0,bool),X6 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & finite_fold_graph(X0,X0,X3,X4,X5,X6) & X1 = X6 & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X2) | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1))))),
% 4.58/1.03 inference(nnf_transformation,[],[f222])).
% 4.58/1.03 tff(f222,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)) <=> ? [X4 : X0,X5 : fun(X0,bool),X6 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & finite_fold_graph(X0,X0,X3,X4,X5,X6) & X1 = X6 & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X2))),
% 4.58/1.03 inference(rectify,[],[f97])).
% 4.58/1.03 tff(f97,axiom,(
% 4.58/1.03 ! [X1 : $tType,X63 : X1,X64 : fun(X1,bool),X53 : fun(X1,fun(X1,X1))] : (pp(aa(X1,bool,finite_fold1Set(X1,X53,X64),X63)) <=> ? [X61 : X1,X60 : fun(X1,bool),X29 : X1] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X61),X60)) & finite_fold_graph(X1,X1,X53,X61,X60,X29) & X29 = X63 & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X61),X60) = X64))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_fold1Set_Osimps)).
% 4.58/1.03 tff(f2830,plain,(
% 4.58/1.03 spl53_173),
% 4.58/1.03 inference(avatar_split_clause,[],[f540,f2828])).
% 4.58/1.03 tff(f540,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f282])).
% 4.58/1.03 tff(f282,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = X2 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),
% 4.58/1.03 inference(ennf_transformation,[],[f197])).
% 4.58/1.03 tff(f197,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) => X1 = X2)),
% 4.58/1.03 inference(rectify,[],[f34])).
% 4.58/1.03 tff(f34,axiom,(
% 4.58/1.03 ! [X1 : $tType,X27 : X1,X18 : X1] : (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),bot_bot(fun(X1,bool))) = aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X27),bot_bot(fun(X1,bool))) => X18 = X27)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_singleton__inject)).
% 4.58/1.03 tff(f2822,plain,(
% 4.58/1.03 spl53_172),
% 4.58/1.03 inference(avatar_split_clause,[],[f709,f2820])).
% 4.58/1.03 tff(f2820,plain,(
% 4.58/1.03 spl53_172 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,X2) | ~finite_finite1(X0,X1) | finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_172])])).
% 4.58/1.03 tff(f709,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,X2) | ~finite_finite1(X0,X1) | finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f708,f456])).
% 4.58/1.03 tff(f708,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,X1) | finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)) | ~finite_finite1(X0,collect(X0,X2))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f707,f456])).
% 4.58/1.03 tff(f707,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)) | ~finite_finite1(X0,collect(X0,X1)) | ~finite_finite1(X0,collect(X0,X2))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f557,f456])).
% 4.58/1.03 tff(f557,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1))) | ~finite_finite1(X0,collect(X0,X1)) | ~finite_finite1(X0,collect(X0,X2))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f391])).
% 4.58/1.03 tff(f391,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : ((finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1))) | ~finite_finite1(X0,collect(X0,X1)) | ~finite_finite1(X0,collect(X0,X2))) & ((finite_finite1(X0,collect(X0,X1)) & finite_finite1(X0,collect(X0,X2))) | ~finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)))))),
% 4.58/1.03 inference(flattening,[],[f390])).
% 4.58/1.03 tff(f390,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : ((finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1))) | (~finite_finite1(X0,collect(X0,X1)) | ~finite_finite1(X0,collect(X0,X2)))) & ((finite_finite1(X0,collect(X0,X1)) & finite_finite1(X0,collect(X0,X2))) | ~finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)))))),
% 4.58/1.03 inference(nnf_transformation,[],[f204])).
% 4.58/1.03 tff(f204,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1))) <=> (finite_finite1(X0,collect(X0,X1)) & finite_finite1(X0,collect(X0,X2))))),
% 4.58/1.03 inference(rectify,[],[f80])).
% 4.58/1.03 tff(f80,axiom,(
% 4.58/1.03 ! [X1 : $tType,X14 : fun(X1,bool),X16 : fun(X1,bool)] : (finite_finite1(X1,collect(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fdisj),X16)),X14))) <=> (finite_finite1(X1,collect(X1,X14)) & finite_finite1(X1,collect(X1,X16))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_finite__Collect__disjI)).
% 4.58/1.03 tff(f2806,plain,(
% 4.58/1.03 spl53_171),
% 4.58/1.03 inference(avatar_split_clause,[],[f715,f2804])).
% 4.58/1.03 tff(f715,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),X2)) | hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1)) | ~hoare_992312373derivs(X0,X3,X1)) )),
% 4.58/1.03 inference(forward_demodulation,[],[f569,f685])).
% 4.58/1.03 tff(f569,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1)) | ~hoare_992312373derivs(X0,X3,X1) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f297])).
% 4.58/1.03 tff(f297,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool),X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1)) | ~hoare_992312373derivs(X0,X3,X1) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(flattening,[],[f296])).
% 4.58/1.03 tff(f296,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool),X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool)] : ((hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1)) | ~hoare_992312373derivs(X0,X3,X1)) | ~hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 4.58/1.03 inference(ennf_transformation,[],[f217])).
% 4.58/1.03 tff(f217,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool),X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),bot_bot(fun(hoare_28830079triple(X0),bool)))) => (hoare_992312373derivs(X0,X3,X1) => hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1))))),
% 4.58/1.03 inference(rectify,[],[f4])).
% 4.58/1.03 tff(f4,axiom,(
% 4.58/1.03 ! [X1 : $tType,X11 : fun(hoare_28830079triple(X1),bool),X13 : hoare_28830079triple(X1),X10 : fun(hoare_28830079triple(X1),bool)] : (hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),X13),bot_bot(fun(hoare_28830079triple(X1),bool)))) => (hoare_992312373derivs(X1,X10,X11) => hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),X13),X11))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert)).
% 4.58/1.03 tff(f2802,plain,(
% 4.58/1.03 spl53_170 | spl53_25 | ~spl53_43 | ~spl53_72),
% 4.58/1.03 inference(avatar_split_clause,[],[f1280,f1160,f967,f861,f2800])).
% 4.58/1.03 tff(f861,plain,(
% 4.58/1.03 spl53_25 <=> fFalse = fTrue),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_25])])).
% 4.58/1.03 tff(f967,plain,(
% 4.58/1.03 spl53_43 <=> fFalse = bot_bot(bool)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_43])])).
% 4.58/1.03 tff(f1160,plain,(
% 4.58/1.03 spl53_72 <=> ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_72])])).
% 4.58/1.03 tff(f1280,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (fFalse = fTrue | bot_bot(bool) = X0 | fTrue = X0) ) | (~spl53_43 | ~spl53_72)),
% 4.58/1.03 inference(superposition,[],[f969,f1161])).
% 4.58/1.03 tff(f1161,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl53_72),
% 4.58/1.03 inference(avatar_component_clause,[],[f1160])).
% 4.58/1.03 tff(f969,plain,(
% 4.58/1.03 fFalse = bot_bot(bool) | ~spl53_43),
% 4.58/1.03 inference(avatar_component_clause,[],[f967])).
% 4.58/1.03 tff(f2798,plain,(
% 4.58/1.03 spl53_169),
% 4.58/1.03 inference(avatar_split_clause,[],[f713,f2796])).
% 4.58/1.03 tff(f2796,plain,(
% 4.58/1.03 spl53_169 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)) | finite_finite1(X0,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_169])])).
% 4.58/1.03 tff(f713,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)) | finite_finite1(X0,X2)) )),
% 4.58/1.03 inference(forward_demodulation,[],[f712,f456])).
% 4.58/1.03 tff(f712,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,X2) | ~finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f555,f456])).
% 4.58/1.03 tff(f555,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,collect(X0,X2)) | ~finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f391])).
% 4.58/1.03 tff(f2794,plain,(
% 4.58/1.03 spl53_168),
% 4.58/1.03 inference(avatar_split_clause,[],[f711,f2792])).
% 4.58/1.03 tff(f2792,plain,(
% 4.58/1.03 spl53_168 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)) | finite_finite1(X0,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_168])])).
% 4.58/1.03 tff(f711,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)) | finite_finite1(X0,X1)) )),
% 4.58/1.03 inference(forward_demodulation,[],[f710,f456])).
% 4.58/1.03 tff(f710,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f556,f456])).
% 4.58/1.03 tff(f556,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,collect(X0,X1)) | ~finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fdisj),X2)),X1)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f391])).
% 4.58/1.03 tff(f2790,plain,(
% 4.58/1.03 spl53_167),
% 4.58/1.03 inference(avatar_split_clause,[],[f705,f2788])).
% 4.58/1.03 tff(f2788,plain,(
% 4.58/1.03 spl53_167 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,X2) | finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_167])])).
% 4.58/1.03 tff(f705,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,X2) | finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f704,f456])).
% 4.58/1.03 tff(f704,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1)) | ~finite_finite1(X0,collect(X0,X2))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f541,f456])).
% 4.58/1.03 tff(f541,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1))) | ~finite_finite1(X0,collect(X0,X2))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f283])).
% 4.58/1.03 tff(f283,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1))) | (~finite_finite1(X0,collect(X0,X1)) & ~finite_finite1(X0,collect(X0,X2))))),
% 4.58/1.03 inference(ennf_transformation,[],[f198])).
% 4.58/1.03 tff(f198,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : ((finite_finite1(X0,collect(X0,X1)) | finite_finite1(X0,collect(X0,X2))) => finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1))))),
% 4.58/1.03 inference(rectify,[],[f79])).
% 4.58/1.03 tff(f79,axiom,(
% 4.58/1.03 ! [X1 : $tType,X14 : fun(X1,bool),X16 : fun(X1,bool)] : ((finite_finite1(X1,collect(X1,X14)) | finite_finite1(X1,collect(X1,X16))) => finite_finite1(X1,collect(X1,aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),combb(bool,fun(bool,bool),X1,fconj),X16)),X14))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_finite__Collect__conjI)).
% 4.58/1.03 tff(f2786,plain,(
% 4.58/1.03 spl53_166),
% 4.58/1.03 inference(avatar_split_clause,[],[f703,f2784])).
% 4.58/1.03 tff(f2784,plain,(
% 4.58/1.03 spl53_166 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,X1) | finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_166])])).
% 4.58/1.03 tff(f703,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,X1) | finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f702,f456])).
% 4.58/1.03 tff(f702,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1)) | ~finite_finite1(X0,collect(X0,X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f542,f456])).
% 4.58/1.03 tff(f542,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),combb(bool,fun(bool,bool),X0,fconj),X2)),X1))) | ~finite_finite1(X0,collect(X0,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f283])).
% 4.58/1.03 tff(f2704,plain,(
% 4.58/1.03 spl53_165),
% 4.58/1.03 inference(avatar_split_clause,[],[f623,f2702])).
% 4.58/1.03 tff(f623,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : (aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f240])).
% 4.58/1.03 tff(f240,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))),
% 4.58/1.03 inference(rectify,[],[f112])).
% 4.58/1.03 tff(f112,axiom,(
% 4.58/1.03 ! [X2 : $tType,X1 : $tType,X0 : $tType,X69 : X0,X70 : fun(X0,X1),X68 : fun(X0,fun(X1,X2))] : aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),X68),X70),X69) = aa(X1,X2,aa(X0,fun(X1,X2),X68,X69),aa(X0,X1,X70,X69))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U)).
% 4.58/1.03 tff(f2646,plain,(
% 4.58/1.03 spl53_164),
% 4.58/1.03 inference(avatar_split_clause,[],[f621,f2644])).
% 4.58/1.03 tff(f2644,plain,(
% 4.58/1.03 spl53_164 <=> ! [X1 : $tType,X0 : $tType,X3 : com,X4 : fun(X1,fun(state,bool)),X5 : fun(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0))),X2 : fun(X1,fun(state,bool))] : hoare_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2)) = aa(fun(X1,fun(state,bool)),X0,aa(com,fun(fun(X1,fun(state,bool)),X0),aa(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)),X5,X4),X3),X2)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_164])])).
% 4.58/1.03 tff(f621,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(state,bool)),X3 : com,X4 : fun(X1,fun(state,bool)),X5 : fun(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)))] : (hoare_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2)) = aa(fun(X1,fun(state,bool)),X0,aa(com,fun(fun(X1,fun(state,bool)),X0),aa(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)),X5,X4),X3),X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f238])).
% 4.58/1.03 tff(f238,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,fun(state,bool)),X3 : com,X4 : fun(X1,fun(state,bool)),X5 : fun(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)))] : hoare_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2)) = aa(fun(X1,fun(state,bool)),X0,aa(com,fun(fun(X1,fun(state,bool)),X0),aa(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)),X5,X4),X3),X2)),
% 4.58/1.03 inference(rectify,[],[f43])).
% 4.58/1.03 tff(f43,axiom,(
% 4.58/1.03 ! [X1 : $tType,X2 : $tType,X7 : fun(X2,fun(state,bool)),X8 : com,X9 : fun(X2,fun(state,bool)),X35 : fun(fun(X2,fun(state,bool)),fun(com,fun(fun(X2,fun(state,bool)),X1)))] : hoare_376461865e_case(X2,X1,X35,hoare_1841697145triple(X2,X9,X8,X7)) = aa(fun(X2,fun(state,bool)),X1,aa(com,fun(fun(X2,fun(state,bool)),X1),aa(fun(X2,fun(state,bool)),fun(com,fun(fun(X2,fun(state,bool)),X1)),X35,X9),X8),X7)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_triple_Osimps_I2_J)).
% 4.58/1.03 tff(f2642,plain,(
% 4.58/1.03 spl53_163),
% 4.58/1.03 inference(avatar_split_clause,[],[f604,f2640])).
% 4.58/1.03 tff(f604,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (finite_fold_graph(X0,X0,X4,sK36(X0,X1,X2,X3,X4),sK37(X0,X1,X2,X3,X4),X1) | ~pp(aa(X0,bool,finite_fold1Set(X0,X4,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f416])).
% 4.58/1.03 tff(f2598,plain,(
% 4.58/1.03 spl53_162),
% 4.58/1.03 inference(avatar_split_clause,[],[f537,f2596])).
% 4.58/1.03 tff(f537,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK26(X0,X1,X2)) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f380])).
% 4.58/1.03 tff(f380,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : ((~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK26(X0,X1,X2))) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK26(X0,X1,X2)) = X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f280,f379])).
% 4.58/1.03 tff(f379,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (? [X3 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = X1) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK26(X0,X1,X2))) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK26(X0,X1,X2)) = X1))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f280,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (? [X3 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.03 inference(ennf_transformation,[],[f195])).
% 4.58/1.03 tff(f195,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) => ? [X3 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = X1))),
% 4.58/1.03 inference(rectify,[],[f62])).
% 4.58/1.03 tff(f62,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X18 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),X25)) => ? [X47 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),X47)) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X47) = X25))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_mk__disjoint__insert)).
% 4.58/1.03 tff(f2594,plain,(
% 4.58/1.03 spl53_161),
% 4.58/1.03 inference(avatar_split_clause,[],[f535,f2592])).
% 4.58/1.03 tff(f535,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK25(X0,X1,X2)) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f378])).
% 4.58/1.03 tff(f378,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : ((~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK25(X0,X1,X2))) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK25(X0,X1,X2)) = X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f279,f377])).
% 4.58/1.03 tff(f377,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (? [X3 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = X1) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK25(X0,X1,X2))) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),sK25(X0,X1,X2)) = X1))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f279,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (? [X3 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.03 inference(ennf_transformation,[],[f194])).
% 4.58/1.03 tff(f194,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) => ~! [X3 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = X1 => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))))),
% 4.58/1.03 inference(rectify,[],[f57])).
% 4.58/1.03 tff(f57,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X26 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X26),X25)) => ~! [X47 : fun(X1,bool)] : (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),X47) = X25 => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X26),X47))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Set_Oset__insert)).
% 4.58/1.03 tff(f2577,plain,(
% 4.58/1.03 spl53_160 | ~spl53_34 | ~spl53_158),
% 4.58/1.03 inference(avatar_split_clause,[],[f2569,f2566,f912,f2575])).
% 4.58/1.03 tff(f2566,plain,(
% 4.58/1.03 spl53_158 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK21(X0,X1)),sK22(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_158])])).
% 4.58/1.03 tff(f2569,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK21(X0,X1)),sK22(X0,X1))) | ~finite_finite1(X0,X2)) ) | (~spl53_34 | ~spl53_158)),
% 4.58/1.03 inference(forward_demodulation,[],[f2567,f913])).
% 4.58/1.03 tff(f2567,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK21(X0,X1)),sK22(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | ~spl53_158),
% 4.58/1.03 inference(avatar_component_clause,[],[f2566])).
% 4.58/1.03 tff(f2573,plain,(
% 4.58/1.03 spl53_159),
% 4.58/1.03 inference(avatar_split_clause,[],[f630,f2571])).
% 4.58/1.03 tff(f2571,plain,(
% 4.58/1.03 spl53_159 <=> ! [X3 : $tType,X2 : $tType,X4 : X2,X0 : X2,X5 : fun(X3,bool),X1 : fun(X3,fun(X2,X2))] : (aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),sK47(X2,X3,X0,X1,X4,X5)),sK48(X2,X3,X0,X1,X4,X5)) = X5 | ~sP3(X2,X3,X0,X1,X4,X5))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_159])])).
% 4.58/1.03 tff(f630,plain,(
% 4.58/1.03 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (aa(fun(X3,bool),fun(X3,bool),aa(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),sK47(X2,X3,X0,X1,X4,X5)),sK48(X2,X3,X0,X1,X4,X5)) = X5 | ~sP3(X2,X3,X0,X1,X4,X5)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f433])).
% 4.58/1.03 tff(f2568,plain,(
% 4.58/1.03 spl53_158),
% 4.58/1.03 inference(avatar_split_clause,[],[f526,f2566])).
% 4.58/1.03 tff(f526,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK21(X0,X1)),sK22(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f372])).
% 4.58/1.03 tff(f2527,plain,(
% 4.58/1.03 spl53_157),
% 4.58/1.03 inference(avatar_split_clause,[],[f577,f2525])).
% 4.58/1.03 tff(f2525,plain,(
% 4.58/1.03 spl53_157 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2 | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_157])])).
% 4.58/1.03 tff(f577,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2 | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f400])).
% 4.58/1.03 tff(f2523,plain,(
% 4.58/1.03 spl53_156),
% 4.58/1.03 inference(avatar_split_clause,[],[f534,f2521])).
% 4.58/1.03 tff(f534,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f278])).
% 4.58/1.03 tff(f278,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.03 inference(ennf_transformation,[],[f193])).
% 4.58/1.03 tff(f193,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) => aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) = X1)),
% 4.58/1.03 inference(rectify,[],[f24])).
% 4.58/1.03 tff(f24,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X18 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),X25)) => aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X25) = X25)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_insert__absorb)).
% 4.58/1.03 tff(f2473,plain,(
% 4.58/1.03 spl53_155),
% 4.58/1.03 inference(avatar_split_clause,[],[f725,f2471])).
% 4.58/1.03 tff(f725,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK40(X0,X1,X2,X3,X4)),sK41(X0,X1,X2,X3,X4)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f608,f685])).
% 4.58/1.03 tff(f608,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK40(X0,X1,X2,X3,X4)),sK41(X0,X1,X2,X3,X4)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f421])).
% 4.58/1.03 tff(f2469,plain,(
% 4.58/1.03 spl53_154),
% 4.58/1.03 inference(avatar_split_clause,[],[f720,f2467])).
% 4.58/1.03 tff(f720,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK38(X0,X1,X2,X3,X4)),sK39(X0,X1,X2,X3,X4)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f606,f685])).
% 4.58/1.03 tff(f606,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)),bot_bot(fun(hoare_28830079triple(X0),bool)))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK38(X0,X1,X2,X3,X4)),sK39(X0,X1,X2,X3,X4)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f418])).
% 4.58/1.03 tff(f2460,plain,(
% 4.58/1.03 ~spl53_153 | ~spl53_34 | ~spl53_135 | spl53_152),
% 4.58/1.03 inference(avatar_split_clause,[],[f2455,f2450,f2238,f912,f2457])).
% 4.58/1.03 tff(f2450,plain,(
% 4.58/1.03 spl53_152 <=> hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b)))),bot_bot(fun(hoare_28830079triple(a),bool))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_152])])).
% 4.58/1.03 tff(f2455,plain,(
% 4.58/1.03 ~hoare_992312373derivs(a,g,aa(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b))))) | (~spl53_34 | ~spl53_135 | spl53_152)),
% 4.58/1.03 inference(forward_demodulation,[],[f2454,f2239])).
% 4.58/1.03 tff(f2454,plain,(
% 4.58/1.03 ~hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b)))),combk(bool,hoare_28830079triple(a),fFalse))) | (~spl53_34 | spl53_152)),
% 4.58/1.03 inference(forward_demodulation,[],[f2452,f913])).
% 4.58/1.03 tff(f2452,plain,(
% 4.58/1.03 ~hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b)))),bot_bot(fun(hoare_28830079triple(a),bool)))) | spl53_152),
% 4.58/1.03 inference(avatar_component_clause,[],[f2450])).
% 4.58/1.03 tff(f2453,plain,(
% 4.58/1.03 ~spl53_152),
% 4.58/1.03 inference(avatar_split_clause,[],[f441,f2450])).
% 4.58/1.03 tff(f441,plain,(
% 4.58/1.03 ~hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b)))),bot_bot(fun(hoare_28830079triple(a),bool))))),
% 4.58/1.03 inference(cnf_transformation,[],[f128])).
% 4.58/1.03 tff(f128,plain,(
% 4.58/1.03 ~hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b)))),bot_bot(fun(hoare_28830079triple(a),bool))))),
% 4.58/1.03 inference(flattening,[],[f127])).
% 4.58/1.03 tff(f127,negated_conjecture,(
% 4.58/1.03 ~hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b)))),bot_bot(fun(hoare_28830079triple(a),bool))))),
% 4.58/1.03 inference(negated_conjecture,[],[f126])).
% 4.58/1.03 tff(f126,conjecture,(
% 4.58/1.03 hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combk(bool,state,fFalse)),c,aa(fun(state,bool),fun(a,fun(state,bool)),aa(fun(a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(a,fun(state,bool))),combc(a,fun(state,bool),fun(state,bool)),aa(fun(a,fun(state,fun(bool,bool))),fun(a,fun(fun(state,bool),fun(state,bool))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),a,combs(state,bool,bool)),aa(fun(a,fun(state,bool)),fun(a,fun(state,fun(bool,bool))),combb(fun(state,bool),fun(state,fun(bool,bool)),a,combb(bool,fun(bool,bool),state,fconj)),p))),aa(fun(state,bool),fun(state,bool),combb(bool,bool,state,fNot),b)))),bot_bot(fun(hoare_28830079triple(a),bool))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 4.58/1.03 tff(f2448,plain,(
% 4.58/1.03 spl53_151 | ~spl53_20 | ~spl53_130),
% 4.58/1.03 inference(avatar_split_clause,[],[f2205,f2170,f840,f2446])).
% 4.58/1.03 tff(f2446,plain,(
% 4.58/1.03 spl53_151 <=> ! [X0 : $tType,X1 : bool] : (~pp(X1) | ~sP0(X0,combk(bool,fun(X0,bool),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_151])])).
% 4.58/1.03 tff(f2205,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : bool] : (~pp(X1) | ~sP0(X0,combk(bool,fun(X0,bool),X1))) ) | (~spl53_20 | ~spl53_130)),
% 4.58/1.03 inference(superposition,[],[f2171,f841])).
% 4.58/1.03 tff(f2412,plain,(
% 4.58/1.03 spl53_150 | ~spl53_34 | ~spl53_148),
% 4.58/1.03 inference(avatar_split_clause,[],[f2404,f2401,f912,f2410])).
% 4.58/1.03 tff(f2401,plain,(
% 4.58/1.03 spl53_148 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(X0,fun(X0,bool),fequal(X0),sK19(X0,X1)))) | pp(aa(fun(X0,bool),bool,X1,X2)) | sP0(X0,X1) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_148])])).
% 4.58/1.03 tff(f2404,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (combk(bool,X0,fFalse) = X2 | ~pp(aa(fun(X0,bool),bool,X1,aa(X0,fun(X0,bool),fequal(X0),sK19(X0,X1)))) | pp(aa(fun(X0,bool),bool,X1,X2)) | sP0(X0,X1) | ~finite_finite1(X0,X2)) ) | (~spl53_34 | ~spl53_148)),
% 4.58/1.03 inference(forward_demodulation,[],[f2402,f913])).
% 4.58/1.03 tff(f2402,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(X0,fun(X0,bool),fequal(X0),sK19(X0,X1)))) | pp(aa(fun(X0,bool),bool,X1,X2)) | sP0(X0,X1) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2)) ) | ~spl53_148),
% 4.58/1.03 inference(avatar_component_clause,[],[f2401])).
% 4.58/1.03 tff(f2408,plain,(
% 4.58/1.03 spl53_149 | ~spl53_34 | ~spl53_147),
% 4.58/1.03 inference(avatar_split_clause,[],[f2399,f2396,f912,f2406])).
% 4.58/1.03 tff(f2396,plain,(
% 4.58/1.03 spl53_147 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1 | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_147])])).
% 4.58/1.03 tff(f2399,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1 | ~finite_finite1(X0,X1)) ) | (~spl53_34 | ~spl53_147)),
% 4.58/1.03 inference(forward_demodulation,[],[f2397,f913])).
% 4.58/1.03 tff(f2397,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1 | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) ) | ~spl53_147),
% 4.58/1.03 inference(avatar_component_clause,[],[f2396])).
% 4.58/1.03 tff(f2403,plain,(
% 4.58/1.03 spl53_148),
% 4.58/1.03 inference(avatar_split_clause,[],[f700,f2401])).
% 4.58/1.03 tff(f700,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(X0,fun(X0,bool),fequal(X0),sK19(X0,X1)))) | pp(aa(fun(X0,bool),bool,X1,X2)) | sP0(X0,X1) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2)) )),
% 4.58/1.03 inference(forward_demodulation,[],[f523,f685])).
% 4.58/1.03 tff(f523,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | sP0(X0,X1) | ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK19(X0,X1)),bot_bot(fun(X0,bool))))) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f368])).
% 4.58/1.03 tff(f368,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | sP0(X0,X1) | ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK19(X0,X1)),bot_bot(fun(X0,bool))))) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f324,f367])).
% 4.58/1.03 tff(f367,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (? [X3 : X0] : ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool))))) => ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK19(X0,X1)),bot_bot(fun(X0,bool))))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f324,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | sP0(X0,X1) | ? [X3 : X0] : ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool))))) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(definition_folding,[],[f268,f323])).
% 4.58/1.03 tff(f323,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (? [X4 : X0,X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5))) & pp(aa(fun(X0,bool),bool,X1,X5)) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & bot_bot(fun(X0,bool)) != X5 & finite_finite1(X0,X5)) | ~sP0(X0,X1))),
% 4.58/1.03 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 4.58/1.03 tff(f268,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | ? [X4 : X0,X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5))) & pp(aa(fun(X0,bool),bool,X1,X5)) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & bot_bot(fun(X0,bool)) != X5 & finite_finite1(X0,X5)) | ? [X3 : X0] : ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool))))) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(flattening,[],[f267])).
% 4.58/1.03 tff(f267,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : ((((pp(aa(fun(X0,bool),bool,X1,X2)) | ? [X4 : X0,X5 : fun(X0,bool)] : ((((~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5))) & pp(aa(fun(X0,bool),bool,X1,X5))) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))) & bot_bot(fun(X0,bool)) != X5) & finite_finite1(X0,X5))) | ? [X3 : X0] : ~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))))) | bot_bot(fun(X0,bool)) = X2) | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(ennf_transformation,[],[f187])).
% 4.58/1.03 tff(f187,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (finite_finite1(X0,X2) => (bot_bot(fun(X0,bool)) != X2 => (! [X3 : X0] : pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool))))) => (! [X4 : X0,X5 : fun(X0,bool)] : (finite_finite1(X0,X5) => (bot_bot(fun(X0,bool)) != X5 => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) => (pp(aa(fun(X0,bool),bool,X1,X5)) => pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5))))))) => pp(aa(fun(X0,bool),bool,X1,X2))))))),
% 4.58/1.03 inference(rectify,[],[f100])).
% 4.58/1.03 tff(f100,axiom,(
% 4.58/1.03 ! [X1 : $tType,X16 : fun(fun(X1,bool),bool),X54 : fun(X1,bool)] : (finite_finite1(X1,X54) => (bot_bot(fun(X1,bool)) != X54 => (! [X48 : X1] : pp(aa(fun(X1,bool),bool,X16,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X48),bot_bot(fun(X1,bool))))) => (! [X48 : X1,X62 : fun(X1,bool)] : (finite_finite1(X1,X62) => (bot_bot(fun(X1,bool)) != X62 => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X48),X62)) => (pp(aa(fun(X1,bool),bool,X16,X62)) => pp(aa(fun(X1,bool),bool,X16,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X48),X62))))))) => pp(aa(fun(X1,bool),bool,X16,X54))))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_finite__ne__induct)).
% 4.58/1.03 tff(f2398,plain,(
% 4.58/1.03 spl53_147),
% 4.58/1.03 inference(avatar_split_clause,[],[f482,f2396])).
% 4.58/1.03 tff(f482,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1 | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f339])).
% 4.58/1.03 tff(f339,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((finite_finite1(X0,X1) | (! [X2 : fun(X0,bool),X3 : X0] : (~finite_finite1(X0,X2) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) != X1) & bot_bot(fun(X0,bool)) != X1)) & ((finite_finite1(X0,sK6(X0,X1)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f337,f338])).
% 4.58/1.03 tff(f338,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X4 : fun(X0,bool),X5 : X0] : (finite_finite1(X0,X4) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X4) = X1) => (finite_finite1(X0,sK6(X0,X1)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK7(X0,X1)),sK6(X0,X1)) = X1))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f337,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((finite_finite1(X0,X1) | (! [X2 : fun(X0,bool),X3 : X0] : (~finite_finite1(X0,X2) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) != X1) & bot_bot(fun(X0,bool)) != X1)) & (? [X4 : fun(X0,bool),X5 : X0] : (finite_finite1(X0,X4) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X4) = X1) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)))),
% 4.58/1.03 inference(rectify,[],[f336])).
% 4.58/1.03 tff(f336,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((finite_finite1(X0,X1) | (! [X2 : fun(X0,bool),X3 : X0] : (~finite_finite1(X0,X2) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) != X1) & bot_bot(fun(X0,bool)) != X1)) & (? [X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,X2) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = X1) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)))),
% 4.58/1.03 inference(flattening,[],[f335])).
% 4.58/1.03 tff(f335,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((finite_finite1(X0,X1) | (! [X2 : fun(X0,bool),X3 : X0] : (~finite_finite1(X0,X2) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) != X1) & bot_bot(fun(X0,bool)) != X1)) & ((? [X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,X2) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = X1) | bot_bot(fun(X0,bool)) = X1) | ~finite_finite1(X0,X1)))),
% 4.58/1.03 inference(nnf_transformation,[],[f163])).
% 4.58/1.03 tff(f163,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) <=> (? [X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,X2) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) = X1) | bot_bot(fun(X0,bool)) = X1))),
% 4.58/1.03 inference(rectify,[],[f94])).
% 4.58/1.03 tff(f94,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : fun(X1,bool)] : (finite_finite1(X1,X18) <=> (? [X60 : fun(X1,bool),X61 : X1] : (finite_finite1(X1,X60) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X61),X60) = X18) | bot_bot(fun(X1,bool)) = X18))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_finite_Osimps)).
% 4.58/1.03 tff(f2357,plain,(
% 4.58/1.03 spl53_146),
% 4.58/1.03 inference(avatar_split_clause,[],[f620,f2355])).
% 4.58/1.03 tff(f2355,plain,(
% 4.58/1.03 spl53_146 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_146])])).
% 4.58/1.03 tff(f620,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : (aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f237])).
% 4.58/1.03 tff(f237,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)),
% 4.58/1.03 inference(rectify,[],[f110])).
% 4.58/1.03 tff(f110,axiom,(
% 4.58/1.03 ! [X0 : $tType,X2 : $tType,X1 : $tType,X69 : X0,X70 : X1,X68 : fun(X0,fun(X1,X2))] : aa(X0,X2,aa(X1,fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2)),combc(X0,X1,X2),X68),X70),X69) = aa(X1,X2,aa(X0,fun(X1,X2),X68,X69),X70)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U)).
% 4.58/1.03 tff(f2345,plain,(
% 4.58/1.03 spl53_145),
% 4.58/1.03 inference(avatar_split_clause,[],[f595,f2343])).
% 4.58/1.03 tff(f2343,plain,(
% 4.58/1.03 spl53_145 <=> ! [X1 : $tType,X4 : fun(X1,bool),X0 : X1,X3 : X1,X2 : fun(X1,bool)] : (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),sK35(X1,X0,X2,X3,X4)) = X2 | X0 = X3 | ~sP1(X1,X0,X2,X3,X4))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_145])])).
% 4.58/1.03 tff(f595,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X0),sK35(X1,X0,X2,X3,X4)) = X2 | X0 = X3 | ~sP1(X1,X0,X2,X3,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f412])).
% 4.58/1.03 tff(f2341,plain,(
% 4.58/1.03 spl53_144),
% 4.58/1.03 inference(avatar_split_clause,[],[f593,f2339])).
% 4.58/1.03 tff(f2339,plain,(
% 4.58/1.03 spl53_144 <=> ! [X1 : $tType,X4 : fun(X1,bool),X0 : X1,X3 : X1,X2 : fun(X1,bool)] : (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),sK35(X1,X0,X2,X3,X4)) = X4 | X0 = X3 | ~sP1(X1,X0,X2,X3,X4))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_144])])).
% 4.58/1.03 tff(f593,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),sK35(X1,X0,X2,X3,X4)) = X4 | X0 = X3 | ~sP1(X1,X0,X2,X3,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f412])).
% 4.58/1.03 tff(f2321,plain,(
% 4.58/1.03 spl53_143),
% 4.58/1.03 inference(avatar_split_clause,[],[f538,f2319])).
% 4.58/1.03 tff(f538,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK26(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f380])).
% 4.58/1.03 tff(f2317,plain,(
% 4.58/1.03 spl53_142),
% 4.58/1.03 inference(avatar_split_clause,[],[f536,f2315])).
% 4.58/1.03 tff(f536,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK25(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f378])).
% 4.58/1.03 tff(f2277,plain,(
% 4.58/1.03 spl53_141 | ~spl53_20 | ~spl53_38),
% 4.58/1.03 inference(avatar_split_clause,[],[f956,f933,f840,f2275])).
% 4.58/1.03 tff(f2275,plain,(
% 4.58/1.03 spl53_141 <=> ! [X0 : $tType,X1 : bool] : (pp(X1) | ~sP0(X0,combk(bool,fun(X0,bool),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_141])])).
% 4.58/1.03 tff(f956,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : bool] : (pp(X1) | ~sP0(X0,combk(bool,fun(X0,bool),X1))) ) | (~spl53_20 | ~spl53_38)),
% 4.58/1.03 inference(superposition,[],[f934,f841])).
% 4.58/1.03 tff(f2273,plain,(
% 4.58/1.03 spl53_140 | ~spl53_34 | ~spl53_136),
% 4.58/1.03 inference(avatar_split_clause,[],[f2257,f2254,f912,f2271])).
% 4.58/1.03 tff(f2254,plain,(
% 4.58/1.03 spl53_136 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),sK9(X0,X1)) = X1 | bot_bot(fun(X0,bool)) = X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_136])])).
% 4.58/1.03 tff(f2257,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),sK9(X0,X1)) = X1) ) | (~spl53_34 | ~spl53_136)),
% 4.58/1.03 inference(forward_demodulation,[],[f2255,f913])).
% 4.58/1.03 tff(f2255,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),sK9(X0,X1)) = X1 | bot_bot(fun(X0,bool)) = X1) ) | ~spl53_136),
% 4.58/1.03 inference(avatar_component_clause,[],[f2254])).
% 4.58/1.03 tff(f2269,plain,(
% 4.58/1.03 spl53_139),
% 4.58/1.03 inference(avatar_split_clause,[],[f686,f2267])).
% 4.58/1.03 tff(f686,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = collect(X0,aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f464,f685])).
% 4.58/1.03 tff(f464,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f146])).
% 4.58/1.03 tff(f146,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0] : aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = collect(X0,aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),
% 4.58/1.03 inference(rectify,[],[f7])).
% 4.58/1.03 tff(f7,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1] : aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),bot_bot(fun(X1,bool))) = collect(X1,aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X18))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_singleton__conv)).
% 4.58/1.03 tff(f2265,plain,(
% 4.58/1.03 spl53_138),
% 4.58/1.03 inference(avatar_split_clause,[],[f632,f2263])).
% 4.58/1.03 tff(f632,plain,(
% 4.58/1.03 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (~pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),sK47(X2,X3,X0,X1,X4,X5)),sK48(X2,X3,X0,X1,X4,X5))) | ~sP3(X2,X3,X0,X1,X4,X5)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f433])).
% 4.58/1.03 tff(f2261,plain,(
% 4.58/1.03 spl53_137),
% 4.58/1.03 inference(avatar_split_clause,[],[f505,f2259])).
% 4.58/1.03 tff(f505,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f176])).
% 4.58/1.03 tff(f176,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))),
% 4.58/1.03 inference(rectify,[],[f32])).
% 4.58/1.03 tff(f32,axiom,(
% 4.58/1.03 ! [X1 : $tType,X28 : fun(X1,bool),X18 : X1] : pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X28)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_insertI1)).
% 4.58/1.03 tff(f2256,plain,(
% 4.58/1.03 spl53_136),
% 4.58/1.03 inference(avatar_split_clause,[],[f486,f2254])).
% 4.58/1.03 tff(f486,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),sK9(X0,X1)) = X1 | bot_bot(fun(X0,bool)) = X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f343])).
% 4.58/1.03 tff(f343,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) != X1 | ! [X2 : X0,X3 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) != X1)) & ((~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),sK9(X0,X1))) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),sK9(X0,X1)) = X1) | bot_bot(fun(X0,bool)) = X1))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f341,f342])).
% 4.58/1.03 tff(f342,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X4 : X0,X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X1) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),sK9(X0,X1))) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK8(X0,X1)),sK9(X0,X1)) = X1))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f341,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) != X1 | ! [X2 : X0,X3 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) != X1)) & (? [X4 : X0,X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) = X1) | bot_bot(fun(X0,bool)) = X1))),
% 4.58/1.03 inference(rectify,[],[f340])).
% 4.58/1.03 tff(f340,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) != X1 | ! [X2 : X0,X3 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) != X1)) & (? [X2 : X0,X3 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = X1) | bot_bot(fun(X0,bool)) = X1))),
% 4.58/1.03 inference(nnf_transformation,[],[f164])).
% 4.58/1.03 tff(f164,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != X1 <=> ? [X2 : X0,X3 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = X1))),
% 4.58/1.03 inference(rectify,[],[f65])).
% 4.58/1.03 tff(f65,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool)] : (bot_bot(fun(X1,bool)) != X25 <=> ? [X29 : X1,X52 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X29),X52)) & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X29),X52) = X25))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_nonempty__iff)).
% 4.58/1.03 tff(f2240,plain,(
% 4.58/1.03 spl53_135 | ~spl53_34 | ~spl53_133),
% 4.58/1.03 inference(avatar_split_clause,[],[f2185,f2182,f912,f2238])).
% 4.58/1.03 tff(f2182,plain,(
% 4.58/1.03 spl53_133 <=> ! [X0 : $tType,X1 : X0] : aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_133])])).
% 4.58/1.03 tff(f2185,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),combk(bool,X0,fFalse))) ) | (~spl53_34 | ~spl53_133)),
% 4.58/1.03 inference(forward_demodulation,[],[f2183,f913])).
% 4.58/1.03 tff(f2183,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) ) | ~spl53_133),
% 4.58/1.03 inference(avatar_component_clause,[],[f2182])).
% 4.58/1.03 tff(f2189,plain,(
% 4.58/1.03 spl53_134 | ~spl53_21 | ~spl53_34),
% 4.58/1.03 inference(avatar_split_clause,[],[f916,f912,f844,f2187])).
% 4.58/1.03 tff(f2187,plain,(
% 4.58/1.03 spl53_134 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : fun(X0,fun(X1,X1))] : finite_fold_graph(X0,X1,X2,X3,combk(bool,X0,fFalse),X3)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_134])])).
% 4.58/1.03 tff(f844,plain,(
% 4.58/1.03 spl53_21 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,fun(X1,X1)),X2 : X1] : finite_fold_graph(X0,X1,X3,X2,bot_bot(fun(X0,bool)),X2)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_21])])).
% 4.58/1.03 tff(f916,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X1)),X3 : X1] : (finite_fold_graph(X0,X1,X2,X3,combk(bool,X0,fFalse),X3)) ) | (~spl53_21 | ~spl53_34)),
% 4.58/1.03 inference(superposition,[],[f845,f913])).
% 4.58/1.03 tff(f845,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : (finite_fold_graph(X0,X1,X3,X2,bot_bot(fun(X0,bool)),X2)) ) | ~spl53_21),
% 4.58/1.03 inference(avatar_component_clause,[],[f844])).
% 4.58/1.03 tff(f2184,plain,(
% 4.58/1.03 spl53_133),
% 4.58/1.03 inference(avatar_split_clause,[],[f685,f2182])).
% 4.58/1.03 tff(f2180,plain,(
% 4.58/1.03 spl53_132),
% 4.58/1.03 inference(avatar_split_clause,[],[f582,f2178])).
% 4.58/1.03 tff(f582,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,X2,X1)) | X1 = X3 | ~pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f402])).
% 4.58/1.03 tff(f402,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0] : ((pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1)) | (~pp(aa(X0,bool,X2,X1)) & X1 != X3)) & (pp(aa(X0,bool,X2,X1)) | X1 = X3 | ~pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1))))),
% 4.58/1.03 inference(flattening,[],[f401])).
% 4.58/1.03 tff(f401,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0] : ((pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1)) | (~pp(aa(X0,bool,X2,X1)) & X1 != X3)) & ((pp(aa(X0,bool,X2,X1)) | X1 = X3) | ~pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1))))),
% 4.58/1.03 inference(nnf_transformation,[],[f223])).
% 4.58/1.03 tff(f223,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0] : (pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1)) <=> (pp(aa(X0,bool,X2,X1)) | X1 = X3))),
% 4.58/1.03 inference(rectify,[],[f28])).
% 4.58/1.03 tff(f28,axiom,(
% 4.58/1.03 ! [X1 : $tType,X26 : X1,X25 : fun(X1,bool),X31 : X1] : (pp(aa(X1,bool,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X31),X25),X26)) <=> (pp(aa(X1,bool,X25,X26)) | X26 = X31))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_insert__code)).
% 4.58/1.03 tff(f2176,plain,(
% 4.58/1.03 spl53_131),
% 4.58/1.03 inference(avatar_split_clause,[],[f580,f2174])).
% 4.58/1.03 tff(f580,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3))) | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f400])).
% 4.58/1.03 tff(f2172,plain,(
% 4.58/1.03 spl53_130),
% 4.58/1.03 inference(avatar_split_clause,[],[f522,f2170])).
% 4.58/1.03 tff(f522,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK17(X0,X1)),sK18(X0,X1)))) | ~sP0(X0,X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f366])).
% 4.58/1.03 tff(f366,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : ((~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK17(X0,X1)),sK18(X0,X1)))) & pp(aa(fun(X0,bool),bool,X1,sK18(X0,X1))) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK17(X0,X1)),sK18(X0,X1))) & bot_bot(fun(X0,bool)) != sK18(X0,X1) & finite_finite1(X0,sK18(X0,X1))) | ~sP0(X0,X1))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f364,f365])).
% 4.58/1.03 tff(f365,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (? [X2 : X0,X3 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) & pp(aa(fun(X0,bool),bool,X1,X3)) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) & bot_bot(fun(X0,bool)) != X3 & finite_finite1(X0,X3)) => (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK17(X0,X1)),sK18(X0,X1)))) & pp(aa(fun(X0,bool),bool,X1,sK18(X0,X1))) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK17(X0,X1)),sK18(X0,X1))) & bot_bot(fun(X0,bool)) != sK18(X0,X1) & finite_finite1(X0,sK18(X0,X1))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f364,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (? [X2 : X0,X3 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) & pp(aa(fun(X0,bool),bool,X1,X3)) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) & bot_bot(fun(X0,bool)) != X3 & finite_finite1(X0,X3)) | ~sP0(X0,X1))),
% 4.58/1.03 inference(rectify,[],[f363])).
% 4.58/1.03 tff(f363,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (? [X4 : X0,X5 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5))) & pp(aa(fun(X0,bool),bool,X1,X5)) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X5)) & bot_bot(fun(X0,bool)) != X5 & finite_finite1(X0,X5)) | ~sP0(X0,X1))),
% 4.58/1.03 inference(nnf_transformation,[],[f323])).
% 4.58/1.03 tff(f2042,plain,(
% 4.58/1.03 spl53_129 | ~spl53_34 | ~spl53_125),
% 4.58/1.03 inference(avatar_split_clause,[],[f2026,f2023,f912,f2040])).
% 4.58/1.03 tff(f2023,plain,(
% 4.58/1.03 spl53_125 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | pp(aa(fun(X0,bool),bool,X1,sK22(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_125])])).
% 4.58/1.03 tff(f2026,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | pp(aa(fun(X0,bool),bool,X1,sK22(X0,X1))) | ~finite_finite1(X0,X2)) ) | (~spl53_34 | ~spl53_125)),
% 4.58/1.03 inference(forward_demodulation,[],[f2024,f913])).
% 4.58/1.03 tff(f2024,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | pp(aa(fun(X0,bool),bool,X1,sK22(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | ~spl53_125),
% 4.58/1.03 inference(avatar_component_clause,[],[f2023])).
% 4.58/1.03 tff(f2038,plain,(
% 4.58/1.03 spl53_128),
% 4.58/1.03 inference(avatar_split_clause,[],[f631,f2036])).
% 4.58/1.03 tff(f2036,plain,(
% 4.58/1.03 spl53_128 <=> ! [X3 : $tType,X2 : $tType,X4 : X2,X0 : X2,X5 : fun(X3,bool),X1 : fun(X3,fun(X2,X2))] : (aa(X2,X2,aa(X3,fun(X2,X2),X1,sK47(X2,X3,X0,X1,X4,X5)),sK49(X2,X3,X0,X1,X4,X5)) = X4 | ~sP3(X2,X3,X0,X1,X4,X5))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_128])])).
% 4.58/1.03 tff(f631,plain,(
% 4.58/1.03 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (aa(X2,X2,aa(X3,fun(X2,X2),X1,sK47(X2,X3,X0,X1,X4,X5)),sK49(X2,X3,X0,X1,X4,X5)) = X4 | ~sP3(X2,X3,X0,X1,X4,X5)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f433])).
% 4.58/1.03 tff(f2034,plain,(
% 4.58/1.03 spl53_127),
% 4.58/1.03 inference(avatar_split_clause,[],[f547,f2032])).
% 4.58/1.03 tff(f547,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,X1,the(X0,X2))) | ~pp(aa(X0,bool,X1,sK28(X0,X1,X2))) | pp(aa(X0,bool,X2,sK29(X0,X2,X4))) | ~pp(aa(X0,bool,X2,X4))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f386])).
% 4.58/1.03 tff(f386,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X2))) | (~pp(aa(X0,bool,X1,sK28(X0,X1,X2))) & pp(aa(X0,bool,X2,sK28(X0,X1,X2)))) | ! [X4 : X0] : ((sK29(X0,X2,X4) != X4 & pp(aa(X0,bool,X2,sK29(X0,X2,X4)))) | ~pp(aa(X0,bool,X2,X4))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f383,f385,f384])).
% 4.58/1.03 tff(f384,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (? [X3 : X0] : (~pp(aa(X0,bool,X1,X3)) & pp(aa(X0,bool,X2,X3))) => (~pp(aa(X0,bool,X1,sK28(X0,X1,X2))) & pp(aa(X0,bool,X2,sK28(X0,X1,X2)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f385,plain,(
% 4.58/1.03 ! [X0 : $tType,X2 : fun(X0,bool),X4 : X0] : (? [X5 : X0] : (X4 != X5 & pp(aa(X0,bool,X2,X5))) => (sK29(X0,X2,X4) != X4 & pp(aa(X0,bool,X2,sK29(X0,X2,X4)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f383,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X2))) | ? [X3 : X0] : (~pp(aa(X0,bool,X1,X3)) & pp(aa(X0,bool,X2,X3))) | ! [X4 : X0] : (? [X5 : X0] : (X4 != X5 & pp(aa(X0,bool,X2,X5))) | ~pp(aa(X0,bool,X2,X4))))),
% 4.58/1.03 inference(rectify,[],[f287])).
% 4.58/1.03 tff(f287,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X2))) | ? [X5 : X0] : (~pp(aa(X0,bool,X1,X5)) & pp(aa(X0,bool,X2,X5))) | ! [X3 : X0] : (? [X4 : X0] : (X3 != X4 & pp(aa(X0,bool,X2,X4))) | ~pp(aa(X0,bool,X2,X3))))),
% 4.58/1.03 inference(flattening,[],[f286])).
% 4.58/1.03 tff(f286,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : ((pp(aa(X0,bool,X1,the(X0,X2))) | ? [X5 : X0] : (~pp(aa(X0,bool,X1,X5)) & pp(aa(X0,bool,X2,X5)))) | ! [X3 : X0] : (? [X4 : X0] : (X3 != X4 & pp(aa(X0,bool,X2,X4))) | ~pp(aa(X0,bool,X2,X3))))),
% 4.58/1.03 inference(ennf_transformation,[],[f200])).
% 4.58/1.03 tff(f200,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (? [X3 : X0] : (! [X4 : X0] : (pp(aa(X0,bool,X2,X4)) => X3 = X4) & pp(aa(X0,bool,X2,X3))) => (! [X5 : X0] : (pp(aa(X0,bool,X2,X5)) => pp(aa(X0,bool,X1,X5))) => pp(aa(X0,bool,X1,the(X0,X2)))))),
% 4.58/1.03 inference(rectify,[],[f69])).
% 4.58/1.03 tff(f69,axiom,(
% 4.58/1.03 ! [X1 : $tType,X14 : fun(X1,bool),X16 : fun(X1,bool)] : (? [X32 : X1] : (! [X49 : X1] : (pp(aa(X1,bool,X16,X49)) => X32 = X49) & pp(aa(X1,bool,X16,X32))) => (! [X48 : X1] : (pp(aa(X1,bool,X16,X48)) => pp(aa(X1,bool,X14,X48))) => pp(aa(X1,bool,X14,the(X1,X16)))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_the1I2)).
% 4.58/1.03 tff(f2030,plain,(
% 4.58/1.03 spl53_126),
% 4.58/1.03 inference(avatar_split_clause,[],[f545,f2028])).
% 4.58/1.03 tff(f545,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,X1,the(X0,X2))) | pp(aa(X0,bool,X2,sK28(X0,X1,X2))) | pp(aa(X0,bool,X2,sK29(X0,X2,X4))) | ~pp(aa(X0,bool,X2,X4))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f386])).
% 4.58/1.03 tff(f2025,plain,(
% 4.58/1.03 spl53_125),
% 4.58/1.03 inference(avatar_split_clause,[],[f527,f2023])).
% 4.58/1.03 tff(f527,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | pp(aa(fun(X0,bool),bool,X1,sK22(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f372])).
% 4.58/1.03 tff(f1997,plain,(
% 4.58/1.03 spl53_124),
% 4.58/1.03 inference(avatar_split_clause,[],[f596,f1995])).
% 4.58/1.03 tff(f596,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),sK35(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP1(X1,X0,X2,X3,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f412])).
% 4.58/1.03 tff(f1993,plain,(
% 4.58/1.03 spl53_123),
% 4.58/1.03 inference(avatar_split_clause,[],[f594,f1991])).
% 4.58/1.03 tff(f594,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),sK35(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP1(X1,X0,X2,X3,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f412])).
% 4.58/1.03 tff(f1989,plain,(
% 4.58/1.03 spl53_122),
% 4.58/1.03 inference(avatar_split_clause,[],[f584,f1987])).
% 4.58/1.03 tff(f584,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1)) | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f402])).
% 4.58/1.03 tff(f1949,plain,(
% 4.58/1.03 spl53_121 | ~spl53_34 | ~spl53_118),
% 4.58/1.03 inference(avatar_split_clause,[],[f1937,f1934,f912,f1947])).
% 4.58/1.03 tff(f1934,plain,(
% 4.58/1.03 spl53_118 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),sK9(X0,X1))) | bot_bot(fun(X0,bool)) = X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_118])])).
% 4.58/1.03 tff(f1937,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),sK9(X0,X1)))) ) | (~spl53_34 | ~spl53_118)),
% 4.58/1.03 inference(forward_demodulation,[],[f1935,f913])).
% 4.58/1.03 tff(f1935,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),sK9(X0,X1))) | bot_bot(fun(X0,bool)) = X1) ) | ~spl53_118),
% 4.58/1.03 inference(avatar_component_clause,[],[f1934])).
% 4.58/1.03 tff(f1945,plain,(
% 4.58/1.03 spl53_120),
% 4.58/1.03 inference(avatar_split_clause,[],[f548,f1943])).
% 4.58/1.03 tff(f548,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,X1,the(X0,X2))) | ~pp(aa(X0,bool,X1,sK28(X0,X1,X2))) | sK29(X0,X2,X4) != X4 | ~pp(aa(X0,bool,X2,X4))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f386])).
% 4.58/1.03 tff(f1941,plain,(
% 4.58/1.03 spl53_119),
% 4.58/1.03 inference(avatar_split_clause,[],[f546,f1939])).
% 4.58/1.03 tff(f546,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,X1,the(X0,X2))) | pp(aa(X0,bool,X2,sK28(X0,X1,X2))) | sK29(X0,X2,X4) != X4 | ~pp(aa(X0,bool,X2,X4))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f386])).
% 4.58/1.03 tff(f1936,plain,(
% 4.58/1.03 spl53_118),
% 4.58/1.03 inference(avatar_split_clause,[],[f487,f1934])).
% 4.58/1.03 tff(f487,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),sK9(X0,X1))) | bot_bot(fun(X0,bool)) = X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f343])).
% 4.58/1.03 tff(f1920,plain,(
% 4.58/1.03 spl53_117),
% 4.58/1.03 inference(avatar_split_clause,[],[f579,f1918])).
% 4.58/1.03 tff(f579,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (finite_fold_graph(X0,X0,X3,sK31(X0,X1,X2,X3),sK32(X0,X1,X2,X3),sK33(X0,X1,X2,X3)) | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f400])).
% 4.58/1.03 tff(f1889,plain,(
% 4.58/1.03 spl53_116 | spl53_1 | ~spl53_96),
% 4.58/1.03 inference(avatar_split_clause,[],[f1773,f1634,f752,f1886])).
% 4.58/1.03 tff(f1773,plain,(
% 4.58/1.03 fTrue = aa(bool,bool,fNot,fFalse) | (spl53_1 | ~spl53_96)),
% 4.58/1.03 inference(resolution,[],[f1635,f754])).
% 4.58/1.03 tff(f754,plain,(
% 4.58/1.03 ~pp(fFalse) | spl53_1),
% 4.58/1.03 inference(avatar_component_clause,[],[f752])).
% 4.58/1.03 tff(f1810,plain,(
% 4.58/1.03 spl53_115 | ~spl53_34 | ~spl53_108),
% 4.58/1.03 inference(avatar_split_clause,[],[f1759,f1756,f912,f1808])).
% 4.58/1.03 tff(f1756,plain,(
% 4.58/1.03 spl53_108 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | finite_finite1(X0,sK22(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_108])])).
% 4.58/1.03 tff(f1759,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | pp(aa(fun(X0,bool),bool,X1,X2)) | finite_finite1(X0,sK22(X0,X1)) | ~finite_finite1(X0,X2)) ) | (~spl53_34 | ~spl53_108)),
% 4.58/1.03 inference(forward_demodulation,[],[f1757,f913])).
% 4.58/1.03 tff(f1757,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | finite_finite1(X0,sK22(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | ~spl53_108),
% 4.58/1.03 inference(avatar_component_clause,[],[f1756])).
% 4.58/1.03 tff(f1806,plain,(
% 4.58/1.03 spl53_114 | ~spl53_34 | ~spl53_107),
% 4.58/1.03 inference(avatar_split_clause,[],[f1754,f1751,f912,f1804])).
% 4.58/1.03 tff(f1751,plain,(
% 4.58/1.03 spl53_107 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : bot_bot(fun(X0,bool)) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_107])])).
% 4.58/1.03 tff(f1754,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) ) | (~spl53_34 | ~spl53_107)),
% 4.58/1.03 inference(forward_demodulation,[],[f1752,f913])).
% 4.58/1.03 tff(f1752,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) ) | ~spl53_107),
% 4.58/1.03 inference(avatar_component_clause,[],[f1751])).
% 4.58/1.03 tff(f1802,plain,(
% 4.58/1.03 spl53_113 | ~spl53_34 | ~spl53_106),
% 4.58/1.03 inference(avatar_split_clause,[],[f1749,f1746,f912,f1800])).
% 4.58/1.03 tff(f1746,plain,(
% 4.58/1.03 spl53_106 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1)),X1)) | bot_bot(fun(X0,bool)) = X1)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_106])])).
% 4.58/1.03 tff(f1749,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1)),X1))) ) | (~spl53_34 | ~spl53_106)),
% 4.58/1.03 inference(forward_demodulation,[],[f1747,f913])).
% 4.58/1.03 tff(f1747,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1)),X1)) | bot_bot(fun(X0,bool)) = X1) ) | ~spl53_106),
% 4.58/1.03 inference(avatar_component_clause,[],[f1746])).
% 4.58/1.03 tff(f1798,plain,(
% 4.58/1.03 spl53_112 | ~spl53_34 | ~spl53_105),
% 4.58/1.03 inference(avatar_split_clause,[],[f1744,f1741,f912,f1796])).
% 4.58/1.03 tff(f1741,plain,(
% 4.58/1.03 spl53_105 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK12(X0,X1)),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_105])])).
% 4.58/1.03 tff(f1744,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK12(X0,X1)),X1))) ) | (~spl53_34 | ~spl53_105)),
% 4.58/1.03 inference(forward_demodulation,[],[f1742,f913])).
% 4.58/1.03 tff(f1742,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK12(X0,X1)),X1))) ) | ~spl53_105),
% 4.58/1.03 inference(avatar_component_clause,[],[f1741])).
% 4.58/1.03 tff(f1794,plain,(
% 4.58/1.03 spl53_111 | ~spl53_34 | ~spl53_104),
% 4.58/1.03 inference(avatar_split_clause,[],[f1739,f1736,f912,f1792])).
% 4.58/1.03 tff(f1736,plain,(
% 4.58/1.03 spl53_104 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),X1)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_104])])).
% 4.58/1.03 tff(f1739,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),X1))) ) | (~spl53_34 | ~spl53_104)),
% 4.58/1.03 inference(forward_demodulation,[],[f1737,f913])).
% 4.58/1.03 tff(f1737,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),X1))) ) | ~spl53_104),
% 4.58/1.03 inference(avatar_component_clause,[],[f1736])).
% 4.58/1.03 tff(f1767,plain,(
% 4.58/1.03 spl53_110),
% 4.58/1.03 inference(avatar_split_clause,[],[f701,f1765])).
% 4.58/1.03 tff(f701,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(X0,fun(X0,bool),fequal(X0),X1))) | X1 = X2) )),
% 4.58/1.03 inference(forward_demodulation,[],[f539,f685])).
% 4.58/1.03 tff(f539,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f281])).
% 4.58/1.03 tff(f281,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = X2 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))),
% 4.58/1.03 inference(ennf_transformation,[],[f196])).
% 4.58/1.03 tff(f196,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))) => X1 = X2)),
% 4.58/1.03 inference(rectify,[],[f35])).
% 4.58/1.03 tff(f35,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1,X27 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X27),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),bot_bot(fun(X1,bool))))) => X18 = X27)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_singletonE)).
% 4.58/1.03 tff(f1763,plain,(
% 4.58/1.03 spl53_109),
% 4.58/1.03 inference(avatar_split_clause,[],[f619,f1761])).
% 4.58/1.03 tff(f619,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : (aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),combb(X1,X0,X2,X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f236])).
% 4.58/1.03 tff(f236,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),combb(X1,X0,X2,X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 4.58/1.03 inference(rectify,[],[f109])).
% 4.58/1.03 tff(f109,axiom,(
% 4.58/1.03 ! [X2 : $tType,X1 : $tType,X0 : $tType,X69 : X0,X70 : fun(X0,X1),X68 : fun(X1,X2)] : aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),combb(X1,X2,X0,X68),X70),X69) = aa(X1,X2,X68,aa(X0,X1,X70,X69))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U)).
% 4.58/1.03 tff(f1758,plain,(
% 4.58/1.03 spl53_108),
% 4.58/1.03 inference(avatar_split_clause,[],[f525,f1756])).
% 4.58/1.03 tff(f525,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | finite_finite1(X0,sK22(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f372])).
% 4.58/1.03 tff(f1753,plain,(
% 4.58/1.03 spl53_107),
% 4.58/1.03 inference(avatar_split_clause,[],[f502,f1751])).
% 4.58/1.03 tff(f502,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f173])).
% 4.58/1.03 tff(f173,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : bot_bot(fun(X0,bool)) != aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),
% 4.58/1.03 inference(rectify,[],[f38])).
% 4.58/1.03 tff(f38,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X18 : X1] : bot_bot(fun(X1,bool)) != aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X25)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_insert__not__empty)).
% 4.58/1.03 tff(f1748,plain,(
% 4.58/1.03 spl53_106),
% 4.58/1.03 inference(avatar_split_clause,[],[f498,f1746])).
% 4.58/1.03 tff(f498,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1)),X1)) | bot_bot(fun(X0,bool)) = X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f360])).
% 4.58/1.03 tff(f360,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1)),X1)) | bot_bot(fun(X0,bool)) = X1) & (bot_bot(fun(X0,bool)) != X1 | ! [X3 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f358,f359])).
% 4.58/1.03 tff(f359,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X2 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1)),X1)))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f358,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((? [X2 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | bot_bot(fun(X0,bool)) = X1) & (bot_bot(fun(X0,bool)) != X1 | ! [X3 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))))),
% 4.58/1.03 inference(rectify,[],[f357])).
% 4.58/1.03 tff(f357,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((? [X2 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | bot_bot(fun(X0,bool)) = X1) & (bot_bot(fun(X0,bool)) != X1 | ! [X2 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))))),
% 4.58/1.03 inference(nnf_transformation,[],[f169])).
% 4.58/1.03 tff(f169,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X2 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) <=> bot_bot(fun(X0,bool)) != X1)),
% 4.58/1.03 inference(rectify,[],[f22])).
% 4.58/1.03 tff(f22,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool)] : (? [X29 : X1] : pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X29),X25)) <=> bot_bot(fun(X1,bool)) != X25)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_ex__in__conv)).
% 4.58/1.03 tff(f1743,plain,(
% 4.58/1.03 spl53_105),
% 4.58/1.03 inference(avatar_split_clause,[],[f495,f1741])).
% 4.58/1.03 tff(f495,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK12(X0,X1)),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f356])).
% 4.58/1.03 tff(f356,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((! [X2 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | bot_bot(fun(X0,bool)) != X1) & (bot_bot(fun(X0,bool)) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK12(X0,X1)),X1))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f354,f355])).
% 4.58/1.03 tff(f355,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X3 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK12(X0,X1)),X1)))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f354,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((! [X2 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | bot_bot(fun(X0,bool)) != X1) & (bot_bot(fun(X0,bool)) = X1 | ? [X3 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))))),
% 4.58/1.03 inference(rectify,[],[f353])).
% 4.58/1.03 tff(f353,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((! [X2 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | bot_bot(fun(X0,bool)) != X1) & (bot_bot(fun(X0,bool)) = X1 | ? [X2 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))))),
% 4.58/1.03 inference(nnf_transformation,[],[f168])).
% 4.58/1.03 tff(f168,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (! [X2 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) <=> bot_bot(fun(X0,bool)) = X1)),
% 4.58/1.03 inference(rectify,[],[f16])).
% 4.58/1.03 tff(f16,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool)] : (! [X29 : X1] : ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X29),X25)) <=> bot_bot(fun(X1,bool)) = X25)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_all__not__in__conv)).
% 4.58/1.03 tff(f1738,plain,(
% 4.58/1.03 spl53_104),
% 4.58/1.03 inference(avatar_split_clause,[],[f479,f1736])).
% 4.58/1.03 tff(f479,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f332])).
% 4.58/1.03 tff(f332,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),X1)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f261,f331])).
% 4.58/1.03 tff(f331,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X2 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),X1)))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f261,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | ? [X2 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 4.58/1.03 inference(ennf_transformation,[],[f161])).
% 4.58/1.03 tff(f161,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (! [X2 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) => bot_bot(fun(X0,bool)) = X1)),
% 4.58/1.03 inference(rectify,[],[f63])).
% 4.58/1.03 tff(f63,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool)] : (! [X49 : X1] : ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X49),X25)) => bot_bot(fun(X1,bool)) = X25)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_equals0I)).
% 4.58/1.03 tff(f1734,plain,(
% 4.58/1.03 spl53_103),
% 4.58/1.03 inference(avatar_split_clause,[],[f462,f1732])).
% 4.58/1.03 tff(f462,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (the(X0,aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) = X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f144])).
% 4.58/1.03 tff(f144,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0] : the(X0,aa(X0,fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) = X1),
% 4.58/1.03 inference(rectify,[],[f55])).
% 4.58/1.03 tff(f55,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1] : the(X1,aa(X1,fun(X1,bool),aa(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X18)) = X18),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_the__eq__trivial)).
% 4.58/1.03 tff(f1723,plain,(
% 4.58/1.03 spl53_102 | ~spl53_8 | ~spl53_37),
% 4.58/1.03 inference(avatar_split_clause,[],[f1029,f929,f784,f1721])).
% 4.58/1.03 tff(f1721,plain,(
% 4.58/1.03 spl53_102 <=> ! [X1 : $tType,X0 : bool] : (finite_finite1(X1,combk(bool,X1,X0)) | fTrue = X0)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_102])])).
% 4.58/1.03 tff(f1029,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : bool] : (finite_finite1(X1,combk(bool,X1,X0)) | fTrue = X0) ) | (~spl53_8 | ~spl53_37)),
% 4.58/1.03 inference(superposition,[],[f930,f785])).
% 4.58/1.03 tff(f1684,plain,(
% 4.58/1.03 spl53_101),
% 4.58/1.03 inference(avatar_split_clause,[],[f633,f1682])).
% 4.58/1.03 tff(f633,plain,(
% 4.58/1.03 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (finite_fold_graph(X3,X2,X1,X0,sK48(X2,X3,X0,X1,X4,X5),sK49(X2,X3,X0,X1,X4,X5)) | ~sP3(X2,X3,X0,X1,X4,X5)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f433])).
% 4.58/1.03 tff(f1680,plain,(
% 4.58/1.03 spl53_100),
% 4.58/1.03 inference(avatar_split_clause,[],[f543,f1678])).
% 4.58/1.03 tff(f543,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X1)) | pp(aa(X0,bool,X2,sK27(X0,X2,X3))) | ~pp(aa(X0,bool,X2,X3))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f382])).
% 4.58/1.03 tff(f382,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X1)) | ! [X3 : X0] : ((sK27(X0,X2,X3) != X3 & pp(aa(X0,bool,X2,sK27(X0,X2,X3)))) | ~pp(aa(X0,bool,X2,X3))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f285,f381])).
% 4.58/1.03 tff(f381,plain,(
% 4.58/1.03 ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (? [X4 : X0] : (X3 != X4 & pp(aa(X0,bool,X2,X4))) => (sK27(X0,X2,X3) != X3 & pp(aa(X0,bool,X2,sK27(X0,X2,X3)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f285,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X1)) | ! [X3 : X0] : (? [X4 : X0] : (X3 != X4 & pp(aa(X0,bool,X2,X4))) | ~pp(aa(X0,bool,X2,X3))))),
% 4.58/1.03 inference(flattening,[],[f284])).
% 4.58/1.03 tff(f284,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : ((the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X1))) | ! [X3 : X0] : (? [X4 : X0] : (X3 != X4 & pp(aa(X0,bool,X2,X4))) | ~pp(aa(X0,bool,X2,X3))))),
% 4.58/1.03 inference(ennf_transformation,[],[f199])).
% 4.58/1.03 tff(f199,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (? [X3 : X0] : (! [X4 : X0] : (pp(aa(X0,bool,X2,X4)) => X3 = X4) & pp(aa(X0,bool,X2,X3))) => (pp(aa(X0,bool,X2,X1)) => the(X0,X2) = X1))),
% 4.58/1.03 inference(rectify,[],[f60])).
% 4.58/1.03 tff(f60,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1,X16 : fun(X1,bool)] : (? [X32 : X1] : (! [X49 : X1] : (pp(aa(X1,bool,X16,X49)) => X32 = X49) & pp(aa(X1,bool,X16,X32))) => (pp(aa(X1,bool,X16,X18)) => the(X1,X16) = X18))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_the1__equality)).
% 4.58/1.03 tff(f1668,plain,(
% 4.58/1.03 spl53_99),
% 4.58/1.03 inference(avatar_split_clause,[],[f665,f1666])).
% 4.58/1.03 tff(f665,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X3))) )),
% 4.58/1.03 inference(equality_resolution,[],[f583])).
% 4.58/1.03 tff(f583,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2),X1)) | X1 != X3) )),
% 4.58/1.03 inference(cnf_transformation,[],[f402])).
% 4.58/1.03 tff(f1664,plain,(
% 4.58/1.03 spl53_98),
% 4.58/1.03 inference(avatar_split_clause,[],[f649,f1662])).
% 4.58/1.03 tff(f649,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)) | ~finite_finite1(X0,X2)) )),
% 4.58/1.03 inference(equality_resolution,[],[f485])).
% 4.58/1.03 tff(f485,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,X2) | aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) != X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f339])).
% 4.58/1.03 tff(f1660,plain,(
% 4.58/1.03 spl53_97),
% 4.58/1.03 inference(avatar_split_clause,[],[f551,f1658])).
% 4.58/1.03 tff(f551,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f388])).
% 4.58/1.03 tff(f388,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : ((finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) | ~finite_finite1(X0,X1)) & (finite_finite1(X0,X1) | ~finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))))),
% 4.58/1.03 inference(nnf_transformation,[],[f202])).
% 4.58/1.03 tff(f202,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)) <=> finite_finite1(X0,X1))),
% 4.58/1.03 inference(rectify,[],[f83])).
% 4.58/1.03 tff(f83,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X18 : X1] : (finite_finite1(X1,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),X25)) <=> finite_finite1(X1,X25))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_finite__insert)).
% 4.58/1.03 tff(f1636,plain,(
% 4.58/1.03 spl53_96 | ~spl53_13 | ~spl53_15),
% 4.58/1.03 inference(avatar_split_clause,[],[f838,f815,f807,f1634])).
% 4.58/1.03 tff(f838,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (fTrue = aa(bool,bool,fNot,X0) | pp(X0)) ) | (~spl53_13 | ~spl53_15)),
% 4.58/1.03 inference(resolution,[],[f808,f816])).
% 4.58/1.03 tff(f1620,plain,(
% 4.58/1.03 spl53_95),
% 4.58/1.03 inference(avatar_split_clause,[],[f573,f1618])).
% 4.58/1.03 tff(f573,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK30(X0,X1,X2,X3)) != aa(X1,X0,X2,sK30(X0,X1,X2,X3))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f394])).
% 4.58/1.03 tff(f394,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK30(X0,X1,X2,X3)) != aa(X1,X0,X2,sK30(X0,X1,X2,X3)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f301,f393])).
% 4.58/1.03 tff(f393,plain,(
% 4.58/1.03 ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (? [X4 : X1] : aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) => aa(X1,X0,X3,sK30(X0,X1,X2,X3)) != aa(X1,X0,X2,sK30(X0,X1,X2,X3)))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f301,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | ? [X4 : X1] : aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4))),
% 4.58/1.03 inference(ennf_transformation,[],[f220])).
% 4.58/1.03 tff(f220,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (! [X4 : X1] : aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) => X2 = X3)),
% 4.58/1.03 inference(rectify,[],[f76])).
% 4.58/1.03 tff(f76,axiom,(
% 4.58/1.03 ! [X2 : $tType,X1 : $tType,X55 : fun(X1,X2),X53 : fun(X1,X2)] : (! [X48 : X1] : aa(X1,X2,X53,X48) = aa(X1,X2,X55,X48) => X53 = X55)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext)).
% 4.58/1.03 tff(f1616,plain,(
% 4.58/1.03 spl53_94),
% 4.58/1.03 inference(avatar_split_clause,[],[f520,f1614])).
% 4.58/1.03 tff(f520,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK17(X0,X1)),sK18(X0,X1))) | ~sP0(X0,X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f366])).
% 4.58/1.03 tff(f1543,plain,(
% 4.58/1.03 spl53_93 | ~spl53_34 | ~spl53_88),
% 4.58/1.03 inference(avatar_split_clause,[],[f1480,f1477,f912,f1541])).
% 4.58/1.03 tff(f1477,plain,(
% 4.58/1.03 spl53_88 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),sK20(X0,X1,X2))) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_88])])).
% 4.58/1.03 tff(f1480,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = X2 | pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),sK20(X0,X1,X2))) | ~finite_finite1(X0,X2)) ) | (~spl53_34 | ~spl53_88)),
% 4.58/1.03 inference(forward_demodulation,[],[f1478,f913])).
% 4.58/1.03 tff(f1478,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),sK20(X0,X1,X2))) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2)) ) | ~spl53_88),
% 4.58/1.03 inference(avatar_component_clause,[],[f1477])).
% 4.58/1.03 tff(f1496,plain,(
% 4.58/1.03 spl53_92),
% 4.58/1.03 inference(avatar_split_clause,[],[f550,f1494])).
% 4.58/1.03 tff(f550,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | ~pp(aa(X0,bool,X1,X2))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f387])).
% 4.58/1.03 tff(f387,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : ((pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) | ~pp(aa(X0,bool,X1,X2))) & (pp(aa(X0,bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))))),
% 4.58/1.03 inference(nnf_transformation,[],[f201])).
% 4.58/1.03 tff(f201,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) <=> pp(aa(X0,bool,X1,X2)))),
% 4.58/1.03 inference(rectify,[],[f77])).
% 4.58/1.03 tff(f77,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X26 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X26),X25)) <=> pp(aa(X1,bool,X25,X26)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def)).
% 4.58/1.03 tff(f1492,plain,(
% 4.58/1.03 spl53_91),
% 4.58/1.03 inference(avatar_split_clause,[],[f549,f1490])).
% 4.58/1.03 tff(f549,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f387])).
% 4.58/1.03 tff(f1488,plain,(
% 4.58/1.03 spl53_90),
% 4.58/1.03 inference(avatar_split_clause,[],[f544,f1486])).
% 4.58/1.03 tff(f544,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (the(X0,X2) = X1 | ~pp(aa(X0,bool,X2,X1)) | sK27(X0,X2,X3) != X3 | ~pp(aa(X0,bool,X2,X3))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f382])).
% 4.58/1.03 tff(f1484,plain,(
% 4.58/1.03 spl53_89),
% 4.58/1.03 inference(avatar_split_clause,[],[f531,f1482])).
% 4.58/1.03 tff(f531,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (pp(aa(X0,bool,X2,the(X0,X2))) | pp(aa(X0,bool,X2,sK24(X0,X1,X2))) | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f376])).
% 4.58/1.03 tff(f376,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (pp(aa(X0,bool,X2,the(X0,X2))) | (sK24(X0,X1,X2) != X1 & pp(aa(X0,bool,X2,sK24(X0,X1,X2)))) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f276,f375])).
% 4.58/1.03 tff(f375,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (? [X3 : X0] : (X1 != X3 & pp(aa(X0,bool,X2,X3))) => (sK24(X0,X1,X2) != X1 & pp(aa(X0,bool,X2,sK24(X0,X1,X2)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f276,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (pp(aa(X0,bool,X2,the(X0,X2))) | ? [X3 : X0] : (X1 != X3 & pp(aa(X0,bool,X2,X3))) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 inference(flattening,[],[f275])).
% 4.58/1.03 tff(f275,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : ((pp(aa(X0,bool,X2,the(X0,X2))) | ? [X3 : X0] : (X1 != X3 & pp(aa(X0,bool,X2,X3)))) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 inference(ennf_transformation,[],[f191])).
% 4.58/1.03 tff(f191,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (pp(aa(X0,bool,X2,X1)) => (! [X3 : X0] : (pp(aa(X0,bool,X2,X3)) => X1 = X3) => pp(aa(X0,bool,X2,the(X0,X2)))))),
% 4.58/1.03 inference(rectify,[],[f59])).
% 4.58/1.03 tff(f59,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1,X16 : fun(X1,bool)] : (pp(aa(X1,bool,X16,X18)) => (! [X48 : X1] : (pp(aa(X1,bool,X16,X48)) => X18 = X48) => pp(aa(X1,bool,X16,the(X1,X16)))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_theI)).
% 4.58/1.03 tff(f1479,plain,(
% 4.58/1.03 spl53_88),
% 4.58/1.03 inference(avatar_split_clause,[],[f524,f1477])).
% 4.58/1.03 tff(f524,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),sK20(X0,X1,X2))) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f370])).
% 4.58/1.03 tff(f370,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : (pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),sK20(X0,X1,X2))) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f270,f369])).
% 4.58/1.03 tff(f369,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : (? [X3 : X0] : pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3)) => pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),sK20(X0,X1,X2))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f270,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : (? [X3 : X0] : pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3)) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(flattening,[],[f269])).
% 4.58/1.03 tff(f269,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : ((? [X3 : X0] : pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3)) | bot_bot(fun(X0,bool)) = X2) | ~finite_finite1(X0,X2))),
% 4.58/1.03 inference(ennf_transformation,[],[f188])).
% 4.58/1.03 tff(f188,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : (finite_finite1(X0,X2) => (bot_bot(fun(X0,bool)) != X2 => ? [X3 : X0] : pp(aa(X0,bool,finite_fold1Set(X0,X1,X2),X3))))),
% 4.58/1.03 inference(rectify,[],[f93])).
% 4.58/1.03 tff(f93,axiom,(
% 4.58/1.03 ! [X1 : $tType,X53 : fun(X1,fun(X1,X1)),X25 : fun(X1,bool)] : (finite_finite1(X1,X25) => (bot_bot(fun(X1,bool)) != X25 => ? [X59 : X1] : pp(aa(X1,bool,finite_fold1Set(X1,X53,X25),X59))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_finite__nonempty__imp__fold1Set)).
% 4.58/1.03 tff(f1475,plain,(
% 4.58/1.03 spl53_87),
% 4.58/1.03 inference(avatar_split_clause,[],[f480,f1473])).
% 4.58/1.03 tff(f480,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X1))) | pp(aa(X0,bool,X1,sK5(X0,X1,X2))) | ~pp(aa(X0,bool,X1,X2))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f334])).
% 4.58/1.03 tff(f334,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X1))) | ! [X2 : X0] : ((sK5(X0,X1,X2) != X2 & pp(aa(X0,bool,X1,sK5(X0,X1,X2)))) | ~pp(aa(X0,bool,X1,X2))))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f262,f333])).
% 4.58/1.03 tff(f333,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (? [X3 : X0] : (X2 != X3 & pp(aa(X0,bool,X1,X3))) => (sK5(X0,X1,X2) != X2 & pp(aa(X0,bool,X1,sK5(X0,X1,X2)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f262,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X1))) | ! [X2 : X0] : (? [X3 : X0] : (X2 != X3 & pp(aa(X0,bool,X1,X3))) | ~pp(aa(X0,bool,X1,X2))))),
% 4.58/1.03 inference(ennf_transformation,[],[f162])).
% 4.58/1.03 tff(f162,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X2 : X0] : (! [X3 : X0] : (pp(aa(X0,bool,X1,X3)) => X2 = X3) & pp(aa(X0,bool,X1,X2))) => pp(aa(X0,bool,X1,the(X0,X1))))),
% 4.58/1.03 inference(rectify,[],[f61])).
% 4.58/1.03 tff(f61,axiom,(
% 4.58/1.03 ! [X1 : $tType,X16 : fun(X1,bool)] : (? [X32 : X1] : (! [X49 : X1] : (pp(aa(X1,bool,X16,X49)) => X32 = X49) & pp(aa(X1,bool,X16,X32))) => pp(aa(X1,bool,X16,the(X1,X16))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_theI_H)).
% 4.58/1.03 tff(f1469,plain,(
% 4.58/1.03 spl53_86 | ~spl53_34 | ~spl53_85),
% 4.58/1.03 inference(avatar_split_clause,[],[f1465,f1462,f912,f1467])).
% 4.58/1.03 tff(f1462,plain,(
% 4.58/1.03 spl53_85 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1)),X2 : X1] : (sP3(X1,X0,X4,X5,X2,X3) | bot_bot(fun(X0,bool)) = X3 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_85])])).
% 4.58/1.03 tff(f1465,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (combk(bool,X0,fFalse) = X3 | sP3(X1,X0,X4,X5,X2,X3) | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)) ) | (~spl53_34 | ~spl53_85)),
% 4.58/1.03 inference(forward_demodulation,[],[f1463,f913])).
% 4.58/1.03 tff(f1463,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (sP3(X1,X0,X4,X5,X2,X3) | bot_bot(fun(X0,bool)) = X3 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)) ) | ~spl53_85),
% 4.58/1.03 inference(avatar_component_clause,[],[f1462])).
% 4.58/1.03 tff(f1464,plain,(
% 4.58/1.03 spl53_85),
% 4.58/1.03 inference(avatar_split_clause,[],[f635,f1462])).
% 4.58/1.03 tff(f635,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (sP3(X1,X0,X4,X5,X2,X3) | bot_bot(fun(X0,bool)) = X3 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f435])).
% 4.58/1.03 tff(f435,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : ((finite_fold_graph(X0,X1,X5,X4,X3,X2) | (~sP3(X1,X0,X4,X5,X2,X3) & (X2 != X4 | bot_bot(fun(X0,bool)) != X3))) & (sP3(X1,X0,X4,X5,X2,X3) | (X2 = X4 & bot_bot(fun(X0,bool)) = X3) | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)))),
% 4.58/1.03 inference(flattening,[],[f434])).
% 4.58/1.03 tff(f434,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : ((finite_fold_graph(X0,X1,X5,X4,X3,X2) | (~sP3(X1,X0,X4,X5,X2,X3) & (X2 != X4 | bot_bot(fun(X0,bool)) != X3))) & ((sP3(X1,X0,X4,X5,X2,X3) | (X2 = X4 & bot_bot(fun(X0,bool)) = X3)) | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)))),
% 4.58/1.03 inference(nnf_transformation,[],[f330])).
% 4.58/1.03 tff(f330,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (finite_fold_graph(X0,X1,X5,X4,X3,X2) <=> (sP3(X1,X0,X4,X5,X2,X3) | (X2 = X4 & bot_bot(fun(X0,bool)) = X3)))),
% 4.58/1.03 inference(definition_folding,[],[f244,f329])).
% 4.58/1.03 tff(f244,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (finite_fold_graph(X0,X1,X5,X4,X3,X2) <=> (? [X6 : X0,X7 : fun(X0,bool),X8 : X1] : (finite_fold_graph(X0,X1,X5,X4,X7,X8) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X7)) & aa(X1,X1,aa(X0,fun(X1,X1),X5,X6),X8) = X2 & aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X6),X7) = X3) | (X2 = X4 & bot_bot(fun(X0,bool)) = X3)))),
% 4.58/1.03 inference(rectify,[],[f98])).
% 4.58/1.03 tff(f98,axiom,(
% 4.58/1.03 ! [X1 : $tType,X2 : $tType,X63 : X2,X64 : fun(X1,bool),X56 : X2,X53 : fun(X1,fun(X2,X2))] : (finite_fold_graph(X1,X2,X53,X56,X64,X63) <=> (? [X29 : X1,X60 : fun(X1,bool),X65 : X2] : (finite_fold_graph(X1,X2,X53,X56,X60,X65) & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X29),X60)) & aa(X2,X2,aa(X1,fun(X2,X2),X53,X29),X65) = X63 & aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X29),X60) = X64) | (X56 = X63 & bot_bot(fun(X1,bool)) = X64)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_fold__graph_Osimps)).
% 4.58/1.03 tff(f1450,plain,(
% 4.58/1.03 spl53_84 | ~spl53_4 | ~spl53_72),
% 4.58/1.03 inference(avatar_split_clause,[],[f1279,f1160,f767,f1448])).
% 4.58/1.03 tff(f1279,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(X0) | X0 = X1 | fTrue = X1) ) | (~spl53_4 | ~spl53_72)),
% 4.58/1.03 inference(superposition,[],[f769,f1161])).
% 4.58/1.03 tff(f769,plain,(
% 4.58/1.03 pp(fTrue) | ~spl53_4),
% 4.58/1.03 inference(avatar_component_clause,[],[f767])).
% 4.58/1.03 tff(f1410,plain,(
% 4.58/1.03 spl53_83 | ~spl53_34 | ~spl53_79),
% 4.58/1.03 inference(avatar_split_clause,[],[f1394,f1391,f912,f1408])).
% 4.58/1.03 tff(f1391,plain,(
% 4.58/1.03 spl53_79 <=> ! [X0 : $tType,X1 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_79])])).
% 4.58/1.03 tff(f1394,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),combk(bool,X0,fFalse)))) ) | (~spl53_34 | ~spl53_79)),
% 4.58/1.03 inference(forward_demodulation,[],[f1392,f913])).
% 4.58/1.03 tff(f1392,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))) ) | ~spl53_79),
% 4.58/1.03 inference(avatar_component_clause,[],[f1391])).
% 4.58/1.03 tff(f1406,plain,(
% 4.58/1.03 spl53_82),
% 4.58/1.03 inference(avatar_split_clause,[],[f532,f1404])).
% 4.58/1.03 tff(f532,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (pp(aa(X0,bool,X2,the(X0,X2))) | sK24(X0,X1,X2) != X1 | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f376])).
% 4.58/1.03 tff(f1402,plain,(
% 4.58/1.03 spl53_81),
% 4.58/1.03 inference(avatar_split_clause,[],[f529,f1400])).
% 4.58/1.03 tff(f529,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (the(X0,X2) = X1 | pp(aa(X0,bool,X2,sK23(X0,X1,X2))) | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f374])).
% 4.58/1.03 tff(f374,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (the(X0,X2) = X1 | (sK23(X0,X1,X2) != X1 & pp(aa(X0,bool,X2,sK23(X0,X1,X2)))) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f274,f373])).
% 4.58/1.03 tff(f373,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (? [X3 : X0] : (X1 != X3 & pp(aa(X0,bool,X2,X3))) => (sK23(X0,X1,X2) != X1 & pp(aa(X0,bool,X2,sK23(X0,X1,X2)))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f274,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (the(X0,X2) = X1 | ? [X3 : X0] : (X1 != X3 & pp(aa(X0,bool,X2,X3))) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 inference(flattening,[],[f273])).
% 4.58/1.03 tff(f273,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : ((the(X0,X2) = X1 | ? [X3 : X0] : (X1 != X3 & pp(aa(X0,bool,X2,X3)))) | ~pp(aa(X0,bool,X2,X1)))),
% 4.58/1.03 inference(ennf_transformation,[],[f190])).
% 4.58/1.03 tff(f190,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool)] : (pp(aa(X0,bool,X2,X1)) => (! [X3 : X0] : (pp(aa(X0,bool,X2,X3)) => X1 = X3) => the(X0,X2) = X1))),
% 4.58/1.03 inference(rectify,[],[f58])).
% 4.58/1.03 tff(f58,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1,X16 : fun(X1,bool)] : (pp(aa(X1,bool,X16,X18)) => (! [X48 : X1] : (pp(aa(X1,bool,X16,X48)) => X18 = X48) => the(X1,X16) = X18))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_the__equality)).
% 4.58/1.03 tff(f1398,plain,(
% 4.58/1.03 spl53_80),
% 4.58/1.03 inference(avatar_split_clause,[],[f481,f1396])).
% 4.58/1.03 tff(f481,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,the(X0,X1))) | sK5(X0,X1,X2) != X2 | ~pp(aa(X0,bool,X1,X2))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f334])).
% 4.58/1.03 tff(f1393,plain,(
% 4.58/1.03 spl53_79),
% 4.58/1.03 inference(avatar_split_clause,[],[f459,f1391])).
% 4.58/1.03 tff(f459,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f141])).
% 4.58/1.03 tff(f141,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0] : ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))),
% 4.58/1.03 inference(rectify,[],[f18])).
% 4.58/1.03 tff(f18,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1] : ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X18),bot_bot(fun(X1,bool))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_emptyE)).
% 4.58/1.03 tff(f1190,plain,(
% 4.58/1.03 spl53_78),
% 4.58/1.03 inference(avatar_split_clause,[],[f730,f1188])).
% 4.58/1.03 tff(f730,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(state,bool)),X3 : com,X4 : fun(X1,fun(state,bool)),X5 : fun(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)))] : (hoare_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2)) = hoare_678420151le_rec(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f622,f621])).
% 4.58/1.03 tff(f622,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(state,bool)),X3 : com,X4 : fun(X1,fun(state,bool)),X5 : fun(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)))] : (aa(fun(X1,fun(state,bool)),X0,aa(com,fun(fun(X1,fun(state,bool)),X0),aa(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)),X5,X4),X3),X2) = hoare_678420151le_rec(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f239])).
% 4.58/1.03 tff(f239,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,fun(state,bool)),X3 : com,X4 : fun(X1,fun(state,bool)),X5 : fun(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)))] : aa(fun(X1,fun(state,bool)),X0,aa(com,fun(fun(X1,fun(state,bool)),X0),aa(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),X0)),X5,X4),X3),X2) = hoare_678420151le_rec(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))),
% 4.58/1.03 inference(rectify,[],[f44])).
% 4.58/1.03 tff(f44,axiom,(
% 4.58/1.03 ! [X1 : $tType,X2 : $tType,X7 : fun(X2,fun(state,bool)),X8 : com,X9 : fun(X2,fun(state,bool)),X35 : fun(fun(X2,fun(state,bool)),fun(com,fun(fun(X2,fun(state,bool)),X1)))] : aa(fun(X2,fun(state,bool)),X1,aa(com,fun(fun(X2,fun(state,bool)),X1),aa(fun(X2,fun(state,bool)),fun(com,fun(fun(X2,fun(state,bool)),X1)),X35,X9),X8),X7) = hoare_678420151le_rec(X2,X1,X35,hoare_1841697145triple(X2,X9,X8,X7))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_triple_Orecs)).
% 4.58/1.03 tff(f1186,plain,(
% 4.58/1.03 spl53_77),
% 4.58/1.03 inference(avatar_split_clause,[],[f717,f1184])).
% 4.58/1.03 tff(f717,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(X0,fun(X0,bool),fequal(X0),X2)),X1)) | X1 = X2) )),
% 4.58/1.03 inference(forward_demodulation,[],[f585,f685])).
% 4.58/1.03 tff(f585,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (X1 = X2 | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f403])).
% 4.58/1.03 tff(f403,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : fun(X0,fun(X0,X0))] : ((pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))),X1)) | X1 != X2) & (X1 = X2 | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))),X1))))),
% 4.58/1.03 inference(nnf_transformation,[],[f224])).
% 4.58/1.03 tff(f224,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))),X1)) <=> X1 = X2)),
% 4.58/1.03 inference(rectify,[],[f67])).
% 4.58/1.03 tff(f67,axiom,(
% 4.58/1.03 ! [X1 : $tType,X27 : X1,X18 : X1,X53 : fun(X1,fun(X1,X1))] : (pp(aa(X1,bool,finite_fold1Set(X1,X53,aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),bot_bot(fun(X1,bool)))),X27)) <=> X18 = X27)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_fold1Set__sing)).
% 4.58/1.03 tff(f1182,plain,(
% 4.58/1.03 spl53_76),
% 4.58/1.03 inference(avatar_split_clause,[],[f646,f1180])).
% 4.58/1.03 tff(f646,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : com] : (X1 = X4 | hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f440])).
% 4.58/1.03 tff(f440,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : com,X6 : fun(X0,fun(state,bool))] : ((hoare_1841697145triple(X0,X3,X2,X1) = hoare_1841697145triple(X0,X6,X5,X4) | X1 != X4 | X2 != X5 | X3 != X6) & ((X1 = X4 & X2 = X5 & X3 = X6) | hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4)))),
% 4.58/1.03 inference(flattening,[],[f439])).
% 4.58/1.03 tff(f439,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : com,X6 : fun(X0,fun(state,bool))] : ((hoare_1841697145triple(X0,X3,X2,X1) = hoare_1841697145triple(X0,X6,X5,X4) | (X1 != X4 | X2 != X5 | X3 != X6)) & ((X1 = X4 & X2 = X5 & X3 = X6) | hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4)))),
% 4.58/1.03 inference(nnf_transformation,[],[f248])).
% 4.58/1.03 tff(f248,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : com,X3 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : com,X6 : fun(X0,fun(state,bool))] : (hoare_1841697145triple(X0,X3,X2,X1) = hoare_1841697145triple(X0,X6,X5,X4) <=> (X1 = X4 & X2 = X5 & X3 = X6))),
% 4.58/1.03 inference(rectify,[],[f1])).
% 4.58/1.03 tff(f1,axiom,(
% 4.58/1.03 ! [X1 : $tType,X4 : fun(X1,fun(state,bool)),X5 : com,X6 : fun(X1,fun(state,bool)),X7 : fun(X1,fun(state,bool)),X8 : com,X9 : fun(X1,fun(state,bool))] : (hoare_1841697145triple(X1,X9,X8,X7) = hoare_1841697145triple(X1,X6,X5,X4) <=> (X4 = X7 & X5 = X8 & X6 = X9))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_triple_Oinject)).
% 4.58/1.03 tff(f1178,plain,(
% 4.58/1.03 spl53_75),
% 4.58/1.03 inference(avatar_split_clause,[],[f644,f1176])).
% 4.58/1.03 tff(f644,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : com] : (X3 = X6 | hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f440])).
% 4.58/1.03 tff(f1170,plain,(
% 4.58/1.03 spl53_74),
% 4.58/1.03 inference(avatar_split_clause,[],[f692,f1168])).
% 4.58/1.03 tff(f692,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X2,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f506,f685])).
% 4.58/1.03 tff(f506,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X2,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1)),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f177])).
% 4.58/1.03 tff(f177,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(hoare_28830079triple(X0),bool)] : hoare_992312373derivs(X0,X2,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1)),bot_bot(fun(hoare_28830079triple(X0),bool))))),
% 4.58/1.03 inference(rectify,[],[f47])).
% 4.58/1.03 tff(f47,axiom,(
% 4.58/1.03 ! [X1 : $tType,X16 : fun(X1,fun(state,bool)),X10 : fun(hoare_28830079triple(X1),bool)] : hoare_992312373derivs(X1,X10,aa(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool),aa(hoare_28830079triple(X1),fun(fun(hoare_28830079triple(X1),bool),fun(hoare_28830079triple(X1),bool)),insert(hoare_28830079triple(X1)),hoare_1841697145triple(X1,X16,skip,X16)),bot_bot(fun(hoare_28830079triple(X1),bool))))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_hoare__derivs_OSkip)).
% 4.58/1.03 tff(f1166,plain,(
% 4.58/1.03 spl53_73),
% 4.58/1.03 inference(avatar_split_clause,[],[f691,f1164])).
% 4.58/1.03 tff(f691,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (aa(fun(X0,bool),X0,finite_fold1(X0,X2),aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) )),
% 4.58/1.03 inference(forward_demodulation,[],[f504,f685])).
% 4.58/1.03 tff(f504,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (aa(fun(X0,bool),X0,finite_fold1(X0,X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f175])).
% 4.58/1.03 tff(f175,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,fun(X0,X0))] : aa(fun(X0,bool),X0,finite_fold1(X0,X2),aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = X1),
% 4.58/1.03 inference(rectify,[],[f89])).
% 4.58/1.03 tff(f89,axiom,(
% 4.58/1.03 ! [X1 : $tType,X18 : X1,X53 : fun(X1,fun(X1,X1))] : aa(fun(X1,bool),X1,finite_fold1(X1,X53),aa(fun(X1,bool),fun(X1,bool),aa(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X18),bot_bot(fun(X1,bool)))) = X18),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_fold1__singleton)).
% 4.58/1.03 tff(f1162,plain,(
% 4.58/1.03 spl53_72 | ~spl53_8),
% 4.58/1.03 inference(avatar_split_clause,[],[f803,f784,f1160])).
% 4.58/1.03 tff(f803,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl53_8),
% 4.58/1.03 inference(superposition,[],[f785,f785])).
% 4.58/1.03 tff(f1155,plain,(
% 4.58/1.03 spl53_71),
% 4.58/1.03 inference(avatar_split_clause,[],[f636,f1153])).
% 4.58/1.03 tff(f636,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (sP3(X1,X0,X4,X5,X2,X3) | X2 = X4 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f435])).
% 4.58/1.03 tff(f1151,plain,(
% 4.58/1.03 spl53_70),
% 4.58/1.03 inference(avatar_split_clause,[],[f530,f1149])).
% 4.58/1.03 tff(f530,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (the(X0,X2) = X1 | sK23(X0,X1,X2) != X1 | ~pp(aa(X0,bool,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f374])).
% 4.58/1.03 tff(f1116,plain,(
% 4.58/1.03 spl53_69 | ~spl53_34 | ~spl53_65),
% 4.58/1.03 inference(avatar_split_clause,[],[f1081,f1078,f912,f1114])).
% 4.58/1.03 tff(f1078,plain,(
% 4.58/1.03 spl53_65 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK11(X0,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_65])])).
% 4.58/1.03 tff(f1081,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK11(X0,X1)))) ) | (~spl53_34 | ~spl53_65)),
% 4.58/1.03 inference(forward_demodulation,[],[f1079,f913])).
% 4.58/1.03 tff(f1079,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK11(X0,X1)))) ) | ~spl53_65),
% 4.58/1.03 inference(avatar_component_clause,[],[f1078])).
% 4.58/1.03 tff(f1112,plain,(
% 4.58/1.03 spl53_68 | ~spl53_34 | ~spl53_64),
% 4.58/1.03 inference(avatar_split_clause,[],[f1076,f1073,f912,f1110])).
% 4.58/1.03 tff(f1073,plain,(
% 4.58/1.03 spl53_64 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK10(X0,X1))))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_64])])).
% 4.58/1.03 tff(f1076,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK10(X0,X1)))) ) | (~spl53_34 | ~spl53_64)),
% 4.58/1.03 inference(forward_demodulation,[],[f1074,f913])).
% 4.58/1.03 tff(f1074,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK10(X0,X1)))) ) | ~spl53_64),
% 4.58/1.03 inference(avatar_component_clause,[],[f1073])).
% 4.58/1.03 tff(f1099,plain,(
% 4.58/1.03 spl53_67 | ~spl53_34 | ~spl53_59),
% 4.58/1.03 inference(avatar_split_clause,[],[f1055,f1052,f912,f1097])).
% 4.58/1.03 tff(f1097,plain,(
% 4.58/1.03 spl53_67 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | finite_finite1(X0,sK6(X0,X1)) | ~finite_finite1(X0,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_67])])).
% 4.58/1.03 tff(f1052,plain,(
% 4.58/1.03 spl53_59 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,sK6(X0,X1)) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_59])])).
% 4.58/1.03 tff(f1055,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | finite_finite1(X0,sK6(X0,X1)) | ~finite_finite1(X0,X1)) ) | (~spl53_34 | ~spl53_59)),
% 4.58/1.03 inference(forward_demodulation,[],[f1053,f913])).
% 4.58/1.03 tff(f1053,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,sK6(X0,X1)) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) ) | ~spl53_59),
% 4.58/1.03 inference(avatar_component_clause,[],[f1052])).
% 4.58/1.03 tff(f1085,plain,(
% 4.58/1.03 spl53_66),
% 4.58/1.03 inference(avatar_split_clause,[],[f716,f1083])).
% 4.58/1.03 tff(f716,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(X0,fun(X0,bool),fequal(X0),X2)),X2))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f666,f685])).
% 4.58/1.03 tff(f666,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))),X2))) )),
% 4.58/1.03 inference(equality_resolution,[],[f586])).
% 4.58/1.03 tff(f586,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (pp(aa(X0,bool,finite_fold1Set(X0,X3,aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))),X1)) | X1 != X2) )),
% 4.58/1.03 inference(cnf_transformation,[],[f403])).
% 4.58/1.03 tff(f1080,plain,(
% 4.58/1.03 spl53_65),
% 4.58/1.03 inference(avatar_split_clause,[],[f689,f1078])).
% 4.58/1.03 tff(f689,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK11(X0,X1)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f494,f456])).
% 4.58/1.03 tff(f494,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = collect(X0,X1) | pp(aa(X0,bool,X1,sK11(X0,X1)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f352])).
% 4.58/1.03 tff(f352,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,X1) | pp(aa(X0,bool,X1,sK11(X0,X1)))) & (! [X3 : X0] : ~pp(aa(X0,bool,X1,X3)) | bot_bot(fun(X0,bool)) != collect(X0,X1)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f350,f351])).
% 4.58/1.03 tff(f351,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X2 : X0] : pp(aa(X0,bool,X1,X2)) => pp(aa(X0,bool,X1,sK11(X0,X1))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f350,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,X1) | ? [X2 : X0] : pp(aa(X0,bool,X1,X2))) & (! [X3 : X0] : ~pp(aa(X0,bool,X1,X3)) | bot_bot(fun(X0,bool)) != collect(X0,X1)))),
% 4.58/1.03 inference(rectify,[],[f349])).
% 4.58/1.03 tff(f349,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,X1) | ? [X2 : X0] : pp(aa(X0,bool,X1,X2))) & (! [X2 : X0] : ~pp(aa(X0,bool,X1,X2)) | bot_bot(fun(X0,bool)) != collect(X0,X1)))),
% 4.58/1.03 inference(nnf_transformation,[],[f167])).
% 4.58/1.03 tff(f167,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = collect(X0,X1) <=> ! [X2 : X0] : ~pp(aa(X0,bool,X1,X2)))),
% 4.58/1.03 inference(rectify,[],[f17])).
% 4.58/1.03 tff(f17,axiom,(
% 4.58/1.03 ! [X1 : $tType,X16 : fun(X1,bool)] : (bot_bot(fun(X1,bool)) = collect(X1,X16) <=> ! [X29 : X1] : ~pp(aa(X1,bool,X16,X29)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_empty__Collect__eq)).
% 4.58/1.03 tff(f1075,plain,(
% 4.58/1.03 spl53_64),
% 4.58/1.03 inference(avatar_split_clause,[],[f687,f1073])).
% 4.58/1.03 tff(f687,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK10(X0,X1)))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f492,f456])).
% 4.58/1.03 tff(f492,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = collect(X0,X1) | pp(aa(X0,bool,X1,sK10(X0,X1)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f348])).
% 4.58/1.03 tff(f348,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,X1) | pp(aa(X0,bool,X1,sK10(X0,X1)))) & (! [X3 : X0] : ~pp(aa(X0,bool,X1,X3)) | bot_bot(fun(X0,bool)) != collect(X0,X1)))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f346,f347])).
% 4.58/1.03 tff(f347,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X2 : X0] : pp(aa(X0,bool,X1,X2)) => pp(aa(X0,bool,X1,sK10(X0,X1))))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f346,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,X1) | ? [X2 : X0] : pp(aa(X0,bool,X1,X2))) & (! [X3 : X0] : ~pp(aa(X0,bool,X1,X3)) | bot_bot(fun(X0,bool)) != collect(X0,X1)))),
% 4.58/1.03 inference(rectify,[],[f345])).
% 4.58/1.03 tff(f345,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,X1) | ? [X2 : X0] : pp(aa(X0,bool,X1,X2))) & (! [X2 : X0] : ~pp(aa(X0,bool,X1,X2)) | bot_bot(fun(X0,bool)) != collect(X0,X1)))),
% 4.58/1.03 inference(nnf_transformation,[],[f166])).
% 4.58/1.03 tff(f166,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = collect(X0,X1) <=> ! [X2 : X0] : ~pp(aa(X0,bool,X1,X2)))),
% 4.58/1.03 inference(rectify,[],[f19])).
% 4.58/1.03 tff(f19,axiom,(
% 4.58/1.03 ! [X1 : $tType,X16 : fun(X1,bool)] : (bot_bot(fun(X1,bool)) = collect(X1,X16) <=> ! [X29 : X1] : ~pp(aa(X1,bool,X16,X29)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Collect__empty__eq)).
% 4.58/1.03 tff(f1071,plain,(
% 4.58/1.03 spl53_63 | ~spl53_17 | ~spl53_34),
% 4.58/1.03 inference(avatar_split_clause,[],[f918,f912,f823,f1069])).
% 4.58/1.03 tff(f823,plain,(
% 4.58/1.03 spl53_17 <=> ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : hoare_992312373derivs(X0,X1,bot_bot(fun(hoare_28830079triple(X0),bool)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_17])])).
% 4.58/1.03 tff(f918,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,combk(bool,hoare_28830079triple(X0),fFalse))) ) | (~spl53_17 | ~spl53_34)),
% 4.58/1.03 inference(superposition,[],[f824,f913])).
% 4.58/1.03 tff(f824,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,bot_bot(fun(hoare_28830079triple(X0),bool)))) ) | ~spl53_17),
% 4.58/1.03 inference(avatar_component_clause,[],[f823])).
% 4.58/1.03 tff(f1067,plain,(
% 4.58/1.03 spl53_62),
% 4.58/1.03 inference(avatar_split_clause,[],[f578,f1065])).
% 4.58/1.03 tff(f578,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (sK33(X0,X1,X2,X3) = X1 | ~pp(aa(X0,bool,finite_fold1Set(X0,X3,X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f400])).
% 4.58/1.03 tff(f1063,plain,(
% 4.58/1.03 spl53_61),
% 4.58/1.03 inference(avatar_split_clause,[],[f516,f1061])).
% 4.58/1.03 tff(f516,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f185])).
% 4.58/1.03 tff(f185,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = X2 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)))),
% 4.58/1.03 inference(rectify,[],[f121])).
% 4.58/1.03 tff(f121,axiom,(
% 4.58/1.03 ! [X0 : $tType,X71 : X0,X72 : X0] : (X71 = X72 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X72),X71)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T)).
% 4.58/1.03 tff(f1059,plain,(
% 4.58/1.03 spl53_60),
% 4.58/1.03 inference(avatar_split_clause,[],[f501,f1057])).
% 4.58/1.03 tff(f501,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : fun(X0,bool)] : (aa(fun(X0,bool),X0,finite_fold1(X0,X2),X1) = the(X0,finite_fold1Set(X0,X2,X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f172])).
% 4.58/1.03 tff(f172,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,fun(X0,X0))] : aa(fun(X0,bool),X0,finite_fold1(X0,X2),X1) = the(X0,finite_fold1Set(X0,X2,X1))),
% 4.58/1.03 inference(rectify,[],[f74])).
% 4.58/1.03 tff(f74,axiom,(
% 4.58/1.03 ! [X1 : $tType,X25 : fun(X1,bool),X53 : fun(X1,fun(X1,X1))] : aa(fun(X1,bool),X1,finite_fold1(X1,X53),X25) = the(X1,finite_fold1Set(X1,X53,X25))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_fold1__def)).
% 4.58/1.03 tff(f1054,plain,(
% 4.58/1.03 spl53_59),
% 4.58/1.03 inference(avatar_split_clause,[],[f483,f1052])).
% 4.58/1.03 tff(f483,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,sK6(X0,X1)) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f339])).
% 4.58/1.03 tff(f1050,plain,(
% 4.58/1.03 spl53_58),
% 4.58/1.03 inference(avatar_split_clause,[],[f472,f1048])).
% 4.58/1.03 tff(f472,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f154])).
% 4.58/1.03 tff(f154,plain,(
% 4.58/1.03 ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)))),
% 4.58/1.03 inference(rectify,[],[f125])).
% 4.58/1.03 tff(f125,axiom,(
% 4.58/1.03 ! [X70 : bool,X68 : bool] : (pp(X70) | ~pp(X68) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X68),X70)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U)).
% 4.58/1.03 tff(f1046,plain,(
% 4.58/1.03 spl53_57),
% 4.58/1.03 inference(avatar_split_clause,[],[f471,f1044])).
% 4.58/1.03 tff(f471,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f153])).
% 4.58/1.03 tff(f153,plain,(
% 4.58/1.03 ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)))),
% 4.58/1.03 inference(rectify,[],[f118])).
% 4.58/1.03 tff(f118,axiom,(
% 4.58/1.03 ! [X70 : bool,X68 : bool] : (pp(X70) | pp(X68) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X68),X70)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U)).
% 4.58/1.03 tff(f1042,plain,(
% 4.58/1.03 spl53_56),
% 4.58/1.03 inference(avatar_split_clause,[],[f466,f1040])).
% 4.58/1.03 tff(f466,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f148])).
% 4.58/1.03 tff(f148,plain,(
% 4.58/1.03 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 4.58/1.03 inference(rectify,[],[f113])).
% 4.58/1.03 tff(f113,axiom,(
% 4.58/1.03 ! [X70 : bool,X68 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X68),X70)) | ~pp(X70) | ~pp(X68))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U)).
% 4.58/1.03 tff(f1033,plain,(
% 4.58/1.03 spl53_55),
% 4.58/1.03 inference(avatar_split_clause,[],[f645,f1031])).
% 4.58/1.03 tff(f645,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : com,X3 : fun(X0,fun(state,bool)),X1 : fun(X0,fun(state,bool)),X6 : fun(X0,fun(state,bool)),X4 : fun(X0,fun(state,bool)),X5 : com] : (X2 = X5 | hoare_1841697145triple(X0,X3,X2,X1) != hoare_1841697145triple(X0,X6,X5,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f440])).
% 4.58/1.03 tff(f1028,plain,(
% 4.58/1.03 spl53_54),
% 4.58/1.03 inference(avatar_split_clause,[],[f590,f1026])).
% 4.58/1.03 tff(f590,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1)),X4 : fun(X0,bool)] : (finite_fold_graph(X0,X1,X3,X2,X4,sK34(X0,X1,X2,X3,X4)) | ~finite_finite1(X0,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f407])).
% 4.58/1.03 tff(f407,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1)),X4 : fun(X0,bool)] : (finite_fold_graph(X0,X1,X3,X2,X4,sK34(X0,X1,X2,X3,X4)) | ~finite_finite1(X0,X4))),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f302,f406])).
% 4.58/1.03 tff(f406,plain,(
% 4.58/1.03 ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1)),X4 : fun(X0,bool)] : (? [X5 : X1] : finite_fold_graph(X0,X1,X3,X2,X4,X5) => finite_fold_graph(X0,X1,X3,X2,X4,sK34(X0,X1,X2,X3,X4)))),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f302,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1)),X4 : fun(X0,bool)] : (? [X5 : X1] : finite_fold_graph(X0,X1,X3,X2,X4,X5) | ~finite_finite1(X0,X4))),
% 4.58/1.03 inference(ennf_transformation,[],[f226])).
% 4.58/1.03 tff(f226,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1)),X4 : fun(X0,bool)] : (finite_finite1(X0,X4) => ? [X5 : X1] : finite_fold_graph(X0,X1,X3,X2,X4,X5))),
% 4.58/1.03 inference(rectify,[],[f96])).
% 4.58/1.03 tff(f96,axiom,(
% 4.58/1.03 ! [X1 : $tType,X2 : $tType,X56 : X2,X53 : fun(X1,fun(X2,X2)),X25 : fun(X1,bool)] : (finite_finite1(X1,X25) => ? [X59 : X2] : finite_fold_graph(X1,X2,X53,X56,X25,X59))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_finite__imp__fold__graph)).
% 4.58/1.03 tff(f1021,plain,(
% 4.58/1.03 spl53_53 | ~spl53_34 | ~spl53_52),
% 4.58/1.03 inference(avatar_split_clause,[],[f1007,f1004,f912,f1019])).
% 4.58/1.03 tff(f1004,plain,(
% 4.58/1.03 spl53_52 <=> ! [X0 : $tType,X1 : fun(X0,bool),X3 : X0] : (bot_bot(fun(X0,bool)) != X1 | ~pp(aa(X0,bool,X1,X3)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_52])])).
% 4.58/1.03 tff(f1007,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X3 : X0,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) != X1 | ~pp(aa(X0,bool,X1,X3))) ) | (~spl53_34 | ~spl53_52)),
% 4.58/1.03 inference(forward_demodulation,[],[f1005,f913])).
% 4.58/1.03 tff(f1005,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X3 : X0,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != X1 | ~pp(aa(X0,bool,X1,X3))) ) | ~spl53_52),
% 4.58/1.03 inference(avatar_component_clause,[],[f1004])).
% 4.58/1.03 tff(f1006,plain,(
% 4.58/1.03 spl53_52),
% 4.58/1.03 inference(avatar_split_clause,[],[f688,f1004])).
% 4.58/1.03 tff(f688,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X3 : X0,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != X1 | ~pp(aa(X0,bool,X1,X3))) )),
% 4.58/1.03 inference(forward_demodulation,[],[f491,f456])).
% 4.58/1.03 tff(f491,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X3)) | bot_bot(fun(X0,bool)) != collect(X0,X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f348])).
% 4.58/1.03 tff(f1002,plain,(
% 4.58/1.03 spl53_51),
% 4.58/1.03 inference(avatar_split_clause,[],[f638,f1000])).
% 4.58/1.03 tff(f1000,plain,(
% 4.58/1.03 spl53_51 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1)),X2 : X1] : (finite_fold_graph(X0,X1,X5,X4,X3,X2) | ~sP3(X1,X0,X4,X5,X2,X3))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_51])])).
% 4.58/1.03 tff(f638,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (finite_fold_graph(X0,X1,X5,X4,X3,X2) | ~sP3(X1,X0,X4,X5,X2,X3)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f435])).
% 4.58/1.03 tff(f998,plain,(
% 4.58/1.03 spl53_50),
% 4.58/1.03 inference(avatar_split_clause,[],[f499,f996])).
% 4.58/1.03 tff(f499,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : (hoare_1841697145triple(X0,sK14(X0,X1),sK15(X0,X1),sK16(X0,X1)) = X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f362])).
% 4.58/1.03 tff(f362,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : hoare_1841697145triple(X0,sK14(X0,X1),sK15(X0,X1),sK16(X0,X1)) = X1),
% 4.58/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f263,f361])).
% 4.58/1.03 tff(f361,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : (? [X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool))] : hoare_1841697145triple(X0,X2,X3,X4) = X1 => hoare_1841697145triple(X0,sK14(X0,X1),sK15(X0,X1),sK16(X0,X1)) = X1)),
% 4.58/1.03 introduced(choice_axiom,[])).
% 4.58/1.03 tff(f263,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : ? [X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool))] : hoare_1841697145triple(X0,X2,X3,X4) = X1),
% 4.58/1.03 inference(ennf_transformation,[],[f170])).
% 4.58/1.03 tff(f170,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : ~! [X2 : fun(X0,fun(state,bool)),X3 : com,X4 : fun(X0,fun(state,bool))] : hoare_1841697145triple(X0,X2,X3,X4) != X1),
% 4.58/1.03 inference(rectify,[],[f49])).
% 4.58/1.03 tff(f49,axiom,(
% 4.58/1.03 ! [X1 : $tType,X31 : hoare_28830079triple(X1)] : ~! [X37 : fun(X1,fun(state,bool)),X38 : com,X39 : fun(X1,fun(state,bool))] : hoare_1841697145triple(X1,X37,X38,X39) != X31),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_triple_Oexhaust)).
% 4.58/1.03 tff(f994,plain,(
% 4.58/1.03 spl53_49),
% 4.58/1.03 inference(avatar_split_clause,[],[f474,f992])).
% 4.58/1.03 tff(f474,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f156])).
% 4.58/1.03 tff(f156,plain,(
% 4.58/1.03 ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 4.58/1.03 inference(rectify,[],[f115])).
% 4.58/1.03 tff(f115,axiom,(
% 4.58/1.03 ! [X70 : bool,X68 : bool] : (pp(X70) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X68),X70)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U)).
% 4.58/1.03 tff(f990,plain,(
% 4.58/1.03 spl53_48),
% 4.58/1.03 inference(avatar_split_clause,[],[f473,f988])).
% 4.58/1.03 tff(f473,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f155])).
% 4.58/1.03 tff(f155,plain,(
% 4.58/1.03 ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 4.58/1.03 inference(rectify,[],[f114])).
% 4.58/1.03 tff(f114,axiom,(
% 4.58/1.03 ! [X70 : bool,X68 : bool] : (pp(X68) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X68),X70)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U)).
% 4.58/1.03 tff(f986,plain,(
% 4.58/1.03 spl53_47),
% 4.58/1.03 inference(avatar_split_clause,[],[f470,f984])).
% 4.58/1.03 tff(f470,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) | pp(X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f152])).
% 4.58/1.03 tff(f152,plain,(
% 4.58/1.03 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) | pp(X1))),
% 4.58/1.03 inference(rectify,[],[f123])).
% 4.58/1.03 tff(f123,axiom,(
% 4.58/1.03 ! [X70 : bool,X68 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X68),X70)) | pp(X68))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U)).
% 4.58/1.03 tff(f982,plain,(
% 4.58/1.03 spl53_46),
% 4.58/1.03 inference(avatar_split_clause,[],[f469,f980])).
% 4.58/1.03 tff(f469,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f151])).
% 4.58/1.03 tff(f151,plain,(
% 4.58/1.03 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X1))),
% 4.58/1.03 inference(rectify,[],[f124])).
% 4.58/1.03 tff(f124,axiom,(
% 4.58/1.03 ! [X68 : bool,X70 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X68),X70)) | ~pp(X70))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U)).
% 4.58/1.03 tff(f978,plain,(
% 4.58/1.03 spl53_45),
% 4.58/1.03 inference(avatar_split_clause,[],[f468,f976])).
% 4.58/1.03 tff(f468,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f150])).
% 4.58/1.03 tff(f150,plain,(
% 4.58/1.03 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1))),
% 4.58/1.03 inference(rectify,[],[f116])).
% 4.58/1.03 tff(f116,axiom,(
% 4.58/1.03 ! [X70 : bool,X68 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X68),X70)) | ~pp(X68))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U)).
% 4.58/1.03 tff(f974,plain,(
% 4.58/1.03 spl53_44),
% 4.58/1.03 inference(avatar_split_clause,[],[f467,f972])).
% 4.58/1.03 tff(f467,plain,(
% 4.58/1.03 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f149])).
% 4.58/1.03 tff(f149,plain,(
% 4.58/1.03 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1))),
% 4.58/1.03 inference(rectify,[],[f117])).
% 4.58/1.03 tff(f117,axiom,(
% 4.58/1.03 ! [X68 : bool,X70 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X68),X70)) | ~pp(X70))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U)).
% 4.58/1.03 tff(f970,plain,(
% 4.58/1.03 spl53_43 | ~spl53_2 | ~spl53_20 | ~spl53_34 | ~spl53_35),
% 4.58/1.03 inference(avatar_split_clause,[],[f948,f920,f912,f840,f757,f967])).
% 4.58/1.03 tff(f757,plain,(
% 4.58/1.03 spl53_2 <=> bot(bool)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_2])])).
% 4.58/1.03 tff(f948,plain,(
% 4.58/1.03 fFalse = bot_bot(bool) | (~spl53_2 | ~spl53_20 | ~spl53_34 | ~spl53_35)),
% 4.58/1.03 inference(forward_demodulation,[],[f947,f841])).
% 4.58/1.03 tff(f947,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (bot_bot(bool) = aa(X0,bool,combk(bool,X0,fFalse),X1)) ) | (~spl53_2 | ~spl53_34 | ~spl53_35)),
% 4.58/1.03 inference(forward_demodulation,[],[f945,f913])).
% 4.58/1.03 tff(f945,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (aa(X0,bool,bot_bot(fun(X0,bool)),X1) = bot_bot(bool)) ) | (~spl53_2 | ~spl53_35)),
% 4.58/1.03 inference(resolution,[],[f921,f759])).
% 4.58/1.03 tff(f759,plain,(
% 4.58/1.03 bot(bool) | ~spl53_2),
% 4.58/1.03 inference(avatar_component_clause,[],[f757])).
% 4.58/1.03 tff(f961,plain,(
% 4.58/1.03 spl53_42 | ~spl53_34 | ~spl53_39),
% 4.58/1.03 inference(avatar_split_clause,[],[f940,f937,f912,f959])).
% 4.58/1.03 tff(f937,plain,(
% 4.58/1.03 spl53_39 <=> ! [X1 : $tType,X0 : $tType,X4 : fun(X0,fun(X1,X1)),X3 : X1,X2 : X1] : (X2 = X3 | ~finite_fold_graph(X0,X1,X4,X3,bot_bot(fun(X0,bool)),X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_39])])).
% 4.58/1.03 tff(f940,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X1,X4 : fun(X0,fun(X1,X1))] : (~finite_fold_graph(X0,X1,X4,X3,combk(bool,X0,fFalse),X2) | X2 = X3) ) | (~spl53_34 | ~spl53_39)),
% 4.58/1.03 inference(forward_demodulation,[],[f938,f913])).
% 4.58/1.03 tff(f938,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X1,X4 : fun(X0,fun(X1,X1))] : (X2 = X3 | ~finite_fold_graph(X0,X1,X4,X3,bot_bot(fun(X0,bool)),X2)) ) | ~spl53_39),
% 4.58/1.03 inference(avatar_component_clause,[],[f937])).
% 4.58/1.03 tff(f952,plain,(
% 4.58/1.03 spl53_41 | ~spl53_34 | ~spl53_36),
% 4.58/1.03 inference(avatar_split_clause,[],[f927,f924,f912,f950])).
% 4.58/1.03 tff(f924,plain,(
% 4.58/1.03 spl53_36 <=> ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (bot_bot(fun(X0,bool)) != sK18(X0,X1) | ~sP0(X0,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_36])])).
% 4.58/1.03 tff(f927,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (combk(bool,X0,fFalse) != sK18(X0,X1) | ~sP0(X0,X1)) ) | (~spl53_34 | ~spl53_36)),
% 4.58/1.03 inference(forward_demodulation,[],[f925,f913])).
% 4.58/1.03 tff(f925,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (bot_bot(fun(X0,bool)) != sK18(X0,X1) | ~sP0(X0,X1)) ) | ~spl53_36),
% 4.58/1.03 inference(avatar_component_clause,[],[f924])).
% 4.58/1.03 tff(f944,plain,(
% 4.58/1.03 spl53_40),
% 4.58/1.03 inference(avatar_split_clause,[],[f654,f942])).
% 4.58/1.03 tff(f942,plain,(
% 4.58/1.03 spl53_40 <=> ! [X0 : $tType,X2 : X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_40])])).
% 4.58/1.03 tff(f654,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))) )),
% 4.58/1.03 inference(equality_resolution,[],[f515])).
% 4.58/1.03 tff(f515,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) | X1 != X2) )),
% 4.58/1.03 inference(cnf_transformation,[],[f184])).
% 4.58/1.03 tff(f184,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) | X1 != X2)),
% 4.58/1.03 inference(rectify,[],[f122])).
% 4.58/1.03 tff(f122,axiom,(
% 4.58/1.03 ! [X0 : $tType,X71 : X0,X72 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X72),X71)) | X71 != X72)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T)).
% 4.58/1.03 tff(f939,plain,(
% 4.58/1.03 spl53_39),
% 4.58/1.03 inference(avatar_split_clause,[],[f592,f937])).
% 4.58/1.03 tff(f592,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X1,X4 : fun(X0,fun(X1,X1))] : (X2 = X3 | ~finite_fold_graph(X0,X1,X4,X3,bot_bot(fun(X0,bool)),X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f305])).
% 4.58/1.03 tff(f305,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X1,X4 : fun(X0,fun(X1,X1))] : (X2 = X3 | ~finite_fold_graph(X0,X1,X4,X3,bot_bot(fun(X0,bool)),X2))),
% 4.58/1.03 inference(ennf_transformation,[],[f230])).
% 4.58/1.03 tff(f230,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X1,X4 : fun(X0,fun(X1,X1))] : (finite_fold_graph(X0,X1,X4,X3,bot_bot(fun(X0,bool)),X2) => X2 = X3)),
% 4.58/1.03 inference(rectify,[],[f87])).
% 4.58/1.03 tff(f87,axiom,(
% 4.58/1.03 ! [X1 : $tType,X2 : $tType,X26 : X2,X56 : X2,X53 : fun(X1,fun(X2,X2))] : (finite_fold_graph(X1,X2,X53,X56,bot_bot(fun(X1,bool)),X26) => X26 = X56)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_empty__fold__graphE)).
% 4.58/1.03 tff(f935,plain,(
% 4.58/1.03 spl53_38),
% 4.58/1.03 inference(avatar_split_clause,[],[f521,f933])).
% 4.58/1.03 tff(f521,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,sK18(X0,X1))) | ~sP0(X0,X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f366])).
% 4.58/1.03 tff(f931,plain,(
% 4.58/1.03 spl53_37 | ~spl53_7 | ~spl53_34),
% 4.58/1.03 inference(avatar_split_clause,[],[f917,f912,f780,f929])).
% 4.58/1.03 tff(f780,plain,(
% 4.58/1.03 spl53_7 <=> ! [X0 : $tType] : finite_finite1(X0,bot_bot(fun(X0,bool)))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_7])])).
% 4.58/1.03 tff(f917,plain,(
% 4.58/1.03 ( ! [X0 : $tType] : (finite_finite1(X0,combk(bool,X0,fFalse))) ) | (~spl53_7 | ~spl53_34)),
% 4.58/1.03 inference(superposition,[],[f781,f913])).
% 4.58/1.03 tff(f781,plain,(
% 4.58/1.03 ( ! [X0 : $tType] : (finite_finite1(X0,bot_bot(fun(X0,bool)))) ) | ~spl53_7),
% 4.58/1.03 inference(avatar_component_clause,[],[f780])).
% 4.58/1.03 tff(f926,plain,(
% 4.58/1.03 spl53_36),
% 4.58/1.03 inference(avatar_split_clause,[],[f519,f924])).
% 4.58/1.03 tff(f519,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (bot_bot(fun(X0,bool)) != sK18(X0,X1) | ~sP0(X0,X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f366])).
% 4.58/1.03 tff(f922,plain,(
% 4.58/1.03 spl53_35),
% 4.58/1.03 inference(avatar_split_clause,[],[f476,f920])).
% 4.58/1.03 tff(f476,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X0] : (bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) | ~bot(X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f257])).
% 4.58/1.03 tff(f257,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0] : bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) | ~bot(X1))),
% 4.58/1.03 inference(ennf_transformation,[],[f158])).
% 4.58/1.03 tff(f158,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType] : (bot(X1) => ! [X2 : X0] : bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2))),
% 4.58/1.03 inference(rectify,[],[f45])).
% 4.58/1.03 tff(f45,axiom,(
% 4.58/1.03 ! [X2 : $tType,X1 : $tType] : (bot(X1) => ! [X26 : X2] : aa(X2,X1,bot_bot(fun(X2,X1)),X26) = bot_bot(X1))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_bot__apply)).
% 4.58/1.03 tff(f914,plain,(
% 4.58/1.03 spl53_34 | ~spl53_14 | ~spl53_33),
% 4.58/1.03 inference(avatar_split_clause,[],[f910,f907,f811,f912])).
% 4.58/1.03 tff(f907,plain,(
% 4.58/1.03 spl53_33 <=> ! [X0 : $tType] : bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_33])])).
% 4.58/1.03 tff(f910,plain,(
% 4.58/1.03 ( ! [X0 : $tType] : (bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse)) ) | (~spl53_14 | ~spl53_33)),
% 4.58/1.03 inference(forward_demodulation,[],[f908,f812])).
% 4.58/1.03 tff(f908,plain,(
% 4.58/1.03 ( ! [X0 : $tType] : (bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse))) ) | ~spl53_33),
% 4.58/1.03 inference(avatar_component_clause,[],[f907])).
% 4.58/1.03 tff(f909,plain,(
% 4.58/1.03 spl53_33),
% 4.58/1.03 inference(avatar_split_clause,[],[f448,f907])).
% 4.58/1.03 tff(f448,plain,(
% 4.58/1.03 ( ! [X0 : $tType] : (bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f130])).
% 4.58/1.03 tff(f130,plain,(
% 4.58/1.03 ! [X0 : $tType] : bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse))),
% 4.58/1.03 inference(rectify,[],[f23])).
% 4.58/1.03 tff(f23,axiom,(
% 4.58/1.03 ! [X1 : $tType] : bot_bot(fun(X1,bool)) = collect(X1,combk(bool,X1,fFalse))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_empty__def)).
% 4.58/1.03 tff(f893,plain,(
% 4.58/1.03 spl53_32),
% 4.58/1.03 inference(avatar_split_clause,[],[f614,f891])).
% 4.58/1.03 tff(f891,plain,(
% 4.58/1.03 spl53_32 <=> ! [X2 : $tType,X4 : X2,X0 : X2,X3 : X2,X1 : X2] : (X0 = X1 | X0 = X4 | ~sP2(X2,X0,X1,X3,X4))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_32])])).
% 4.58/1.03 tff(f614,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (X0 = X1 | X0 = X4 | ~sP2(X2,X0,X1,X3,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f424])).
% 4.58/1.03 tff(f424,plain,(
% 4.58/1.03 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2,X4 : X2] : ((sP2(X2,X0,X1,X3,X4) | ((X0 != X1 | X3 != X4) & (X0 != X4 | X1 != X3))) & ((X0 = X1 & X3 = X4) | (X0 = X4 & X1 = X3) | ~sP2(X2,X0,X1,X3,X4)))),
% 4.58/1.03 inference(rectify,[],[f423])).
% 4.58/1.03 tff(f423,plain,(
% 4.58/1.03 ! [X3 : X0,X2 : X0,X0 : $tType,X4 : X0,X1 : X0] : ((sP2(X0,X3,X2,X4,X1) | ((X2 != X3 | X1 != X4) & (X1 != X3 | X2 != X4))) & ((X2 = X3 & X1 = X4) | (X1 = X3 & X2 = X4) | ~sP2(X0,X3,X2,X4,X1)))),
% 4.58/1.03 inference(flattening,[],[f422])).
% 4.58/1.03 tff(f422,plain,(
% 4.58/1.03 ! [X3 : X0,X2 : X0,X0 : $tType,X4 : X0,X1 : X0] : ((sP2(X0,X3,X2,X4,X1) | ((X2 != X3 | X1 != X4) & (X1 != X3 | X2 != X4))) & (((X2 = X3 & X1 = X4) | (X1 = X3 & X2 = X4)) | ~sP2(X0,X3,X2,X4,X1)))),
% 4.58/1.03 inference(nnf_transformation,[],[f327])).
% 4.58/1.03 tff(f889,plain,(
% 4.58/1.03 spl53_31),
% 4.58/1.03 inference(avatar_split_clause,[],[f613,f887])).
% 4.58/1.03 tff(f887,plain,(
% 4.58/1.03 spl53_31 <=> ! [X2 : $tType,X4 : X2,X0 : X2,X3 : X2,X1 : X2] : (X0 = X1 | X1 = X3 | ~sP2(X2,X0,X1,X3,X4))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_31])])).
% 4.58/1.03 tff(f613,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (X0 = X1 | X1 = X3 | ~sP2(X2,X0,X1,X3,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f424])).
% 4.58/1.03 tff(f885,plain,(
% 4.58/1.03 spl53_30),
% 4.58/1.03 inference(avatar_split_clause,[],[f612,f883])).
% 4.58/1.03 tff(f883,plain,(
% 4.58/1.03 spl53_30 <=> ! [X2 : $tType,X4 : X2,X0 : X2,X3 : X2,X1 : X2] : (X3 = X4 | X0 = X4 | ~sP2(X2,X0,X1,X3,X4))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_30])])).
% 4.58/1.03 tff(f612,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (X3 = X4 | X0 = X4 | ~sP2(X2,X0,X1,X3,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f424])).
% 4.58/1.03 tff(f881,plain,(
% 4.58/1.03 spl53_29),
% 4.58/1.03 inference(avatar_split_clause,[],[f611,f879])).
% 4.58/1.03 tff(f879,plain,(
% 4.58/1.03 spl53_29 <=> ! [X2 : $tType,X4 : X2,X0 : X2,X3 : X2,X1 : X2] : (X3 = X4 | X1 = X3 | ~sP2(X2,X0,X1,X3,X4))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_29])])).
% 4.58/1.03 tff(f611,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (X3 = X4 | X1 = X3 | ~sP2(X2,X0,X1,X3,X4)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f424])).
% 4.58/1.03 tff(f877,plain,(
% 4.58/1.03 spl53_28),
% 4.58/1.03 inference(avatar_split_clause,[],[f563,f875])).
% 4.58/1.03 tff(f875,plain,(
% 4.58/1.03 spl53_28 <=> ! [X0 : $tType,X3 : fun(hoare_28830079triple(X0),bool),X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,X2) | ~hoare_992312373derivs(X0,X1,X3) | ~hoare_992312373derivs(X0,X3,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_28])])).
% 4.58/1.03 tff(f563,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,X2) | ~hoare_992312373derivs(X0,X1,X3) | ~hoare_992312373derivs(X0,X3,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f290])).
% 4.58/1.03 tff(f290,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool),X2 : fun(hoare_28830079triple(X0),bool),X3 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,X2) | ~hoare_992312373derivs(X0,X1,X3) | ~hoare_992312373derivs(X0,X3,X2))),
% 4.58/1.03 inference(flattening,[],[f289])).
% 4.58/1.03 tff(f289,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool),X2 : fun(hoare_28830079triple(X0),bool),X3 : fun(hoare_28830079triple(X0),bool)] : ((hoare_992312373derivs(X0,X1,X2) | ~hoare_992312373derivs(X0,X1,X3)) | ~hoare_992312373derivs(X0,X3,X2))),
% 4.58/1.03 inference(ennf_transformation,[],[f212])).
% 4.58/1.03 tff(f212,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool),X2 : fun(hoare_28830079triple(X0),bool),X3 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,X2) => (hoare_992312373derivs(X0,X1,X3) => hoare_992312373derivs(X0,X1,X2)))),
% 4.58/1.03 inference(rectify,[],[f3])).
% 4.58/1.03 tff(f3,axiom,(
% 4.58/1.03 ! [X1 : $tType,X10 : fun(hoare_28830079triple(X1),bool),X11 : fun(hoare_28830079triple(X1),bool),X12 : fun(hoare_28830079triple(X1),bool)] : (hoare_992312373derivs(X1,X12,X11) => (hoare_992312373derivs(X1,X10,X12) => hoare_992312373derivs(X1,X10,X11)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cut)).
% 4.58/1.03 tff(f873,plain,(
% 4.58/1.03 spl53_27),
% 4.58/1.03 inference(avatar_split_clause,[],[f500,f871])).
% 4.58/1.03 tff(f500,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (~pp(aa(X0,bool,finite_fold1Set(X0,X2,bot_bot(fun(X0,bool))),X1))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f171])).
% 4.58/1.03 tff(f171,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0,X2 : fun(X0,fun(X0,X0))] : ~pp(aa(X0,bool,finite_fold1Set(X0,X2,bot_bot(fun(X0,bool))),X1))),
% 4.58/1.03 inference(rectify,[],[f71])).
% 4.58/1.03 tff(f71,axiom,(
% 4.58/1.03 ! [X1 : $tType,X26 : X1,X53 : fun(X1,fun(X1,X1))] : ~pp(aa(X1,bool,finite_fold1Set(X1,X53,bot_bot(fun(X1,bool))),X26))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_empty__fold1SetE)).
% 4.58/1.03 tff(f869,plain,(
% 4.58/1.03 spl53_26),
% 4.58/1.03 inference(avatar_split_clause,[],[f458,f867])).
% 4.58/1.03 tff(f458,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : X0] : (the(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1) )),
% 4.58/1.03 inference(cnf_transformation,[],[f140])).
% 4.58/1.03 tff(f140,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : X0] : the(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1),
% 4.58/1.03 inference(rectify,[],[f54])).
% 4.58/1.03 tff(f54,axiom,(
% 4.58/1.03 ! [X1 : $tType,X26 : X1] : the(X1,aa(X1,fun(X1,bool),fequal(X1),X26)) = X26),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_the__sym__eq__trivial)).
% 4.58/1.03 tff(f864,plain,(
% 4.58/1.03 spl53_24 | ~spl53_25 | ~spl53_8),
% 4.58/1.03 inference(avatar_split_clause,[],[f805,f784,f861,f858])).
% 4.58/1.03 tff(f805,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (fFalse != fTrue | fTrue = X0) ) | ~spl53_8),
% 4.58/1.03 inference(equality_factoring,[],[f785])).
% 4.58/1.03 tff(f854,plain,(
% 4.58/1.03 spl53_23),
% 4.58/1.03 inference(avatar_split_clause,[],[f575,f852])).
% 4.58/1.03 tff(f852,plain,(
% 4.58/1.03 spl53_23 <=> ! [X2 : com,X0 : com,X1 : com,X3 : com] : (X0 = X2 | semi(X1,X0) != semi(X3,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_23])])).
% 4.58/1.03 tff(f575,plain,(
% 4.58/1.03 ( ! [X2 : com,X3 : com,X0 : com,X1 : com] : (X0 = X2 | semi(X1,X0) != semi(X3,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f396])).
% 4.58/1.03 tff(f396,plain,(
% 4.58/1.03 ! [X0 : com,X1 : com,X2 : com,X3 : com] : ((semi(X1,X0) = semi(X3,X2) | X0 != X2 | X1 != X3) & ((X0 = X2 & X1 = X3) | semi(X1,X0) != semi(X3,X2)))),
% 4.58/1.03 inference(flattening,[],[f395])).
% 4.58/1.03 tff(f395,plain,(
% 4.58/1.03 ! [X0 : com,X1 : com,X2 : com,X3 : com] : ((semi(X1,X0) = semi(X3,X2) | (X0 != X2 | X1 != X3)) & ((X0 = X2 & X1 = X3) | semi(X1,X0) != semi(X3,X2)))),
% 4.58/1.03 inference(nnf_transformation,[],[f221])).
% 4.58/1.03 tff(f221,plain,(
% 4.58/1.03 ! [X0 : com,X1 : com,X2 : com,X3 : com] : (semi(X1,X0) = semi(X3,X2) <=> (X0 = X2 & X1 = X3))),
% 4.58/1.03 inference(rectify,[],[f50])).
% 4.58/1.03 tff(f50,axiom,(
% 4.58/1.03 ! [X40 : com,X41 : com,X42 : com,X43 : com] : (semi(X43,X42) = semi(X41,X40) <=> (X40 = X42 & X41 = X43))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_com_Osimps_I3_J)).
% 4.58/1.03 tff(f850,plain,(
% 4.58/1.03 spl53_22),
% 4.58/1.03 inference(avatar_split_clause,[],[f574,f848])).
% 4.58/1.03 tff(f848,plain,(
% 4.58/1.03 spl53_22 <=> ! [X0 : com,X3 : com,X2 : com,X1 : com] : (X1 = X3 | semi(X1,X0) != semi(X3,X2))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_22])])).
% 4.58/1.03 tff(f574,plain,(
% 4.58/1.03 ( ! [X2 : com,X3 : com,X0 : com,X1 : com] : (X1 = X3 | semi(X1,X0) != semi(X3,X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f396])).
% 4.58/1.03 tff(f846,plain,(
% 4.58/1.03 spl53_21),
% 4.58/1.03 inference(avatar_split_clause,[],[f559,f844])).
% 4.58/1.03 tff(f559,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : (finite_fold_graph(X0,X1,X3,X2,bot_bot(fun(X0,bool)),X2)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f206])).
% 4.58/1.03 tff(f206,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : finite_fold_graph(X0,X1,X3,X2,bot_bot(fun(X0,bool)),X2)),
% 4.58/1.03 inference(rectify,[],[f88])).
% 4.58/1.03 tff(f88,axiom,(
% 4.58/1.03 ! [X1 : $tType,X2 : $tType,X56 : X2,X53 : fun(X1,fun(X2,X2))] : finite_fold_graph(X1,X2,X53,X56,bot_bot(fun(X1,bool)),X56)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_fold__graph_OemptyI)).
% 4.58/1.03 tff(f842,plain,(
% 4.58/1.03 spl53_20),
% 4.58/1.03 inference(avatar_split_clause,[],[f558,f840])).
% 4.58/1.03 tff(f558,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (aa(X0,X1,combk(X1,X0,X3),X2) = X3) )),
% 4.58/1.03 inference(cnf_transformation,[],[f205])).
% 4.58/1.03 tff(f205,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : aa(X0,X1,combk(X1,X0,X3),X2) = X3),
% 4.58/1.03 inference(rectify,[],[f111])).
% 4.58/1.03 tff(f111,axiom,(
% 4.58/1.03 ! [X1 : $tType,X0 : $tType,X70 : X1,X68 : X0] : aa(X1,X0,combk(X0,X1,X68),X70) = X68),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U)).
% 4.58/1.03 tff(f833,plain,(
% 4.58/1.03 spl53_19),
% 4.58/1.03 inference(avatar_split_clause,[],[f518,f831])).
% 4.58/1.03 tff(f831,plain,(
% 4.58/1.03 spl53_19 <=> ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (finite_finite1(X0,sK18(X0,X1)) | ~sP0(X0,X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_19])])).
% 4.58/1.03 tff(f518,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (finite_finite1(X0,sK18(X0,X1)) | ~sP0(X0,X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f366])).
% 4.58/1.03 tff(f829,plain,(
% 4.58/1.03 spl53_18),
% 4.58/1.03 inference(avatar_split_clause,[],[f478,f827])).
% 4.58/1.03 tff(f827,plain,(
% 4.58/1.03 spl53_18 <=> ! [X1 : $tType,X0 : $tType] : (finite_finite(fun(X0,X1)) | ~finite_finite(X0) | ~finite_finite(X1))),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_18])])).
% 4.58/1.03 tff(f478,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType] : (finite_finite(fun(X0,X1)) | ~finite_finite(X0) | ~finite_finite(X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f260])).
% 4.58/1.03 tff(f260,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType] : (finite_finite(fun(X0,X1)) | ~finite_finite(X0) | ~finite_finite(X1))),
% 4.58/1.03 inference(flattening,[],[f259])).
% 4.58/1.03 tff(f259,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType] : (finite_finite(fun(X0,X1)) | (~finite_finite(X0) | ~finite_finite(X1)))),
% 4.58/1.03 inference(ennf_transformation,[],[f160])).
% 4.58/1.03 tff(f160,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X0) & finite_finite(X1)) => finite_finite(fun(X0,X1)))),
% 4.58/1.03 inference(rectify,[],[f101])).
% 4.58/1.03 tff(f101,axiom,(
% 4.58/1.03 ! [X66 : $tType,X67 : $tType] : ((finite_finite(X66) & finite_finite(X67)) => finite_finite(fun(X66,X67)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite)).
% 4.58/1.03 tff(f825,plain,(
% 4.58/1.03 spl53_17),
% 4.58/1.03 inference(avatar_split_clause,[],[f457,f823])).
% 4.58/1.03 tff(f457,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,bot_bot(fun(hoare_28830079triple(X0),bool)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f139])).
% 4.58/1.03 tff(f139,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : hoare_992312373derivs(X0,X1,bot_bot(fun(hoare_28830079triple(X0),bool)))),
% 4.58/1.03 inference(rectify,[],[f2])).
% 4.58/1.03 tff(f2,axiom,(
% 4.58/1.03 ! [X1 : $tType,X10 : fun(hoare_28830079triple(X1),bool)] : hoare_992312373derivs(X1,X10,bot_bot(fun(hoare_28830079triple(X1),bool)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_empty)).
% 4.58/1.03 tff(f821,plain,(
% 4.58/1.03 spl53_16),
% 4.58/1.03 inference(avatar_split_clause,[],[f451,f819])).
% 4.58/1.03 tff(f451,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (~pp(X0) | ~pp(aa(bool,bool,fNot,X0))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f133])).
% 4.58/1.03 tff(f133,plain,(
% 4.58/1.03 ! [X0 : bool] : (~pp(X0) | ~pp(aa(bool,bool,fNot,X0)))),
% 4.58/1.03 inference(rectify,[],[f107])).
% 4.58/1.03 tff(f107,axiom,(
% 4.58/1.03 ! [X68 : bool] : (~pp(X68) | ~pp(aa(bool,bool,fNot,X68)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U)).
% 4.58/1.03 tff(f817,plain,(
% 4.58/1.03 spl53_15),
% 4.58/1.03 inference(avatar_split_clause,[],[f449,f815])).
% 4.58/1.03 tff(f449,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f131])).
% 4.58/1.03 tff(f131,plain,(
% 4.58/1.03 ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0))),
% 4.58/1.03 inference(rectify,[],[f108])).
% 4.58/1.03 tff(f108,axiom,(
% 4.58/1.03 ! [X68 : bool] : (pp(aa(bool,bool,fNot,X68)) | pp(X68))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U)).
% 4.58/1.03 tff(f813,plain,(
% 4.58/1.03 spl53_14),
% 4.58/1.03 inference(avatar_split_clause,[],[f456,f811])).
% 4.58/1.03 tff(f809,plain,(
% 4.58/1.03 spl53_13 | spl53_1 | ~spl53_8),
% 4.58/1.03 inference(avatar_split_clause,[],[f804,f784,f752,f807])).
% 4.58/1.03 tff(f804,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | (spl53_1 | ~spl53_8)),
% 4.58/1.03 inference(superposition,[],[f754,f785])).
% 4.58/1.03 tff(f802,plain,(
% 4.58/1.03 spl53_12),
% 4.58/1.03 inference(avatar_split_clause,[],[f676,f800])).
% 4.58/1.03 tff(f800,plain,(
% 4.58/1.03 spl53_12 <=> ! [X2 : $tType,X4 : X2,X3 : X2] : sP2(X2,X4,X3,X3,X4)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_12])])).
% 4.58/1.03 tff(f676,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X3 : X2,X4 : X2] : (sP2(X2,X4,X3,X3,X4)) )),
% 4.58/1.03 inference(equality_resolution,[],[f675])).
% 4.58/1.03 tff(f675,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X3 : X2,X1 : X2,X4 : X2] : (sP2(X2,X4,X1,X3,X4) | X1 != X3) )),
% 4.58/1.03 inference(equality_resolution,[],[f615])).
% 4.58/1.03 tff(f615,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (sP2(X2,X0,X1,X3,X4) | X0 != X4 | X1 != X3) )),
% 4.58/1.03 inference(cnf_transformation,[],[f424])).
% 4.58/1.03 tff(f798,plain,(
% 4.58/1.03 spl53_11),
% 4.58/1.03 inference(avatar_split_clause,[],[f674,f796])).
% 4.58/1.03 tff(f796,plain,(
% 4.58/1.03 spl53_11 <=> ! [X2 : $tType,X4 : X2,X1 : X2] : sP2(X2,X1,X1,X4,X4)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_11])])).
% 4.58/1.03 tff(f674,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X1 : X2,X4 : X2] : (sP2(X2,X1,X1,X4,X4)) )),
% 4.58/1.03 inference(equality_resolution,[],[f673])).
% 4.58/1.03 tff(f673,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X3 : X2,X1 : X2,X4 : X2] : (sP2(X2,X1,X1,X3,X4) | X3 != X4) )),
% 4.58/1.03 inference(equality_resolution,[],[f616])).
% 4.58/1.03 tff(f616,plain,(
% 4.58/1.03 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (sP2(X2,X0,X1,X3,X4) | X0 != X1 | X3 != X4) )),
% 4.58/1.03 inference(cnf_transformation,[],[f424])).
% 4.58/1.03 tff(f794,plain,(
% 4.58/1.03 spl53_10),
% 4.58/1.03 inference(avatar_split_clause,[],[f670,f792])).
% 4.58/1.03 tff(f792,plain,(
% 4.58/1.03 spl53_10 <=> ! [X1 : $tType,X4 : fun(X1,bool),X2 : fun(X1,bool),X3 : X1] : sP1(X1,X3,X2,X3,X4)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_10])])).
% 4.58/1.03 tff(f670,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X4 : fun(X1,bool)] : (sP1(X1,X3,X2,X3,X4)) )),
% 4.58/1.03 inference(equality_resolution,[],[f597])).
% 4.58/1.03 tff(f597,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (sP1(X1,X0,X2,X3,X4) | X0 != X3) )),
% 4.58/1.03 inference(cnf_transformation,[],[f412])).
% 4.58/1.03 tff(f790,plain,(
% 4.58/1.03 spl53_9),
% 4.58/1.03 inference(avatar_split_clause,[],[f475,f788])).
% 4.58/1.03 tff(f475,plain,(
% 4.58/1.03 ( ! [X1 : $tType,X0 : $tType] : (bot(fun(X0,X1)) | ~bot(X1)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f256])).
% 4.58/1.03 tff(f256,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType] : (bot(fun(X0,X1)) | ~bot(X1))),
% 4.58/1.03 inference(ennf_transformation,[],[f157])).
% 4.58/1.03 tff(f157,plain,(
% 4.58/1.03 ! [X0 : $tType,X1 : $tType] : (bot(X1) => bot(fun(X0,X1)))),
% 4.58/1.03 inference(rectify,[],[f102])).
% 4.58/1.03 tff(f102,axiom,(
% 4.58/1.03 ! [X66 : $tType,X67 : $tType] : (bot(X67) => bot(fun(X66,X67)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Obot)).
% 4.58/1.03 tff(f786,plain,(
% 4.58/1.03 spl53_8),
% 4.58/1.03 inference(avatar_split_clause,[],[f450,f784])).
% 4.58/1.03 tff(f450,plain,(
% 4.58/1.03 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) )),
% 4.58/1.03 inference(cnf_transformation,[],[f132])).
% 4.58/1.03 tff(f132,plain,(
% 4.58/1.03 ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 4.58/1.03 inference(rectify,[],[f120])).
% 4.58/1.03 tff(f120,axiom,(
% 4.58/1.03 ! [X68 : bool] : (fFalse = X68 | fTrue = X68)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T)).
% 4.58/1.03 tff(f782,plain,(
% 4.58/1.03 spl53_7),
% 4.58/1.03 inference(avatar_split_clause,[],[f447,f780])).
% 4.58/1.03 tff(f447,plain,(
% 4.58/1.03 ( ! [X0 : $tType] : (finite_finite1(X0,bot_bot(fun(X0,bool)))) )),
% 4.58/1.03 inference(cnf_transformation,[],[f129])).
% 4.58/1.03 tff(f129,plain,(
% 4.58/1.03 ! [X0 : $tType] : finite_finite1(X0,bot_bot(fun(X0,bool)))),
% 4.58/1.03 inference(rectify,[],[f81])).
% 4.58/1.03 tff(f81,axiom,(
% 4.58/1.03 ! [X1 : $tType] : finite_finite1(X1,bot_bot(fun(X1,bool)))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_finite_OemptyI)).
% 4.58/1.03 tff(f778,plain,(
% 4.58/1.03 spl53_6),
% 4.58/1.03 inference(avatar_split_clause,[],[f454,f776])).
% 4.58/1.03 tff(f776,plain,(
% 4.58/1.03 spl53_6 <=> ! [X0 : com,X1 : com] : skip != semi(X1,X0)),
% 4.58/1.03 introduced(avatar_definition,[new_symbols(naming,[spl53_6])])).
% 4.58/1.03 tff(f454,plain,(
% 4.58/1.03 ( ! [X0 : com,X1 : com] : (skip != semi(X1,X0)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f136])).
% 4.58/1.03 tff(f136,plain,(
% 4.58/1.03 ! [X0 : com,X1 : com] : skip != semi(X1,X0)),
% 4.58/1.03 inference(rectify,[],[f51])).
% 4.58/1.03 tff(f51,axiom,(
% 4.58/1.03 ! [X44 : com,X45 : com] : skip != semi(X45,X44)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_com_Osimps_I13_J)).
% 4.58/1.03 tff(f774,plain,(
% 4.58/1.03 spl53_5),
% 4.58/1.03 inference(avatar_split_clause,[],[f452,f772])).
% 4.58/1.03 tff(f452,plain,(
% 4.58/1.03 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite(X0)) )),
% 4.58/1.03 inference(cnf_transformation,[],[f254])).
% 4.58/1.03 tff(f254,plain,(
% 4.58/1.03 ! [X0 : $tType] : (! [X1 : fun(X0,bool)] : finite_finite1(X0,X1) | ~finite_finite(X0))),
% 4.58/1.03 inference(ennf_transformation,[],[f134])).
% 4.58/1.03 tff(f134,plain,(
% 4.58/1.03 ! [X0 : $tType] : (finite_finite(X0) => ! [X1 : fun(X0,bool)] : finite_finite1(X0,X1))),
% 4.58/1.03 inference(rectify,[],[f75])).
% 4.58/1.03 tff(f75,axiom,(
% 4.58/1.03 ! [X1 : $tType] : (finite_finite(X1) => ! [X25 : fun(X1,bool)] : finite_finite1(X1,X25))),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_finite__code)).
% 4.58/1.03 tff(f770,plain,(
% 4.58/1.03 spl53_4),
% 4.58/1.03 inference(avatar_split_clause,[],[f446,f767])).
% 4.58/1.03 tff(f446,plain,(
% 4.58/1.03 pp(fTrue)),
% 4.58/1.03 inference(cnf_transformation,[],[f106])).
% 4.58/1.03 tff(f106,axiom,(
% 4.58/1.03 pp(fTrue)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U)).
% 4.58/1.03 tff(f765,plain,(
% 4.58/1.03 spl53_3),
% 4.58/1.03 inference(avatar_split_clause,[],[f445,f762])).
% 4.58/1.03 tff(f445,plain,(
% 4.58/1.03 finite_finite(bool)),
% 4.58/1.03 inference(cnf_transformation,[],[f103])).
% 4.58/1.03 tff(f103,axiom,(
% 4.58/1.03 finite_finite(bool)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite)).
% 4.58/1.03 tff(f760,plain,(
% 4.58/1.03 spl53_2),
% 4.58/1.03 inference(avatar_split_clause,[],[f444,f757])).
% 4.58/1.03 tff(f444,plain,(
% 4.58/1.03 bot(bool)),
% 4.58/1.03 inference(cnf_transformation,[],[f104])).
% 4.58/1.03 tff(f104,axiom,(
% 4.58/1.03 bot(bool)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot)).
% 4.58/1.03 tff(f755,plain,(
% 4.58/1.03 ~spl53_1),
% 4.58/1.03 inference(avatar_split_clause,[],[f442,f752])).
% 4.58/1.03 tff(f442,plain,(
% 4.58/1.03 ~pp(fFalse)),
% 4.58/1.03 inference(cnf_transformation,[],[f119])).
% 4.58/1.03 tff(f119,axiom,(
% 4.58/1.03 ~pp(fFalse)),
% 4.58/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U)).
% 4.58/1.03 % SZS output end Proof for theBenchmark
% 4.58/1.03 % (8376)------------------------------
% 4.58/1.03 % (8376)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 4.58/1.03 % (8376)Termination reason: Refutation
% 4.58/1.03
% 4.58/1.03 % (8376)Memory used [KB]: 8389
% 4.58/1.03 % (8376)Time elapsed: 0.626 s
% 4.58/1.03 % (8376)Instructions burned: 1789 (million)
% 4.58/1.03 % (8376)------------------------------
% 4.58/1.03 % (8376)------------------------------
% 4.58/1.03 % (8371)Success in time 0.656 s
%------------------------------------------------------------------------------