TSTP Solution File: SWW508_5 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW508_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 : n018.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 17:35:25 EDT 2024
% Result : Theorem 0.19s 0.56s
% Output : Refutation 1.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW508_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35 % Computer : n018.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Apr 30 03:23:28 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % (5592)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.37 % (5595)WARNING: value z3 for option sas not known
% 0.12/0.37 % (5595)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)
% 0.12/0.38 % (5593)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.38 % (5596)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.38 % (5594)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.38 % (5597)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)
% 0.12/0.38 % (5598)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)
% 0.12/0.38 % (5599)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)
% 0.12/0.39 % (5599)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.39 % Exception at run slice level
% 0.12/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.39 % Exception at run slice level
% 0.12/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.39 % Exception at run slice level
% 0.12/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.40 % (5600)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.12/0.40 % (5601)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)
% 0.12/0.41 % (5602)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)
% 0.12/0.41 % (5600)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.41 % (5601)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.41 % Exception at run slice level
% 0.12/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.43 % (5603)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)
% 0.19/0.53 % (5597)First to succeed.
% 0.19/0.56 % (5597)Refutation found. Thanks to Tanya!
% 0.19/0.56 % SZS status Theorem for theBenchmark
% 0.19/0.56 % SZS output start Proof for theBenchmark
% 0.19/0.56 tff(type_def_5, type, a: $tType).
% 0.19/0.56 tff(type_def_6, type, com: $tType).
% 0.19/0.56 tff(type_def_7, type, loc: $tType).
% 0.19/0.56 tff(type_def_8, type, pname: $tType).
% 0.19/0.56 tff(type_def_9, type, state: $tType).
% 0.19/0.56 tff(type_def_10, type, vname: $tType).
% 0.19/0.56 tff(type_def_11, type, bool: $tType).
% 0.19/0.56 tff(type_def_12, type, hoare_28830079triple: $tType > $tType).
% 0.19/0.56 tff(type_def_13, type, nat: $tType).
% 0.19/0.56 tff(type_def_14, type, fun: ($tType * $tType) > $tType).
% 0.19/0.56 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,X1) * fun(X2,X0)) > fun(X2,X1))).
% 0.19/0.56 tff(func_def_1, type, combc: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * X1) > fun(X0,X2))).
% 0.19/0.56 tff(func_def_2, type, combk: !>[X0: $tType, X1: $tType]:((X0) > fun(X1,X0))).
% 0.19/0.56 tff(func_def_3, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * fun(X0,X1)) > fun(X0,X2))).
% 0.19/0.56 tff(func_def_4, type, skip: com).
% 0.19/0.56 tff(func_def_5, type, semi: (com * com) > com).
% 0.19/0.56 tff(func_def_6, type, com_case: !>[X0: $tType]:((X0 * fun(vname,fun(fun(state,nat),X0)) * fun(loc,fun(fun(state,nat),fun(com,X0))) * fun(com,fun(com,X0)) * fun(fun(state,bool),fun(com,fun(com,X0))) * fun(fun(state,bool),fun(com,X0)) * fun(pname,X0) * fun(vname,fun(pname,fun(fun(state,nat),X0))) * com) > X0)).
% 0.19/0.56 tff(func_def_7, type, minus_minus: !>[X0: $tType]:((X0 * X0) > X0)).
% 0.19/0.56 tff(func_def_8, type, hoare_1841697145triple: !>[X0: $tType]:((fun(X0,fun(state,bool)) * com * fun(X0,fun(state,bool))) > hoare_28830079triple(X0))).
% 0.19/0.56 tff(func_def_9, 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)).
% 0.19/0.56 tff(func_def_10, 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)).
% 0.19/0.56 tff(func_def_11, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.19/0.56 tff(func_def_12, type, collect: !>[X0: $tType]:((fun(X0,bool)) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_13, type, insert: !>[X0: $tType]:((X0 * fun(X0,bool)) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_14, type, the_elem: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 0.19/0.56 tff(func_def_15, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 0.19/0.56 tff(func_def_16, type, fFalse: bool).
% 0.19/0.56 tff(func_def_17, type, fNot: fun(bool,bool)).
% 0.19/0.56 tff(func_def_18, type, fTrue: bool).
% 0.19/0.56 tff(func_def_19, type, fconj: fun(bool,fun(bool,bool))).
% 0.19/0.56 tff(func_def_20, type, fdisj: fun(bool,fun(bool,bool))).
% 0.19/0.56 tff(func_def_21, type, fequal: !>[X0: $tType]:(fun(X0,fun(X0,bool)))).
% 0.19/0.56 tff(func_def_22, type, fimplies: fun(bool,fun(bool,bool))).
% 0.19/0.56 tff(func_def_23, type, member: !>[X0: $tType]:(fun(X0,fun(fun(X0,bool),bool)))).
% 0.19/0.56 tff(func_def_24, type, g: fun(hoare_28830079triple(a),bool)).
% 0.19/0.56 tff(func_def_25, type, p1: fun(a,fun(state,bool))).
% 0.19/0.56 tff(func_def_26, type, q1: fun(a,fun(state,bool))).
% 0.19/0.56 tff(func_def_27, type, c: com).
% 0.19/0.56 tff(func_def_28, type, sK3: a).
% 0.19/0.56 tff(func_def_29, type, sK4: state).
% 0.19/0.56 tff(func_def_30, type, sK5: (fun(a,fun(state,bool)) * fun(a,fun(state,bool))) > state).
% 0.19/0.56 tff(func_def_31, type, sK6: (state * state) > a).
% 0.19/0.56 tff(func_def_32, type, sK7: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 0.19/0.56 tff(func_def_33, type, sK8: !>[X0: $tType]:((fun(X0,bool)) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_34, type, sK9: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 0.19/0.56 tff(func_def_35, type, sK10: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 0.19/0.56 tff(func_def_36, type, sK11: !>[X0: $tType]:((fun(X0,bool)) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_37, type, sK12: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 0.19/0.56 tff(func_def_38, type, sK13: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 0.19/0.56 tff(func_def_39, type, sK14: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 0.19/0.56 tff(func_def_40, type, sK15: !>[X0: $tType]:((fun(X0,bool)) > X0)).
% 0.19/0.56 tff(func_def_41, type, sK16: !>[X0: $tType]:((hoare_28830079triple(X0)) > fun(X0,fun(state,bool)))).
% 0.19/0.56 tff(func_def_42, type, sK17: !>[X0: $tType]:((hoare_28830079triple(X0)) > com)).
% 0.19/0.56 tff(func_def_43, type, sK18: !>[X0: $tType]:((hoare_28830079triple(X0)) > fun(X0,fun(state,bool)))).
% 0.19/0.56 tff(func_def_44, type, sK19: !>[X0: $tType]:((fun(X0,fun(X0,X0)) * fun(X0,bool)) > X0)).
% 0.19/0.56 tff(func_def_45, type, sK20: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > X0)).
% 0.19/0.56 tff(func_def_46, type, sK21: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_47, type, sK22: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > X0)).
% 0.19/0.56 tff(func_def_48, type, sK23: !>[X0: $tType]:((fun(fun(X0,bool),bool)) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_49, type, sK24: !>[X0: $tType]:((fun(X0,bool) * X0) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_50, type, sK25: !>[X0: $tType]:((fun(X0,bool) * X0) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_51, type, sK26: !>[X0: $tType, X1: $tType]:((fun(X1,X0) * fun(X1,X0)) > X1)).
% 0.19/0.56 tff(func_def_52, type, sK27: !>[X0: $tType]:((X0 * fun(X0,bool) * fun(X0,fun(X0,X0))) > X0)).
% 0.19/0.56 tff(func_def_53, type, sK28: !>[X0: $tType]:((X0 * fun(X0,bool) * fun(X0,fun(X0,X0))) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_54, type, sK29: !>[X0: $tType]:((X0 * fun(X0,bool) * fun(X0,fun(X0,X0))) > X0)).
% 0.19/0.56 tff(func_def_55, type, sK30: !>[X0: $tType]:((X0 * fun(X0,bool) * X0 * fun(X0,fun(X0,X0))) > X0)).
% 0.19/0.56 tff(func_def_56, type, sK31: !>[X0: $tType]:((X0 * fun(X0,bool) * X0 * fun(X0,fun(X0,X0))) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_57, type, sK32: !>[X0: $tType]:((X0 * fun(X0,bool) * X0 * fun(X0,bool)) > fun(X0,bool))).
% 0.19/0.56 tff(func_def_58, type, sK33: !>[X0: $tType]:((fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool))) > X0)).
% 0.19/0.56 tff(func_def_59, type, sK34: !>[X0: $tType]:((fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool))) > state)).
% 0.19/0.56 tff(func_def_60, type, sK35: !>[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)).
% 0.19/0.56 tff(func_def_61, type, sK36: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(X0,X0)) * X0 * fun(X1,bool)) > X1)).
% 0.19/0.56 tff(func_def_62, type, sK37: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(X0,X0)) * X0 * fun(X1,bool)) > fun(X1,bool))).
% 0.19/0.56 tff(func_def_63, type, sK38: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(X0,X0)) * X0 * fun(X1,bool)) > X0)).
% 0.19/0.56 tff(pred_def_1, type, cl_Groups_Ominus: !>[X0: $tType]:($o)).
% 0.19/0.56 tff(pred_def_2, type, bot: !>[X0: $tType]:($o)).
% 0.19/0.56 tff(pred_def_3, type, finite_finite: !>[X0: $tType]:($o)).
% 0.19/0.56 tff(pred_def_4, type, finite_finite1: !>[X0: $tType]:((fun(X0,bool)) > $o)).
% 0.19/0.56 tff(pred_def_5, type, finite_fold1Set: !>[X0: $tType]:((fun(X0,fun(X0,X0)) * fun(X0,bool) * X0) > $o)).
% 0.19/0.56 tff(pred_def_6, type, finite_fold_graph: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X1)) * X1 * fun(X0,bool) * X1) > $o)).
% 0.19/0.56 tff(pred_def_7, type, finite_folding_one: !>[X0: $tType]:((fun(X0,fun(X0,X0)) * fun(fun(X0,bool),X0)) > $o)).
% 0.19/0.56 tff(pred_def_8, type, hoare_992312373derivs: !>[X0: $tType]:((fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool)) > $o)).
% 0.19/0.56 tff(pred_def_9, type, inv_imagep: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1) > $o)).
% 0.19/0.56 tff(pred_def_10, type, pp: bool > $o).
% 0.19/0.56 tff(pred_def_11, type, p: (a * state) > $o).
% 0.19/0.56 tff(pred_def_12, type, q: (a * state) > $o).
% 0.19/0.56 tff(pred_def_13, type, sP0: !>[X0: $tType]:((X0 * fun(X0,bool) * X0 * fun(X0,bool)) > $o)).
% 0.19/0.56 tff(pred_def_14, type, sP1: !>[X0: $tType]:((X0 * X0 * X0 * X0) > $o)).
% 0.19/0.56 tff(pred_def_15, type, sP2: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(X0,X0)) * X0 * fun(X1,bool)) > $o)).
% 0.19/0.56 tff(f3526,plain,(
% 0.19/0.56 $false),
% 0.19/0.56 inference(avatar_sat_refutation,[],[f835,f840,f845,f850,f855,f860,f864,f868,f872,f876,f880,f884,f888,f892,f896,f903,f907,f911,f915,f919,f923,f927,f934,f938,f944,f948,f955,f959,f963,f971,f975,f979,f983,f987,f1001,f1006,f1014,f1019,f1024,f1028,f1033,f1037,f1042,f1046,f1052,f1056,f1064,f1073,f1080,f1084,f1089,f1094,f1100,f1105,f1111,f1116,f1122,f1127,f1133,f1138,f1143,f1148,f1154,f1158,f1162,f1166,f1175,f1182,f1186,f1193,f1198,f1203,f1211,f1216,f1223,f1228,f1232,f1239,f1244,f1249,f1255,f1260,f1265,f1269,f1273,f1278,f1305,f1310,f1318,f1325,f1330,f1334,f1338,f1352,f1357,f1362,f1366,f1371,f1376,f1382,f1390,f1394,f1422,f1426,f1448,f1453,f1458,f1466,f1471,f1475,f1485,f1489,f1509,f1513,f1532,f1536,f1568,f1574,f1583,f1589,f1598,f1604,f1608,f1617,f1622,f1627,f1631,f1659,f1665,f1960,f1965,f1980,f1985,f1996,f2001,f2012,f2016,f2021,f2026,f2030,f2034,f2038,f2042,f2046,f2119,f2135,f2141,f2155,f2161,f2165,f2175,f2180,f2185,f2191,f2203,f2209,f2213,f2225,f2231,f2242,f2257,f2263,f2284,f2315,f2337,f2353,f2357,f2371,f2377,f2382,f2409,f2415,f2432,f2437,f2454,f2460,f2477,f2482,f2492,f2496,f2501,f2505,f2539,f2553,f2558,f2564,f2574,f2586,f2591,f2595,f2614,f2620,f2627,f2639,f2646,f2672,f2676,f2680,f2685,f2690,f2709,f2714,f2733,f2739,f2746,f2753,f2779,f2788,f2794,f2816,f2820,f2826,f2831,f2837,f2866,f2873,f2898,f2913,f2932,f2937,f2961,f2966,f2973,f3006,f3012,f3016,f3055,f3062,f3074,f3081,f3106,f3113,f3162,f3171,f3210,f3218,f3245,f3252,f3290,f3294,f3301,f3312,f3318,f3324,f3332,f3340,f3358,f3366,f3372,f3380,f3388,f3396,f3402,f3409,f3413,f3418,f3426,f3432,f3438,f3454,f3461,f3468,f3475,f3485,f3493,f3506,f3514,f3525])).
% 0.19/0.56 tff(f3525,plain,(
% 0.19/0.56 ~spl39_1 | spl39_197 | ~spl39_255),
% 0.19/0.56 inference(avatar_split_clause,[],[f3462,f3407,f2669,f832])).
% 0.19/0.56 tff(f832,plain,(
% 0.19/0.56 spl39_1 <=> p(sK3,sK4)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_1])])).
% 0.19/0.56 tff(f2669,plain,(
% 0.19/0.56 spl39_197 <=> q(sK3,sK5(p1,q1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_197])])).
% 0.19/0.56 tff(f3407,plain,(
% 0.19/0.56 spl39_255 <=> ! [X0 : a] : (q(X0,sK5(p1,q1)) | ~p(X0,sK4))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_255])])).
% 0.19/0.56 tff(f3462,plain,(
% 0.19/0.56 ~p(sK3,sK4) | (spl39_197 | ~spl39_255)),
% 0.19/0.56 inference(resolution,[],[f3408,f2671])).
% 0.19/0.56 tff(f2671,plain,(
% 0.19/0.56 ~q(sK3,sK5(p1,q1)) | spl39_197),
% 0.19/0.56 inference(avatar_component_clause,[],[f2669])).
% 0.19/0.56 tff(f3408,plain,(
% 0.19/0.56 ( ! [X0 : a] : (q(X0,sK5(p1,q1)) | ~p(X0,sK4)) ) | ~spl39_255),
% 0.19/0.56 inference(avatar_component_clause,[],[f3407])).
% 0.19/0.56 tff(f3514,plain,(
% 0.19/0.56 spl39_268 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_267),
% 0.19/0.56 inference(avatar_split_clause,[],[f3510,f3504,f2777,f1004,f901,f3512])).
% 0.19/0.56 tff(f3512,plain,(
% 0.19/0.56 spl39_268 <=> ! [X0 : $tType,X7 : 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,X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))),combk(bool,hoare_28830079triple(X0),fFalse))) | ~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),combk(bool,hoare_28830079triple(X0),fFalse))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_268])])).
% 0.19/0.56 tff(f901,plain,(
% 0.19/0.56 spl39_16 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : collect(X0,X1) = X1),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_16])])).
% 0.19/0.56 tff(f1004,plain,(
% 0.19/0.56 spl39_37 <=> ! [X0 : $tType] : bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_37])])).
% 0.19/0.56 tff(f2777,plain,(
% 0.19/0.56 spl39_208 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_208])])).
% 0.19/0.56 tff(f3504,plain,(
% 0.19/0.56 spl39_267 <=> ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_267])])).
% 0.19/0.56 tff(f3510,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))),combk(bool,hoare_28830079triple(X0),fFalse))) | ~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),combk(bool,hoare_28830079triple(X0),fFalse))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4)))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_267)),
% 0.19/0.56 inference(forward_demodulation,[],[f3509,f1005])).
% 0.19/0.56 tff(f1005,plain,(
% 0.19/0.56 ( ! [X0 : $tType] : (bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse)) ) | ~spl39_37),
% 0.19/0.56 inference(avatar_component_clause,[],[f1004])).
% 0.19/0.56 tff(f3509,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),combk(bool,hoare_28830079triple(X0),fFalse))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4)))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_267)),
% 0.19/0.56 inference(forward_demodulation,[],[f3508,f2781])).
% 0.19/0.56 tff(f2781,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),X2)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),X2)) ) | (~spl39_16 | ~spl39_208)),
% 0.19/0.56 inference(superposition,[],[f2778,f902])).
% 0.19/0.56 tff(f902,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (collect(X0,X1) = X1) ) | ~spl39_16),
% 0.19/0.56 inference(avatar_component_clause,[],[f901])).
% 0.19/0.56 tff(f2778,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) ) | ~spl39_208),
% 0.19/0.56 inference(avatar_component_clause,[],[f2777])).
% 0.19/0.56 tff(f3508,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),combk(bool,hoare_28830079triple(X0),fFalse))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4)))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_267)),
% 0.19/0.56 inference(forward_demodulation,[],[f3507,f1005])).
% 0.19/0.56 tff(f3507,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),bot_bot(fun(hoare_28830079triple(X0),bool)))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4)))) ) | (~spl39_16 | ~spl39_208 | ~spl39_267)),
% 0.19/0.56 inference(forward_demodulation,[],[f3505,f2781])).
% 0.19/0.56 tff(f3505,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4)))) ) | ~spl39_267),
% 0.19/0.56 inference(avatar_component_clause,[],[f3504])).
% 0.19/0.56 tff(f3506,plain,(
% 0.19/0.56 spl39_267),
% 0.19/0.56 inference(avatar_split_clause,[],[f808,f3504])).
% 0.19/0.56 tff(f808,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4)))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f807,f439])).
% 0.19/0.56 tff(f439,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (collect(X0,X1) = X1) )),
% 0.19/0.56 inference(cnf_transformation,[],[f143])).
% 0.19/0.56 tff(f143,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool)] : collect(X0,X1) = X1),
% 0.19/0.56 inference(rectify,[],[f78])).
% 0.19/0.56 tff(f78,axiom,(
% 0.19/0.56 ! [X1 : $tType,X20 : fun(X1,bool)] : collect(X1,X20) = X20),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def)).
% 0.19/0.56 tff(f807,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4))) | ~hoare_992312373derivs(X0,X3,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f682,f439])).
% 0.19/0.56 tff(f682,plain,(
% 0.19/0.56 ( ! [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,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool)))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4))) | ~hoare_992312373derivs(X0,X3,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f584,f491,f491])).
% 0.19/0.56 tff(f491,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (insert(X0,X2,X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f185])).
% 0.19/0.56 tff(f185,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : insert(X0,X2,X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))),
% 0.19/0.56 inference(rectify,[],[f27])).
% 0.19/0.56 tff(f27,axiom,(
% 0.19/0.56 ! [X1 : $tType,X18 : fun(X1,bool),X17 : X1] : insert(X1,X17,X18) = collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X17)),combc(X1,fun(X1,bool),bool,member(X1),X18)))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_insert__compr)).
% 0.19/0.56 tff(f584,plain,(
% 0.19/0.56 ( ! [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,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),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4))) | ~hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),hoare_1841697145triple(X0,X7,X2,X8),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f405])).
% 0.19/0.56 tff(f405,plain,(
% 0.19/0.56 ! [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,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,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8))) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4))))) | ~hoare_992312373derivs(X0,X3,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,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4)))))),
% 0.19/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35])],[f317,f404,f403])).
% 0.19/0.56 tff(f403,plain,(
% 0.19/0.56 ! [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,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,sK33(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),sK34(X0,X1,X2,X3,X4))))) | ~hoare_992312373derivs(X0,X3,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,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4)))))),
% 0.19/0.56 introduced(choice_axiom,[])).
% 0.19/0.56 tff(f404,plain,(
% 0.19/0.56 ! [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,sK33(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),sK34(X0,X1,X2,X3,X4))))) => (~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8))) & ! [X10 : X0] : (pp(aa(state,bool,aa(X0,fun(state,bool),X8,X10),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X7,X10),sK34(X0,X1,X2,X3,X4))))))),
% 0.19/0.56 introduced(choice_axiom,[])).
% 0.19/0.56 tff(f317,plain,(
% 0.19/0.56 ! [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,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,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))))),
% 0.19/0.56 inference(ennf_transformation,[],[f241])).
% 0.19/0.56 tff(f241,plain,(
% 0.19/0.56 ! [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,insert(hoare_28830079triple(X0),hoare_1841697145triple(X0,X7,X2,X8),bot_bot(fun(hoare_28830079triple(X0),bool)))))) => hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),hoare_1841697145triple(X0,X4,X2,X1),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 0.19/0.56 inference(rectify,[],[f46])).
% 0.19/0.56 tff(f46,axiom,(
% 0.19/0.56 ! [X1 : $tType,X28 : fun(X1,fun(state,bool)),X21 : com,X10 : fun(hoare_28830079triple(X1),bool),X20 : fun(X1,fun(state,bool))] : (! [X40 : X1,X41 : state] : (pp(aa(state,bool,aa(X1,fun(state,bool),X20,X40),X41)) => ? [X42 : fun(X1,fun(state,bool)),X43 : fun(X1,fun(state,bool))] : (! [X44 : state] : (! [X45 : X1] : (pp(aa(state,bool,aa(X1,fun(state,bool),X42,X45),X41)) => pp(aa(state,bool,aa(X1,fun(state,bool),X43,X45),X44))) => pp(aa(state,bool,aa(X1,fun(state,bool),X28,X40),X44))) & hoare_992312373derivs(X1,X10,insert(hoare_28830079triple(X1),hoare_1841697145triple(X1,X42,X21,X43),bot_bot(fun(hoare_28830079triple(X1),bool)))))) => hoare_992312373derivs(X1,X10,insert(hoare_28830079triple(X1),hoare_1841697145triple(X1,X20,X21,X28),bot_bot(fun(hoare_28830079triple(X1),bool)))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_conseq)).
% 0.19/0.56 tff(f3493,plain,(
% 0.19/0.56 spl39_266 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_265),
% 0.19/0.56 inference(avatar_split_clause,[],[f3489,f3483,f2777,f1004,f901,f3491])).
% 0.19/0.56 tff(f3491,plain,(
% 0.19/0.56 spl39_266 <=> ! [X0 : $tType,X7 : 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,X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))),combk(bool,hoare_28830079triple(X0),fFalse))) | ~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),combk(bool,hoare_28830079triple(X0),fFalse))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_266])])).
% 0.19/0.56 tff(f3483,plain,(
% 0.19/0.56 spl39_265 <=> ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_265])])).
% 0.19/0.56 tff(f3489,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))),combk(bool,hoare_28830079triple(X0),fFalse))) | ~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),combk(bool,hoare_28830079triple(X0),fFalse))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8)))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_265)),
% 0.19/0.56 inference(forward_demodulation,[],[f3488,f1005])).
% 0.19/0.56 tff(f3488,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))),bot_bot(fun(hoare_28830079triple(X0),bool)))) | ~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),combk(bool,hoare_28830079triple(X0),fFalse))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8)))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_265)),
% 0.19/0.56 inference(forward_demodulation,[],[f3487,f2781])).
% 0.19/0.56 tff(f3487,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),combk(bool,hoare_28830079triple(X0),fFalse))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8)))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_265)),
% 0.19/0.56 inference(forward_demodulation,[],[f3486,f1005])).
% 0.19/0.56 tff(f3486,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8)))),bot_bot(fun(hoare_28830079triple(X0),bool)))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8)))) ) | (~spl39_16 | ~spl39_208 | ~spl39_265)),
% 0.19/0.56 inference(forward_demodulation,[],[f3484,f2781])).
% 0.19/0.56 tff(f3484,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8)))) ) | ~spl39_265),
% 0.19/0.56 inference(avatar_component_clause,[],[f3483])).
% 0.19/0.56 tff(f3485,plain,(
% 0.19/0.56 spl39_265),
% 0.19/0.56 inference(avatar_split_clause,[],[f806,f3483])).
% 0.19/0.56 tff(f806,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8)))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f805,f439])).
% 0.19/0.56 tff(f805,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~hoare_992312373derivs(X0,X3,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f681,f439])).
% 0.19/0.56 tff(f681,plain,(
% 0.19/0.56 ( ! [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,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool)))))) | ~pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~hoare_992312373derivs(X0,X3,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X7,X2,X8))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f585,f491,f491])).
% 0.19/0.56 tff(f585,plain,(
% 0.19/0.56 ( ! [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,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,sK33(X0,X1,X2,X3,X4)),sK35(X0,X1,X2,X3,X4,X7,X8))) | ~hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),hoare_1841697145triple(X0,X7,X2,X8),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f405])).
% 0.19/0.56 tff(f3475,plain,(
% 0.19/0.56 spl39_264 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_263),
% 0.19/0.56 inference(avatar_split_clause,[],[f3471,f3466,f2777,f1004,f901,f3473])).
% 0.19/0.56 tff(f3473,plain,(
% 0.19/0.56 spl39_264 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),combk(bool,X0,fFalse))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) | sP1(X0,X3,X2,X4,X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_264])])).
% 0.19/0.56 tff(f3466,plain,(
% 0.19/0.56 spl39_263 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | sP1(X0,X3,X2,X4,X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_263])])).
% 0.19/0.56 tff(f3471,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),combk(bool,X0,fFalse))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) | sP1(X0,X3,X2,X4,X1)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_263)),
% 0.19/0.56 inference(forward_demodulation,[],[f3470,f2781])).
% 0.19/0.56 tff(f3470,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),combk(bool,X0,fFalse))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)))) | sP1(X0,X3,X2,X4,X1)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_263)),
% 0.19/0.56 inference(forward_demodulation,[],[f3469,f1005])).
% 0.19/0.56 tff(f3469,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),bot_bot(fun(X0,bool)))) | sP1(X0,X3,X2,X4,X1)) ) | (~spl39_16 | ~spl39_208 | ~spl39_263)),
% 0.19/0.56 inference(forward_demodulation,[],[f3467,f2781])).
% 0.19/0.56 tff(f3467,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | sP1(X0,X3,X2,X4,X1)) ) | ~spl39_263),
% 0.19/0.56 inference(avatar_component_clause,[],[f3466])).
% 0.19/0.56 tff(f3468,plain,(
% 0.19/0.56 spl39_263),
% 0.19/0.56 inference(avatar_split_clause,[],[f821,f3466])).
% 0.19/0.56 tff(f821,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f820,f758])).
% 0.19/0.56 tff(f758,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f757,f439])).
% 0.19/0.56 tff(f757,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f756,f739])).
% 0.19/0.56 tff(f739,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f738,f439])).
% 0.19/0.56 tff(f738,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f630,f439])).
% 0.19/0.56 tff(f630,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,X1))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f490,f491])).
% 0.19/0.56 tff(f490,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (insert(X0,X2,collect(X0,X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f184])).
% 0.19/0.56 tff(f184,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : insert(X0,X2,collect(X0,X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1))),
% 0.19/0.56 inference(rectify,[],[f26])).
% 0.19/0.56 tff(f26,axiom,(
% 0.19/0.56 ! [X1 : $tType,X20 : fun(X1,bool),X17 : X1] : insert(X1,X17,collect(X1,X20)) = collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(X1),X17))),X20))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_insert__Collect)).
% 0.19/0.56 tff(f756,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f755,f439])).
% 0.19/0.56 tff(f755,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f645,f439])).
% 0.19/0.56 tff(f645,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1))))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f526,f491,f491,f491,f491])).
% 0.19/0.56 tff(f526,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (insert(X0,X3,insert(X0,X2,X1)) = insert(X0,X2,insert(X0,X3,X1))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f208])).
% 0.19/0.56 tff(f208,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : X0] : insert(X0,X3,insert(X0,X2,X1)) = insert(X0,X2,insert(X0,X3,X1))),
% 0.19/0.56 inference(rectify,[],[f25])).
% 0.19/0.56 tff(f25,axiom,(
% 0.19/0.56 ! [X1 : $tType,X14 : fun(X1,bool),X24 : X1,X15 : X1] : insert(X1,X15,insert(X1,X24,X14)) = insert(X1,X24,insert(X1,X15,X14))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_insert__commute)).
% 0.19/0.56 tff(f820,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) | sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f819,f439])).
% 0.19/0.56 tff(f819,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f818,f439])).
% 0.19/0.56 tff(f818,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f817,f758])).
% 0.19/0.56 tff(f817,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) | sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f816,f439])).
% 0.19/0.56 tff(f816,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) | sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f685,f439])).
% 0.19/0.56 tff(f685,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (sP1(X0,X3,X2,X4,X1) | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f592,f491,f491,f491,f491])).
% 0.19/0.56 tff(f592,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (sP1(X0,X3,X2,X4,X1) | insert(X0,X4,insert(X0,X3,bot_bot(fun(X0,bool)))) != insert(X0,X2,insert(X0,X1,bot_bot(fun(X0,bool))))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f409])).
% 0.19/0.56 tff(f409,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((insert(X0,X4,insert(X0,X3,bot_bot(fun(X0,bool)))) = insert(X0,X2,insert(X0,X1,bot_bot(fun(X0,bool)))) | ~sP1(X0,X3,X2,X4,X1)) & (sP1(X0,X3,X2,X4,X1) | insert(X0,X4,insert(X0,X3,bot_bot(fun(X0,bool)))) != insert(X0,X2,insert(X0,X1,bot_bot(fun(X0,bool))))))),
% 0.19/0.56 inference(nnf_transformation,[],[f325])).
% 0.19/0.56 tff(f325,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (insert(X0,X4,insert(X0,X3,bot_bot(fun(X0,bool)))) = insert(X0,X2,insert(X0,X1,bot_bot(fun(X0,bool)))) <=> sP1(X0,X3,X2,X4,X1))),
% 0.19/0.56 inference(definition_folding,[],[f242,f324])).
% 0.19/0.56 tff(f324,plain,(
% 0.19/0.56 ! [X3 : X0,X2 : X0,X0 : $tType,X4 : X0,X1 : X0] : (sP1(X0,X3,X2,X4,X1) <=> ((X2 = X3 & X1 = X4) | (X1 = X3 & X2 = X4)))),
% 0.19/0.56 introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])).
% 0.19/0.56 tff(f242,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (insert(X0,X4,insert(X0,X3,bot_bot(fun(X0,bool)))) = insert(X0,X2,insert(X0,X1,bot_bot(fun(X0,bool)))) <=> ((X2 = X3 & X1 = X4) | (X1 = X3 & X2 = X4)))),
% 0.19/0.56 inference(rectify,[],[f31])).
% 0.19/0.56 tff(f31,axiom,(
% 0.19/0.56 ! [X1 : $tType,X25 : X1,X21 : X1,X16 : X1,X17 : X1] : (insert(X1,X17,insert(X1,X16,bot_bot(fun(X1,bool)))) = insert(X1,X21,insert(X1,X25,bot_bot(fun(X1,bool)))) <=> ((X16 = X21 & X17 = X25) | (X16 = X25 & X17 = X21)))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_doubleton__eq__iff)).
% 0.19/0.56 tff(f3461,plain,(
% 0.19/0.56 spl39_262 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_261),
% 0.19/0.56 inference(avatar_split_clause,[],[f3457,f3452,f2777,f1004,f901,f3459])).
% 0.19/0.56 tff(f3459,plain,(
% 0.19/0.56 spl39_262 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),combk(bool,X0,fFalse))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) | ~sP1(X0,X3,X2,X4,X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_262])])).
% 0.19/0.56 tff(f3452,plain,(
% 0.19/0.56 spl39_261 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | ~sP1(X0,X3,X2,X4,X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_261])])).
% 0.19/0.56 tff(f3457,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),combk(bool,X0,fFalse))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) | ~sP1(X0,X3,X2,X4,X1)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_261)),
% 0.19/0.56 inference(forward_demodulation,[],[f3456,f2781])).
% 0.19/0.56 tff(f3456,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),combk(bool,X0,fFalse))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)))) | ~sP1(X0,X3,X2,X4,X1)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_261)),
% 0.19/0.56 inference(forward_demodulation,[],[f3455,f1005])).
% 0.19/0.56 tff(f3455,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),bot_bot(fun(X0,bool)))) | ~sP1(X0,X3,X2,X4,X1)) ) | (~spl39_16 | ~spl39_208 | ~spl39_261)),
% 0.19/0.56 inference(forward_demodulation,[],[f3453,f2781])).
% 0.19/0.56 tff(f3453,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | ~sP1(X0,X3,X2,X4,X1)) ) | ~spl39_261),
% 0.19/0.56 inference(avatar_component_clause,[],[f3452])).
% 0.19/0.56 tff(f3454,plain,(
% 0.19/0.56 spl39_261),
% 0.19/0.56 inference(avatar_split_clause,[],[f815,f3452])).
% 0.19/0.56 tff(f815,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | ~sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f814,f758])).
% 0.19/0.56 tff(f814,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) | ~sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f813,f439])).
% 0.19/0.56 tff(f813,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | ~sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f812,f439])).
% 0.19/0.56 tff(f812,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) | ~sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f811,f758])).
% 0.19/0.56 tff(f811,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) | ~sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f810,f439])).
% 0.19/0.56 tff(f810,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) | ~sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f684,f439])).
% 0.19/0.56 tff(f684,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) | ~sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(definition_unfolding,[],[f593,f491,f491,f491,f491])).
% 0.19/0.56 tff(f593,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (insert(X0,X4,insert(X0,X3,bot_bot(fun(X0,bool)))) = insert(X0,X2,insert(X0,X1,bot_bot(fun(X0,bool)))) | ~sP1(X0,X3,X2,X4,X1)) )),
% 0.19/0.56 inference(cnf_transformation,[],[f409])).
% 0.19/0.56 tff(f3438,plain,(
% 0.19/0.56 spl39_260 | ~spl39_16 | ~spl39_208 | ~spl39_259),
% 0.19/0.56 inference(avatar_split_clause,[],[f3434,f3430,f2777,f901,f3436])).
% 0.19/0.56 tff(f3436,plain,(
% 0.19/0.56 spl39_260 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : fun(X0,bool)] : combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_260])])).
% 0.19/0.56 tff(f3430,plain,(
% 0.19/0.56 spl39_259 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : fun(X0,bool)] : combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_259])])).
% 0.19/0.56 tff(f3434,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1))) ) | (~spl39_16 | ~spl39_208 | ~spl39_259)),
% 0.19/0.56 inference(forward_demodulation,[],[f3433,f2781])).
% 0.19/0.56 tff(f3433,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1))) ) | (~spl39_16 | ~spl39_208 | ~spl39_259)),
% 0.19/0.56 inference(forward_demodulation,[],[f3431,f2781])).
% 0.19/0.56 tff(f3431,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) ) | ~spl39_259),
% 0.19/0.56 inference(avatar_component_clause,[],[f3430])).
% 0.19/0.56 tff(f3432,plain,(
% 0.19/0.56 spl39_259),
% 0.19/0.56 inference(avatar_split_clause,[],[f758,f3430])).
% 0.19/0.56 tff(f3426,plain,(
% 0.19/0.56 spl39_258 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_257),
% 0.19/0.56 inference(avatar_split_clause,[],[f3422,f3416,f2777,f1420,f901,f3424])).
% 0.19/0.56 tff(f3424,plain,(
% 0.19/0.56 spl39_258 <=> ! [X0 : $tType,X4 : X0,X3 : fun(X0,bool),X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X3),X4)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(X0,X4,X1,X2,X3) | X2 = X4)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_258])])).
% 0.19/0.56 tff(f1420,plain,(
% 0.19/0.56 spl39_104 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_104])])).
% 0.19/0.56 tff(f3416,plain,(
% 0.19/0.56 spl39_257 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | ~sP0(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)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_257])])).
% 0.19/0.56 tff(f3422,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X3),X4)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(X0,X4,X1,X2,X3) | X2 = X4) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_257)),
% 0.19/0.56 inference(forward_demodulation,[],[f3421,f1421])).
% 0.19/0.56 tff(f1421,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : (aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)) ) | ~spl39_104),
% 0.19/0.56 inference(avatar_component_clause,[],[f1420])).
% 0.19/0.56 tff(f3421,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(X0,X4,X1,X2,X3) | X2 = X4 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3))) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_257)),
% 0.19/0.56 inference(forward_demodulation,[],[f3420,f1421])).
% 0.19/0.56 tff(f3420,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_257)),
% 0.19/0.56 inference(forward_demodulation,[],[f3419,f2781])).
% 0.19/0.56 tff(f3419,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_257)),
% 0.19/0.56 inference(forward_demodulation,[],[f3417,f2781])).
% 0.19/0.56 tff(f3417,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | ~sP0(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))) ) | ~spl39_257),
% 0.19/0.56 inference(avatar_component_clause,[],[f3416])).
% 0.19/0.56 tff(f3418,plain,(
% 0.19/0.56 spl39_257),
% 0.19/0.56 inference(avatar_split_clause,[],[f800,f3416])).
% 0.19/0.56 tff(f800,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | ~sP0(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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f799,f439])).
% 0.19/0.56 tff(f799,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | ~sP0(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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f678,f439])).
% 0.19/0.56 tff(f678,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3))) | ~sP0(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))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f581,f491,f491])).
% 0.19/0.56 tff(f581,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (insert(X0,X2,X1) = insert(X0,X4,X3) | ~sP0(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))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f402])).
% 0.19/0.56 tff(f402,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : (((insert(X0,X2,X1) = insert(X0,X4,X3) | ~sP0(X0,X4,X1,X2,X3) | (X1 != X3 & X2 = X4)) & ((sP0(X0,X4,X1,X2,X3) & (X1 = X3 | X2 != X4)) | insert(X0,X2,X1) != 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)))),
% 0.19/0.56 inference(flattening,[],[f401])).
% 0.19/0.56 tff(f401,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : (((insert(X0,X2,X1) = insert(X0,X4,X3) | (~sP0(X0,X4,X1,X2,X3) | (X1 != X3 & X2 = X4))) & ((sP0(X0,X4,X1,X2,X3) & (X1 = X3 | X2 != X4)) | insert(X0,X2,X1) != 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)))),
% 0.19/0.56 inference(nnf_transformation,[],[f323])).
% 0.19/0.56 tff(f323,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : ((insert(X0,X2,X1) = insert(X0,X4,X3) <=> (sP0(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)))),
% 0.19/0.56 inference(definition_folding,[],[f316,f322])).
% 0.19/0.56 tff(f322,plain,(
% 0.19/0.56 ! [X4 : X0,X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : (sP0(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)) & insert(X0,X4,X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & insert(X0,X2,X5) = X3) | X2 = X4))),
% 0.19/0.56 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 0.19/0.56 tff(f316,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : ((insert(X0,X2,X1) = 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)) & insert(X0,X4,X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & 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)))),
% 0.19/0.56 inference(flattening,[],[f315])).
% 0.19/0.56 tff(f315,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool),X4 : X0] : (((insert(X0,X2,X1) = 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)) & insert(X0,X4,X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & 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)))),
% 0.19/0.56 inference(ennf_transformation,[],[f240])).
% 0.19/0.56 tff(f240,plain,(
% 0.19/0.56 ! [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)) => (insert(X0,X2,X1) = 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)) & insert(X0,X4,X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & insert(X0,X2,X5) = X3)) & (X2 = X4 => X1 = X3)))))),
% 0.19/0.56 inference(rectify,[],[f22])).
% 0.19/0.56 tff(f22,axiom,(
% 0.19/0.56 ! [X1 : $tType,X18 : fun(X1,bool),X16 : X1,X14 : fun(X1,bool),X17 : X1] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),X14)) => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X16),X18)) => (insert(X1,X16,X18) = insert(X1,X17,X14) <=> ((X16 != X17 => ? [X23 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),X23)) & insert(X1,X17,X23) = X18 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X16),X23)) & insert(X1,X16,X23) = X14)) & (X16 = X17 => X14 = X18)))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_insert__eq__iff)).
% 0.19/0.56 tff(f3413,plain,(
% 0.19/0.56 spl39_256 | ~spl39_16 | ~spl39_208 | ~spl39_254),
% 0.19/0.56 inference(avatar_split_clause,[],[f3405,f3400,f2777,f901,f3411])).
% 0.19/0.56 tff(f3411,plain,(
% 0.19/0.56 spl39_256 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,X0)),X3 : X0,X2 : fun(X0,bool),X1 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4)))),sK31(X0,X1,X2,X3,X4)) | ~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2),X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_256])])).
% 0.19/0.56 tff(f3400,plain,(
% 0.19/0.56 spl39_254 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,X0)),X3 : X0,X2 : fun(X0,bool),X1 : X0] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4))),combc(X0,fun(X0,bool),bool,member(X0),sK31(X0,X1,X2,X3,X4))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_254])])).
% 0.19/0.56 tff(f3405,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4)))),sK31(X0,X1,X2,X3,X4)) | ~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2),X1)) ) | (~spl39_16 | ~spl39_208 | ~spl39_254)),
% 0.19/0.56 inference(forward_demodulation,[],[f3404,f2781])).
% 0.19/0.56 tff(f3404,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4)))),sK31(X0,X1,X2,X3,X4)) | ~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2),X1)) ) | (~spl39_16 | ~spl39_208 | ~spl39_254)),
% 0.19/0.56 inference(forward_demodulation,[],[f3403,f2781])).
% 0.19/0.56 tff(f3403,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2),X1) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4))),combc(X0,fun(X0,bool),bool,member(X0),sK31(X0,X1,X2,X3,X4)))) ) | (~spl39_16 | ~spl39_208 | ~spl39_254)),
% 0.19/0.56 inference(forward_demodulation,[],[f3401,f2781])).
% 0.19/0.56 tff(f3401,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4))),combc(X0,fun(X0,bool),bool,member(X0),sK31(X0,X1,X2,X3,X4)))) ) | ~spl39_254),
% 0.19/0.56 inference(avatar_component_clause,[],[f3400])).
% 0.19/0.56 tff(f3409,plain,(
% 0.19/0.56 spl39_255 | ~spl39_6 | ~spl39_211 | ~spl39_240),
% 0.19/0.56 inference(avatar_split_clause,[],[f3349,f3288,f2813,f857,f3407])).
% 0.19/0.56 tff(f857,plain,(
% 0.19/0.56 spl39_6 <=> pp(fTrue)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_6])])).
% 0.19/0.56 tff(f2813,plain,(
% 0.19/0.56 spl39_211 <=> fTrue = aa(a,bool,combc(a,state,bool,p1,sK4),sK6(sK4,sK5(p1,q1)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_211])])).
% 0.19/0.56 tff(f3288,plain,(
% 0.19/0.56 spl39_240 <=> ! [X0 : state,X1 : a] : (~pp(aa(a,bool,combc(a,state,bool,p1,sK4),sK6(X0,sK5(p1,q1)))) | q(X1,sK5(p1,q1)) | ~p(X1,X0))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_240])])).
% 0.19/0.56 tff(f3349,plain,(
% 0.19/0.56 ( ! [X0 : a] : (~pp(fTrue) | q(X0,sK5(p1,q1)) | ~p(X0,sK4)) ) | (~spl39_211 | ~spl39_240)),
% 0.19/0.56 inference(superposition,[],[f3289,f2815])).
% 0.19/0.56 tff(f2815,plain,(
% 0.19/0.56 fTrue = aa(a,bool,combc(a,state,bool,p1,sK4),sK6(sK4,sK5(p1,q1))) | ~spl39_211),
% 0.19/0.56 inference(avatar_component_clause,[],[f2813])).
% 0.19/0.56 tff(f3289,plain,(
% 0.19/0.56 ( ! [X0 : state,X1 : a] : (~pp(aa(a,bool,combc(a,state,bool,p1,sK4),sK6(X0,sK5(p1,q1)))) | q(X1,sK5(p1,q1)) | ~p(X1,X0)) ) | ~spl39_240),
% 0.19/0.56 inference(avatar_component_clause,[],[f3288])).
% 0.19/0.56 tff(f3402,plain,(
% 0.19/0.56 spl39_254),
% 0.19/0.56 inference(avatar_split_clause,[],[f792,f3400])).
% 0.19/0.56 tff(f792,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4))),combc(X0,fun(X0,bool),bool,member(X0),sK31(X0,X1,X2,X3,X4)))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f791,f439])).
% 0.19/0.56 tff(f791,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4))),combc(X0,fun(X0,bool),bool,member(X0),sK31(X0,X1,X2,X3,X4))) | ~finite_fold1Set(X0,X4,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f790,f439])).
% 0.19/0.56 tff(f790,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4))),combc(X0,fun(X0,bool),bool,member(X0),sK31(X0,X1,X2,X3,X4))) | ~finite_fold1Set(X0,X4,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f673,f439])).
% 0.19/0.56 tff(f673,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK30(X0,X1,X2,X3,X4))),combc(X0,fun(X0,bool),bool,member(X0),sK31(X0,X1,X2,X3,X4)))) | ~finite_fold1Set(X0,X4,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X1)) )),
% 0.19/0.56 inference(definition_unfolding,[],[f569,f491,f491,f491])).
% 0.19/0.56 tff(f569,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (insert(X0,X3,X2) = insert(X0,sK30(X0,X1,X2,X3,X4),sK31(X0,X1,X2,X3,X4)) | ~finite_fold1Set(X0,X4,insert(X0,X3,X2),X1)) )),
% 0.19/0.56 inference(cnf_transformation,[],[f395])).
% 0.19/0.56 tff(f395,plain,(
% 0.19/0.56 ! [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),sK30(X0,X1,X2,X3,X4)),sK31(X0,X1,X2,X3,X4))) & finite_fold_graph(X0,X0,X4,sK30(X0,X1,X2,X3,X4),sK31(X0,X1,X2,X3,X4),X1) & insert(X0,X3,X2) = insert(X0,sK30(X0,X1,X2,X3,X4),sK31(X0,X1,X2,X3,X4))) | ~finite_fold1Set(X0,X4,insert(X0,X3,X2),X1))),
% 0.19/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f313,f394])).
% 0.19/0.56 tff(f394,plain,(
% 0.19/0.56 ! [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) & insert(X0,X3,X2) = insert(X0,X5,X6)) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK30(X0,X1,X2,X3,X4)),sK31(X0,X1,X2,X3,X4))) & finite_fold_graph(X0,X0,X4,sK30(X0,X1,X2,X3,X4),sK31(X0,X1,X2,X3,X4),X1) & insert(X0,X3,X2) = insert(X0,sK30(X0,X1,X2,X3,X4),sK31(X0,X1,X2,X3,X4))))),
% 0.19/0.56 introduced(choice_axiom,[])).
% 0.19/0.56 tff(f313,plain,(
% 0.19/0.56 ! [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) & insert(X0,X3,X2) = insert(X0,X5,X6)) | ~finite_fold1Set(X0,X4,insert(X0,X3,X2),X1))),
% 0.19/0.56 inference(flattening,[],[f312])).
% 0.19/0.56 tff(f312,plain,(
% 0.19/0.56 ! [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)) & insert(X0,X3,X2) = insert(X0,X5,X6)) | ~finite_fold1Set(X0,X4,insert(X0,X3,X2),X1))),
% 0.19/0.56 inference(ennf_transformation,[],[f238])).
% 0.19/0.56 tff(f238,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0,X4 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X4,insert(X0,X3,X2),X1) => ~! [X5 : X0,X6 : fun(X0,bool)] : (insert(X0,X3,X2) = 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)))))),
% 0.19/0.56 inference(rectify,[],[f80])).
% 0.19/0.56 tff(f80,axiom,(
% 0.19/0.56 ! [X1 : $tType,X15 : X1,X60 : fun(X1,bool),X17 : X1,X47 : fun(X1,fun(X1,X1))] : (finite_fold1Set(X1,X47,insert(X1,X17,X60),X15) => ~! [X61 : X1,X62 : fun(X1,bool)] : (insert(X1,X17,X60) = insert(X1,X61,X62) => (finite_fold_graph(X1,X1,X47,X61,X62,X15) => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X61),X62)))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_insert__fold1SetE)).
% 0.19/0.56 tff(f3396,plain,(
% 0.19/0.56 spl39_253 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_252),
% 0.19/0.56 inference(avatar_split_clause,[],[f3392,f3386,f2777,f1420,f901,f3394])).
% 0.19/0.56 tff(f3394,plain,(
% 0.19/0.56 spl39_253 <=> ! [X0 : $tType,X4 : X0,X3 : fun(X0,bool),X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X3),X4)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | sP0(X0,X4,X1,X2,X3))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_253])])).
% 0.19/0.56 tff(f3386,plain,(
% 0.19/0.56 spl39_252 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | sP0(X0,X4,X1,X2,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)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_252])])).
% 0.19/0.56 tff(f3392,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X3),X4)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | sP0(X0,X4,X1,X2,X3)) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_252)),
% 0.19/0.56 inference(forward_demodulation,[],[f3391,f1421])).
% 0.19/0.56 tff(f3391,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | sP0(X0,X4,X1,X2,X3) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3))) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_252)),
% 0.19/0.56 inference(forward_demodulation,[],[f3390,f1421])).
% 0.19/0.56 tff(f3390,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | sP0(X0,X4,X1,X2,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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_252)),
% 0.19/0.56 inference(forward_demodulation,[],[f3389,f2781])).
% 0.19/0.56 tff(f3389,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | sP0(X0,X4,X1,X2,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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_252)),
% 0.19/0.56 inference(forward_demodulation,[],[f3387,f2781])).
% 0.19/0.56 tff(f3387,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | sP0(X0,X4,X1,X2,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))) ) | ~spl39_252),
% 0.19/0.56 inference(avatar_component_clause,[],[f3386])).
% 0.19/0.56 tff(f3388,plain,(
% 0.19/0.56 spl39_252),
% 0.19/0.56 inference(avatar_split_clause,[],[f802,f3386])).
% 0.19/0.56 tff(f802,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | sP0(X0,X4,X1,X2,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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f801,f439])).
% 0.19/0.56 tff(f801,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | sP0(X0,X4,X1,X2,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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f679,f439])).
% 0.19/0.56 tff(f679,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (sP0(X0,X4,X1,X2,X3) | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),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))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f580,f491,f491])).
% 0.19/0.56 tff(f580,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (sP0(X0,X4,X1,X2,X3) | insert(X0,X2,X1) != 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))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f402])).
% 0.19/0.56 tff(f3380,plain,(
% 0.19/0.56 spl39_251 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_250),
% 0.19/0.56 inference(avatar_split_clause,[],[f3376,f3370,f2777,f1420,f901,f3378])).
% 0.19/0.56 tff(f3378,plain,(
% 0.19/0.56 spl39_251 <=> ! [X0 : $tType,X4 : X0,X3 : fun(X0,bool),X2 : X0] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X3),X4)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X3),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X3) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(X0,X4,X3,X2,X3))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_251])])).
% 0.19/0.56 tff(f3370,plain,(
% 0.19/0.56 spl39_250 <=> ! [X0 : $tType,X4 : X0,X3 : fun(X0,bool),X2 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | ~sP0(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)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_250])])).
% 0.19/0.56 tff(f3376,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X3),X4)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X3),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X3) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(X0,X4,X3,X2,X3)) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_250)),
% 0.19/0.56 inference(forward_demodulation,[],[f3375,f1421])).
% 0.19/0.56 tff(f3375,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X4 : X0] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X3),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X3) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(X0,X4,X3,X2,X3) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X3))) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_250)),
% 0.19/0.56 inference(forward_demodulation,[],[f3374,f1421])).
% 0.19/0.56 tff(f3374,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X3) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_250)),
% 0.19/0.56 inference(forward_demodulation,[],[f3373,f2781])).
% 0.19/0.56 tff(f3373,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X4))),X3) | ~sP0(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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_250)),
% 0.19/0.56 inference(forward_demodulation,[],[f3371,f2781])).
% 0.19/0.56 tff(f3371,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | ~sP0(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))) ) | ~spl39_250),
% 0.19/0.56 inference(avatar_component_clause,[],[f3370])).
% 0.19/0.56 tff(f3372,plain,(
% 0.19/0.56 spl39_250),
% 0.19/0.56 inference(avatar_split_clause,[],[f798,f3370])).
% 0.19/0.56 tff(f798,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X4 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3)) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | ~sP0(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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f797,f439])).
% 0.19/0.56 tff(f797,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3))) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | ~sP0(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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f711,f439])).
% 0.19/0.56 tff(f711,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3))) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3))) | ~sP0(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))) )),
% 0.19/0.56 inference(equality_resolution,[],[f677])).
% 0.19/0.56 tff(f677,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X3))) | ~sP0(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))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f582,f491,f491])).
% 0.19/0.56 tff(f582,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool),X4 : X0] : (insert(X0,X2,X1) = insert(X0,X4,X3) | ~sP0(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))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f402])).
% 0.19/0.56 tff(f3366,plain,(
% 0.19/0.56 spl39_249 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_248),
% 0.19/0.56 inference(avatar_split_clause,[],[f3362,f3356,f2777,f1420,f901,f3364])).
% 0.19/0.56 tff(f3364,plain,(
% 0.19/0.56 spl39_249 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2) | X1 = X2)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_249])])).
% 0.19/0.56 tff(f3356,plain,(
% 0.19/0.56 spl39_248 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),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)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_248])])).
% 0.19/0.56 tff(f3362,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2) | X1 = X2) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_248)),
% 0.19/0.56 inference(forward_demodulation,[],[f3361,f1421])).
% 0.19/0.56 tff(f3361,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2) | X1 = X2 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_248)),
% 0.19/0.56 inference(forward_demodulation,[],[f3360,f1421])).
% 0.19/0.56 tff(f3360,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2) | 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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_248)),
% 0.19/0.56 inference(forward_demodulation,[],[f3359,f2781])).
% 0.19/0.56 tff(f3359,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_248)),
% 0.19/0.56 inference(forward_demodulation,[],[f3357,f2781])).
% 0.19/0.56 tff(f3357,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),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))) ) | ~spl39_248),
% 0.19/0.56 inference(avatar_component_clause,[],[f3356])).
% 0.19/0.56 tff(f3358,plain,(
% 0.19/0.56 spl39_248),
% 0.19/0.56 inference(avatar_split_clause,[],[f769,f3356])).
% 0.19/0.56 tff(f769,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f768,f439])).
% 0.19/0.56 tff(f768,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f652,f439])).
% 0.19/0.56 tff(f652,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (X1 = X2 | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),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))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f534,f491,f491])).
% 0.19/0.56 tff(f534,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (X1 = X2 | insert(X0,X3,X2) != 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))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f377])).
% 0.19/0.56 tff(f377,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : X0] : (((insert(X0,X3,X2) = insert(X0,X3,X1) | X1 != X2) & (X1 = X2 | insert(X0,X3,X2) != 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)))),
% 0.19/0.56 inference(nnf_transformation,[],[f298])).
% 0.19/0.56 tff(f298,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : X0] : ((insert(X0,X3,X2) = 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)))),
% 0.19/0.56 inference(flattening,[],[f297])).
% 0.19/0.56 tff(f297,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : X0] : (((insert(X0,X3,X2) = 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)))),
% 0.19/0.56 inference(ennf_transformation,[],[f217])).
% 0.19/0.56 tff(f217,plain,(
% 0.19/0.56 ! [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)) => (insert(X0,X3,X2) = insert(X0,X3,X1) <=> X1 = X2)))),
% 0.19/0.56 inference(rectify,[],[f23])).
% 0.19/0.56 tff(f23,axiom,(
% 0.19/0.56 ! [X1 : $tType,X18 : fun(X1,bool),X14 : fun(X1,bool),X15 : X1] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X14)) => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X18)) => (insert(X1,X15,X14) = insert(X1,X15,X18) <=> X14 = X18)))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_insert__ident)).
% 0.19/0.56 tff(f3340,plain,(
% 0.19/0.56 spl39_247),
% 0.19/0.56 inference(avatar_split_clause,[],[f737,f3338])).
% 0.19/0.56 tff(f3338,plain,(
% 0.19/0.56 spl39_247 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_247])])).
% 0.19/0.56 tff(f737,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f736,f439])).
% 0.19/0.56 tff(f736,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f629,f439])).
% 0.19/0.56 tff(f629,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f489,f491,f491,f491])).
% 0.19/0.56 tff(f489,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (insert(X0,X2,X1) = insert(X0,X2,minus_minus(fun(X0,bool),X1,insert(X0,X2,bot_bot(fun(X0,bool)))))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f183])).
% 0.19/0.56 tff(f183,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : insert(X0,X2,X1) = insert(X0,X2,minus_minus(fun(X0,bool),X1,insert(X0,X2,bot_bot(fun(X0,bool)))))),
% 0.19/0.56 inference(rectify,[],[f57])).
% 0.19/0.56 tff(f57,axiom,(
% 0.19/0.56 ! [X1 : $tType,X14 : fun(X1,bool),X17 : X1] : insert(X1,X17,X14) = insert(X1,X17,minus_minus(fun(X1,bool),X14,insert(X1,X17,bot_bot(fun(X1,bool)))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_insert__Diff__single)).
% 0.19/0.56 tff(f3332,plain,(
% 0.19/0.56 spl39_246 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_245),
% 0.19/0.56 inference(avatar_split_clause,[],[f3328,f3322,f2777,f1420,f901,f3330])).
% 0.19/0.56 tff(f3330,plain,(
% 0.19/0.56 spl39_246 <=> ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (pp(aa(X1,bool,combc(X1,fun(X1,bool),bool,member(X1),X5),X3)) | pp(aa(X1,bool,combc(X1,fun(X1,bool),bool,member(X1),X5),X0)) | sP0(X1,X0,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(X1),X0))),X5),X3,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(X1),X3))),X5)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_246])])).
% 0.19/0.56 tff(f3322,plain,(
% 0.19/0.56 spl39_245 <=> ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (sP0(X1,X0,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),X5)),X3,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),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)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_245])])).
% 0.19/0.56 tff(f3328,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (pp(aa(X1,bool,combc(X1,fun(X1,bool),bool,member(X1),X5),X3)) | pp(aa(X1,bool,combc(X1,fun(X1,bool),bool,member(X1),X5),X0)) | sP0(X1,X0,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(X1),X0))),X5),X3,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(X1),X3))),X5))) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_245)),
% 0.19/0.56 inference(forward_demodulation,[],[f3327,f1421])).
% 0.19/0.56 tff(f3327,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (pp(aa(X1,bool,combc(X1,fun(X1,bool),bool,member(X1),X5),X0)) | sP0(X1,X0,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(X1),X0))),X5),X3,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(X1),X3))),X5)) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5))) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_245)),
% 0.19/0.56 inference(forward_demodulation,[],[f3326,f1421])).
% 0.19/0.56 tff(f3326,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (sP0(X1,X0,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(X1),X0))),X5),X3,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_245)),
% 0.19/0.56 inference(forward_demodulation,[],[f3325,f2781])).
% 0.19/0.56 tff(f3325,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (sP0(X1,X0,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),X5)),X3,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fimplies,combb(bool,bool,X1,fNot,combc(X1,X1,bool,fequal(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))) ) | (~spl39_16 | ~spl39_208 | ~spl39_245)),
% 0.19/0.56 inference(forward_demodulation,[],[f3323,f2781])).
% 0.19/0.56 tff(f3323,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (sP0(X1,X0,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),X5)),X3,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),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))) ) | ~spl39_245),
% 0.19/0.56 inference(avatar_component_clause,[],[f3322])).
% 0.19/0.56 tff(f3324,plain,(
% 0.19/0.56 spl39_245),
% 0.19/0.56 inference(avatar_split_clause,[],[f794,f3322])).
% 0.19/0.56 tff(f794,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (sP0(X1,X0,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),X5)),X3,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f793,f439])).
% 0.19/0.56 tff(f793,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (sP0(X1,X0,collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),X5))),X3,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f709,f439])).
% 0.19/0.56 tff(f709,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X3 : X1,X0 : X1,X5 : fun(X1,bool)] : (sP0(X1,X0,collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),X5))),X3,collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),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))) )),
% 0.19/0.56 inference(equality_resolution,[],[f708])).
% 0.19/0.56 tff(f708,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X3 : X1,X0 : X1,X4 : fun(X1,bool),X5 : fun(X1,bool)] : (sP0(X1,X0,collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),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)) | collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),X5))) != X4) )),
% 0.19/0.56 inference(equality_resolution,[],[f674])).
% 0.19/0.56 tff(f674,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool),X5 : fun(X1,bool)] : (sP0(X1,X0,X2,X3,X4) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X5)) | collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),X5))) != X2 | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5)) | collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),X5))) != X4) )),
% 0.19/0.56 inference(definition_unfolding,[],[f578,f491,f491])).
% 0.19/0.56 tff(f578,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool),X5 : fun(X1,bool)] : (sP0(X1,X0,X2,X3,X4) | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),X5)) | insert(X1,X0,X5) != X2 | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5)) | insert(X1,X3,X5) != X4) )),
% 0.19/0.56 inference(cnf_transformation,[],[f400])).
% 0.19/0.56 tff(f400,plain,(
% 0.19/0.56 ! [X0 : X1,X1 : $tType,X2 : fun(X1,bool),X3 : X1,X4 : fun(X1,bool)] : ((sP0(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)) | insert(X1,X0,X5) != X2 | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5)) | insert(X1,X3,X5) != X4) & X0 != X3)) & ((~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),sK32(X1,X0,X2,X3,X4))) & insert(X1,X0,sK32(X1,X0,X2,X3,X4)) = X2 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),sK32(X1,X0,X2,X3,X4))) & insert(X1,X3,sK32(X1,X0,X2,X3,X4)) = X4) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)))),
% 0.19/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f398,f399])).
% 0.19/0.56 tff(f399,plain,(
% 0.19/0.56 ! [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)) & insert(X1,X0,X6) = X2 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X6)) & insert(X1,X3,X6) = X4) => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X0),sK32(X1,X0,X2,X3,X4))) & insert(X1,X0,sK32(X1,X0,X2,X3,X4)) = X2 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),sK32(X1,X0,X2,X3,X4))) & insert(X1,X3,sK32(X1,X0,X2,X3,X4)) = X4))),
% 0.19/0.56 introduced(choice_axiom,[])).
% 0.19/0.56 tff(f398,plain,(
% 0.19/0.56 ! [X0 : X1,X1 : $tType,X2 : fun(X1,bool),X3 : X1,X4 : fun(X1,bool)] : ((sP0(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)) | insert(X1,X0,X5) != X2 | pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X5)) | 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)) & insert(X1,X0,X6) = X2 & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X3),X6)) & insert(X1,X3,X6) = X4) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)))),
% 0.19/0.56 inference(rectify,[],[f397])).
% 0.19/0.56 tff(f397,plain,(
% 0.19/0.56 ! [X4 : X0,X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : ((sP0(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)) | insert(X0,X4,X5) != X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) | 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)) & insert(X0,X4,X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & insert(X0,X2,X5) = X3) | X2 = X4 | ~sP0(X0,X4,X1,X2,X3)))),
% 0.19/0.56 inference(flattening,[],[f396])).
% 0.19/0.56 tff(f396,plain,(
% 0.19/0.56 ! [X4 : X0,X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : ((sP0(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)) | insert(X0,X4,X5) != X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) | 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)) & insert(X0,X4,X5) = X1 & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X5)) & insert(X0,X2,X5) = X3) | X2 = X4) | ~sP0(X0,X4,X1,X2,X3)))),
% 0.19/0.56 inference(nnf_transformation,[],[f322])).
% 0.19/0.56 tff(f3318,plain,(
% 0.19/0.56 spl39_244 | ~spl39_16 | ~spl39_208 | ~spl39_243),
% 0.19/0.56 inference(avatar_split_clause,[],[f3314,f3310,f2777,f901,f3316])).
% 0.19/0.56 tff(f3316,plain,(
% 0.19/0.56 spl39_244 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_244])])).
% 0.19/0.56 tff(f3310,plain,(
% 0.19/0.56 spl39_243 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_243])])).
% 0.19/0.56 tff(f3314,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)))) ) | (~spl39_16 | ~spl39_208 | ~spl39_243)),
% 0.19/0.56 inference(forward_demodulation,[],[f3313,f2781])).
% 0.19/0.56 tff(f3313,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))))) ) | ~spl39_243),
% 0.19/0.56 inference(forward_demodulation,[],[f3311,f758])).
% 0.19/0.56 tff(f3311,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))) ) | ~spl39_243),
% 0.19/0.56 inference(avatar_component_clause,[],[f3310])).
% 0.19/0.56 tff(f3312,plain,(
% 0.19/0.56 spl39_243),
% 0.19/0.56 inference(avatar_split_clause,[],[f733,f3310])).
% 0.19/0.56 tff(f733,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f626,f439])).
% 0.19/0.56 tff(f626,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f485,f491,f491,f491])).
% 0.19/0.56 tff(f485,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (insert(X0,X2,X1) = insert(X0,X2,insert(X0,X2,X1))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f179])).
% 0.19/0.56 tff(f179,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : insert(X0,X2,X1) = insert(X0,X2,insert(X0,X2,X1))),
% 0.19/0.56 inference(rectify,[],[f5])).
% 0.19/0.56 tff(f5,axiom,(
% 0.19/0.56 ! [X1 : $tType,X14 : fun(X1,bool),X15 : X1] : insert(X1,X15,X14) = insert(X1,X15,insert(X1,X15,X14))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_insert__absorb2)).
% 0.19/0.56 tff(f3301,plain,(
% 0.19/0.56 spl39_242 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_241),
% 0.19/0.56 inference(avatar_split_clause,[],[f3297,f3292,f2777,f1004,f901,f3299])).
% 0.19/0.56 tff(f3299,plain,(
% 0.19/0.56 spl39_242 <=> ! [X0 : $tType,X3 : fun(hoare_28830079triple(X0),bool),X2 : hoare_28830079triple(X0),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2))),X1)) | ~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2))),combk(bool,hoare_28830079triple(X0),fFalse))) | ~hoare_992312373derivs(X0,X3,X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_242])])).
% 0.19/0.56 tff(f3292,plain,(
% 0.19/0.56 spl39_241 <=> ! [X0 : $tType,X3 : fun(hoare_28830079triple(X0),bool),X2 : hoare_28830079triple(X0),X1 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),X1))) | ~hoare_992312373derivs(X0,X3,X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_241])])).
% 0.19/0.56 tff(f3297,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2))),X1)) | ~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2))),combk(bool,hoare_28830079triple(X0),fFalse))) | ~hoare_992312373derivs(X0,X3,X1)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_241)),
% 0.19/0.56 inference(forward_demodulation,[],[f3296,f2781])).
% 0.19/0.56 tff(f3296,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2))),combk(bool,hoare_28830079triple(X0),fFalse))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),X1))) | ~hoare_992312373derivs(X0,X3,X1)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_241)),
% 0.19/0.56 inference(forward_demodulation,[],[f3295,f1005])).
% 0.19/0.56 tff(f3295,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2))),bot_bot(fun(hoare_28830079triple(X0),bool)))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),X1))) | ~hoare_992312373derivs(X0,X3,X1)) ) | (~spl39_16 | ~spl39_208 | ~spl39_241)),
% 0.19/0.56 inference(forward_demodulation,[],[f3293,f2781])).
% 0.19/0.56 tff(f3293,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),X1))) | ~hoare_992312373derivs(X0,X3,X1)) ) | ~spl39_241),
% 0.19/0.56 inference(avatar_component_clause,[],[f3292])).
% 0.19/0.56 tff(f3294,plain,(
% 0.19/0.56 spl39_241),
% 0.19/0.56 inference(avatar_split_clause,[],[f767,f3292])).
% 0.19/0.56 tff(f767,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (~hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),X1))) | ~hoare_992312373derivs(X0,X3,X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f766,f439])).
% 0.19/0.56 tff(f766,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),X1))) | ~hoare_992312373derivs(X0,X3,X1) | ~hoare_992312373derivs(X0,X3,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f650,f439])).
% 0.19/0.56 tff(f650,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),X1)))) | ~hoare_992312373derivs(X0,X3,X1) | ~hoare_992312373derivs(X0,X3,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),X2)),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f533,f491,f491])).
% 0.19/0.56 tff(f533,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool),X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),X2,X1)) | ~hoare_992312373derivs(X0,X3,X1) | ~hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),X2,bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f296])).
% 0.19/0.56 tff(f296,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool),X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),X2,X1)) | ~hoare_992312373derivs(X0,X3,X1) | ~hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),X2,bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 0.19/0.56 inference(flattening,[],[f295])).
% 0.19/0.56 tff(f295,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool),X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool)] : ((hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),X2,X1)) | ~hoare_992312373derivs(X0,X3,X1)) | ~hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),X2,bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 0.19/0.56 inference(ennf_transformation,[],[f216])).
% 0.19/0.56 tff(f216,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool),X2 : hoare_28830079triple(X0),X3 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),X2,bot_bot(fun(hoare_28830079triple(X0),bool)))) => (hoare_992312373derivs(X0,X3,X1) => hoare_992312373derivs(X0,X3,insert(hoare_28830079triple(X0),X2,X1))))),
% 0.19/0.56 inference(rectify,[],[f4])).
% 0.19/0.56 tff(f4,axiom,(
% 0.19/0.56 ! [X1 : $tType,X11 : fun(hoare_28830079triple(X1),bool),X13 : hoare_28830079triple(X1),X10 : fun(hoare_28830079triple(X1),bool)] : (hoare_992312373derivs(X1,X10,insert(hoare_28830079triple(X1),X13,bot_bot(fun(hoare_28830079triple(X1),bool)))) => (hoare_992312373derivs(X1,X10,X11) => hoare_992312373derivs(X1,X10,insert(hoare_28830079triple(X1),X13,X11))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert)).
% 0.19/0.56 tff(f3290,plain,(
% 0.19/0.56 spl39_240 | ~spl39_99 | ~spl39_226),
% 0.19/0.56 inference(avatar_split_clause,[],[f3114,f3010,f1369,f3288])).
% 0.19/0.56 tff(f1369,plain,(
% 0.19/0.56 spl39_99 <=> ! [X2 : state,X0 : a,X1 : state] : (~pp(aa(a,bool,combc(a,state,bool,q1,X2),sK6(X1,X2))) | q(X0,X2) | ~p(X0,X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_99])])).
% 0.19/0.56 tff(f3010,plain,(
% 0.19/0.56 spl39_226 <=> ! [X0 : a] : (~pp(aa(a,bool,combc(a,state,bool,p1,sK4),X0)) | pp(aa(a,bool,combc(a,state,bool,q1,sK5(p1,q1)),X0)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_226])])).
% 0.19/0.56 tff(f3114,plain,(
% 0.19/0.56 ( ! [X0 : state,X1 : a] : (~pp(aa(a,bool,combc(a,state,bool,p1,sK4),sK6(X0,sK5(p1,q1)))) | q(X1,sK5(p1,q1)) | ~p(X1,X0)) ) | (~spl39_99 | ~spl39_226)),
% 0.19/0.56 inference(resolution,[],[f3011,f1370])).
% 0.19/0.56 tff(f1370,plain,(
% 0.19/0.56 ( ! [X2 : state,X0 : a,X1 : state] : (~pp(aa(a,bool,combc(a,state,bool,q1,X2),sK6(X1,X2))) | q(X0,X2) | ~p(X0,X1)) ) | ~spl39_99),
% 0.19/0.56 inference(avatar_component_clause,[],[f1369])).
% 0.19/0.56 tff(f3011,plain,(
% 0.19/0.56 ( ! [X0 : a] : (pp(aa(a,bool,combc(a,state,bool,q1,sK5(p1,q1)),X0)) | ~pp(aa(a,bool,combc(a,state,bool,p1,sK4),X0))) ) | ~spl39_226),
% 0.19/0.56 inference(avatar_component_clause,[],[f3010])).
% 0.19/0.56 tff(f3252,plain,(
% 0.19/0.56 spl39_239 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_238),
% 0.19/0.56 inference(avatar_split_clause,[],[f3248,f3243,f2777,f1420,f901,f3250])).
% 0.19/0.56 tff(f3250,plain,(
% 0.19/0.56 spl39_239 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1),X2) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),minus_minus(fun(X0,bool),X1,X2)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_239])])).
% 0.19/0.56 tff(f3243,plain,(
% 0.19/0.56 spl39_238 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,X2))) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)),X2) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_238])])).
% 0.19/0.56 tff(f3248,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1),X2) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),minus_minus(fun(X0,bool),X1,X2))) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_238)),
% 0.19/0.56 inference(forward_demodulation,[],[f3247,f1421])).
% 0.19/0.56 tff(f3247,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1),X2) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),minus_minus(fun(X0,bool),X1,X2)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | (~spl39_16 | ~spl39_208 | ~spl39_238)),
% 0.19/0.56 inference(forward_demodulation,[],[f3246,f2781])).
% 0.19/0.56 tff(f3246,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,X2))) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1),X2) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | (~spl39_16 | ~spl39_208 | ~spl39_238)),
% 0.19/0.56 inference(forward_demodulation,[],[f3244,f2781])).
% 0.19/0.56 tff(f3244,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,X2))) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)),X2) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | ~spl39_238),
% 0.19/0.56 inference(avatar_component_clause,[],[f3243])).
% 0.19/0.56 tff(f3245,plain,(
% 0.19/0.56 spl39_238),
% 0.19/0.56 inference(avatar_split_clause,[],[f764,f3243])).
% 0.19/0.56 tff(f764,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,X2))) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)),X2) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f763,f439])).
% 0.19/0.56 tff(f763,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1))),X2) = combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,X2))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f648,f439])).
% 0.19/0.56 tff(f648,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1))),X2) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,X2)))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f530,f491,f491])).
% 0.19/0.56 tff(f530,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),insert(X0,X3,X1),X2) = insert(X0,X3,minus_minus(fun(X0,bool),X1,X2)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f291])).
% 0.19/0.56 tff(f291,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : X0] : ((minus_minus(fun(X0,bool),insert(X0,X3,X1),X2) = insert(X0,X3,minus_minus(fun(X0,bool),X1,X2)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) & (minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),insert(X0,X3,X1),X2) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))))),
% 0.19/0.56 inference(ennf_transformation,[],[f211])).
% 0.19/0.56 tff(f211,plain,(
% 0.19/0.56 ! [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)) => minus_minus(fun(X0,bool),insert(X0,X3,X1),X2) = insert(X0,X3,minus_minus(fun(X0,bool),X1,X2))) & (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) => minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),insert(X0,X3,X1),X2)))),
% 0.19/0.56 inference(rectify,[],[f65])).
% 0.19/0.56 tff(f65,axiom,(
% 0.19/0.56 ! [X1 : $tType,X14 : fun(X1,bool),X18 : fun(X1,bool),X15 : X1] : ((~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X18)) => minus_minus(fun(X1,bool),insert(X1,X15,X14),X18) = insert(X1,X15,minus_minus(fun(X1,bool),X14,X18))) & (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X18)) => minus_minus(fun(X1,bool),X14,X18) = minus_minus(fun(X1,bool),insert(X1,X15,X14),X18)))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_insert__Diff__if)).
% 0.19/0.56 tff(f3218,plain,(
% 0.19/0.56 spl39_237 | ~spl39_16 | ~spl39_37 | ~spl39_104 | ~spl39_208 | ~spl39_236),
% 0.19/0.56 inference(avatar_split_clause,[],[f3214,f3208,f2777,f1420,f1004,f901,f3216])).
% 0.19/0.56 tff(f3216,plain,(
% 0.19/0.56 spl39_237 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse)))) = X1)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_237])])).
% 0.19/0.56 tff(f3208,plain,(
% 0.19/0.56 spl39_236 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_236])])).
% 0.19/0.56 tff(f3214,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse)))) = X1) ) | (~spl39_16 | ~spl39_37 | ~spl39_104 | ~spl39_208 | ~spl39_236)),
% 0.19/0.56 inference(forward_demodulation,[],[f3213,f1421])).
% 0.19/0.56 tff(f3213,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse)))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_236)),
% 0.19/0.56 inference(forward_demodulation,[],[f3212,f1005])).
% 0.19/0.56 tff(f3212,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),bot_bot(fun(X0,bool))))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | (~spl39_16 | ~spl39_208 | ~spl39_236)),
% 0.19/0.56 inference(forward_demodulation,[],[f3211,f2781])).
% 0.19/0.56 tff(f3211,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | (~spl39_16 | ~spl39_208 | ~spl39_236)),
% 0.19/0.56 inference(forward_demodulation,[],[f3209,f2781])).
% 0.19/0.56 tff(f3209,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | ~spl39_236),
% 0.19/0.56 inference(avatar_component_clause,[],[f3208])).
% 0.19/0.56 tff(f3210,plain,(
% 0.19/0.56 spl39_236),
% 0.19/0.56 inference(avatar_split_clause,[],[f747,f3208])).
% 0.19/0.56 tff(f747,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f746,f439])).
% 0.19/0.56 tff(f746,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f637,f439])).
% 0.19/0.56 tff(f637,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X1,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f512,f491,f491])).
% 0.19/0.56 tff(f512,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (insert(X0,X2,minus_minus(fun(X0,bool),X1,insert(X0,X2,bot_bot(fun(X0,bool))))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f287])).
% 0.19/0.56 tff(f287,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (insert(X0,X2,minus_minus(fun(X0,bool),X1,insert(X0,X2,bot_bot(fun(X0,bool))))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 0.19/0.56 inference(ennf_transformation,[],[f199])).
% 0.19/0.56 tff(f199,plain,(
% 0.19/0.56 ! [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)) => insert(X0,X2,minus_minus(fun(X0,bool),X1,insert(X0,X2,bot_bot(fun(X0,bool))))) = X1)),
% 0.19/0.56 inference(rectify,[],[f73])).
% 0.19/0.56 tff(f73,axiom,(
% 0.19/0.56 ! [X1 : $tType,X14 : fun(X1,bool),X17 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),X14)) => insert(X1,X17,minus_minus(fun(X1,bool),X14,insert(X1,X17,bot_bot(fun(X1,bool))))) = X14)),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_insert__Diff)).
% 0.19/0.56 tff(f3171,plain,(
% 0.19/0.56 spl39_235 | ~spl39_16 | ~spl39_37 | ~spl39_104 | ~spl39_175 | ~spl39_208 | ~spl39_210 | ~spl39_234),
% 0.19/0.56 inference(avatar_split_clause,[],[f3167,f3160,f2792,f2777,f2435,f1420,f1004,f901,f3169])).
% 0.19/0.56 tff(f3169,plain,(
% 0.19/0.56 spl39_235 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) = X1)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_235])])).
% 0.19/0.56 tff(f2435,plain,(
% 0.19/0.56 spl39_175 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))),X2))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_175])])).
% 0.19/0.56 tff(f2792,plain,(
% 0.19/0.56 spl39_210 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1),X2))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_210])])).
% 0.19/0.56 tff(f3160,plain,(
% 0.19/0.56 spl39_234 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_234])])).
% 0.19/0.56 tff(f3167,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) = X1) ) | (~spl39_16 | ~spl39_37 | ~spl39_104 | ~spl39_175 | ~spl39_208 | ~spl39_210 | ~spl39_234)),
% 0.19/0.56 inference(forward_demodulation,[],[f3166,f1421])).
% 0.19/0.56 tff(f3166,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | (~spl39_16 | ~spl39_37 | ~spl39_175 | ~spl39_208 | ~spl39_210 | ~spl39_234)),
% 0.19/0.56 inference(forward_demodulation,[],[f3165,f2811])).
% 0.19/0.56 tff(f2811,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X3)) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X3))) ) | (~spl39_16 | ~spl39_175 | ~spl39_208 | ~spl39_210)),
% 0.19/0.56 inference(forward_demodulation,[],[f2799,f2781])).
% 0.19/0.56 tff(f2799,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3))) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3)))) ) | (~spl39_175 | ~spl39_210)),
% 0.19/0.56 inference(resolution,[],[f2793,f2436])).
% 0.19/0.56 tff(f2436,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))),X2))) ) | ~spl39_175),
% 0.19/0.56 inference(avatar_component_clause,[],[f2435])).
% 0.19/0.56 tff(f2793,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1),X2)) ) | ~spl39_210),
% 0.19/0.56 inference(avatar_component_clause,[],[f2792])).
% 0.19/0.56 tff(f3165,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_234)),
% 0.19/0.56 inference(forward_demodulation,[],[f3164,f2781])).
% 0.19/0.56 tff(f3164,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_234)),
% 0.19/0.56 inference(forward_demodulation,[],[f3163,f1005])).
% 0.19/0.56 tff(f3163,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),bot_bot(fun(X0,bool)))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | (~spl39_16 | ~spl39_208 | ~spl39_234)),
% 0.19/0.56 inference(forward_demodulation,[],[f3161,f2781])).
% 0.19/0.56 tff(f3161,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | ~spl39_234),
% 0.19/0.56 inference(avatar_component_clause,[],[f3160])).
% 0.19/0.56 tff(f3162,plain,(
% 0.19/0.56 spl39_234),
% 0.19/0.56 inference(avatar_split_clause,[],[f744,f3160])).
% 0.19/0.56 tff(f744,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f743,f439])).
% 0.19/0.56 tff(f743,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f634,f439])).
% 0.19/0.56 tff(f634,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f509,f491,f491])).
% 0.19/0.56 tff(f509,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),insert(X0,X2,X1),insert(X0,X2,bot_bot(fun(X0,bool)))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f284])).
% 0.19/0.56 tff(f284,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (minus_minus(fun(X0,bool),insert(X0,X2,X1),insert(X0,X2,bot_bot(fun(X0,bool)))) = X1 | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 0.19/0.56 inference(ennf_transformation,[],[f196])).
% 0.19/0.56 tff(f196,plain,(
% 0.19/0.56 ! [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)) => minus_minus(fun(X0,bool),insert(X0,X2,X1),insert(X0,X2,bot_bot(fun(X0,bool)))) = X1)),
% 0.19/0.56 inference(rectify,[],[f74])).
% 0.19/0.56 tff(f74,axiom,(
% 0.19/0.56 ! [X1 : $tType,X14 : fun(X1,bool),X15 : X1] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X14)) => minus_minus(fun(X1,bool),insert(X1,X15,X14),insert(X1,X15,bot_bot(fun(X1,bool)))) = X14)),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Diff__insert__absorb)).
% 0.19/0.56 tff(f3113,plain,(
% 0.19/0.56 spl39_233 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_232),
% 0.19/0.56 inference(avatar_split_clause,[],[f3109,f3104,f2777,f1004,f901,f3111])).
% 0.19/0.56 tff(f3111,plain,(
% 0.19/0.56 spl39_233 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : fun(X0,bool)] : minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))),X1)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_233])])).
% 0.19/0.56 tff(f3104,plain,(
% 0.19/0.56 spl39_232 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : fun(X0,bool)] : minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))),X1)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_232])])).
% 0.19/0.56 tff(f3109,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))),X1)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_232)),
% 0.19/0.56 inference(forward_demodulation,[],[f3108,f2781])).
% 0.19/0.56 tff(f3108,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))),X1)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_232)),
% 0.19/0.56 inference(forward_demodulation,[],[f3107,f1005])).
% 0.19/0.56 tff(f3107,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),bot_bot(fun(X0,bool)))),X1)) ) | (~spl39_16 | ~spl39_208 | ~spl39_232)),
% 0.19/0.56 inference(forward_demodulation,[],[f3105,f2781])).
% 0.19/0.56 tff(f3105,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))),X1)) ) | ~spl39_232),
% 0.19/0.56 inference(avatar_component_clause,[],[f3104])).
% 0.19/0.56 tff(f3106,plain,(
% 0.19/0.56 spl39_232),
% 0.19/0.56 inference(avatar_split_clause,[],[f762,f3104])).
% 0.19/0.56 tff(f762,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))),X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f761,f439])).
% 0.19/0.56 tff(f761,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))),X1)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f647,f439])).
% 0.19/0.56 tff(f647,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))),X1)) )),
% 0.19/0.56 inference(definition_unfolding,[],[f528,f491,f491])).
% 0.19/0.56 tff(f528,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,insert(X0,X2,X1)) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,insert(X0,X2,bot_bot(fun(X0,bool)))),X1)) )),
% 0.19/0.56 inference(cnf_transformation,[],[f210])).
% 0.19/0.56 tff(f210,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : minus_minus(fun(X0,bool),X3,insert(X0,X2,X1)) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,insert(X0,X2,bot_bot(fun(X0,bool)))),X1)),
% 0.19/0.56 inference(rectify,[],[f75])).
% 0.19/0.56 tff(f75,axiom,(
% 0.19/0.56 ! [X1 : $tType,X18 : fun(X1,bool),X17 : X1,X14 : fun(X1,bool)] : minus_minus(fun(X1,bool),X14,insert(X1,X17,X18)) = minus_minus(fun(X1,bool),minus_minus(fun(X1,bool),X14,insert(X1,X17,bot_bot(fun(X1,bool)))),X18)),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Diff__insert2)).
% 0.19/0.56 tff(f3081,plain,(
% 0.19/0.56 spl39_231 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_230),
% 0.19/0.56 inference(avatar_split_clause,[],[f3077,f3072,f2777,f1004,f901,f3079])).
% 0.19/0.56 tff(f3079,plain,(
% 0.19/0.56 spl39_231 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : fun(X0,bool)] : minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_231])])).
% 0.19/0.56 tff(f3072,plain,(
% 0.19/0.56 spl39_230 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : fun(X0,bool)] : minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_230])])).
% 0.19/0.56 tff(f3077,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse)))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_230)),
% 0.19/0.56 inference(forward_demodulation,[],[f3076,f1005])).
% 0.19/0.56 tff(f3076,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),bot_bot(fun(X0,bool))))) ) | (~spl39_16 | ~spl39_208 | ~spl39_230)),
% 0.19/0.56 inference(forward_demodulation,[],[f3075,f2781])).
% 0.19/0.56 tff(f3075,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1))) ) | (~spl39_16 | ~spl39_208 | ~spl39_230)),
% 0.19/0.56 inference(forward_demodulation,[],[f3073,f2781])).
% 0.19/0.56 tff(f3073,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) ) | ~spl39_230),
% 0.19/0.56 inference(avatar_component_clause,[],[f3072])).
% 0.19/0.56 tff(f3074,plain,(
% 0.19/0.56 spl39_230),
% 0.19/0.56 inference(avatar_split_clause,[],[f760,f3072])).
% 0.19/0.56 tff(f760,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f759,f439])).
% 0.19/0.56 tff(f759,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f646,f439])).
% 0.19/0.56 tff(f646,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f527,f491,f491])).
% 0.19/0.56 tff(f527,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X3,insert(X0,X2,X1)) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),insert(X0,X2,bot_bot(fun(X0,bool))))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f209])).
% 0.19/0.56 tff(f209,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : minus_minus(fun(X0,bool),X3,insert(X0,X2,X1)) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X3,X1),insert(X0,X2,bot_bot(fun(X0,bool))))),
% 0.19/0.56 inference(rectify,[],[f79])).
% 0.19/0.56 tff(f79,axiom,(
% 0.19/0.56 ! [X1 : $tType,X18 : fun(X1,bool),X17 : X1,X14 : fun(X1,bool)] : minus_minus(fun(X1,bool),X14,insert(X1,X17,X18)) = minus_minus(fun(X1,bool),minus_minus(fun(X1,bool),X14,X18),insert(X1,X17,bot_bot(fun(X1,bool))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Diff__insert)).
% 0.19/0.56 tff(f3062,plain,(
% 0.19/0.56 spl39_229 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_228),
% 0.19/0.56 inference(avatar_split_clause,[],[f3058,f3053,f2777,f1004,f901,f3060])).
% 0.19/0.56 tff(f3060,plain,(
% 0.19/0.56 spl39_229 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combk(bool,X0,fFalse))) | X1 = X2)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_229])])).
% 0.19/0.56 tff(f3053,plain,(
% 0.19/0.56 spl39_228 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_228])])).
% 0.19/0.56 tff(f3058,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),combk(bool,X0,fFalse))) | X1 = X2) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_228)),
% 0.19/0.56 inference(forward_demodulation,[],[f3057,f2781])).
% 0.19/0.56 tff(f3057,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),combk(bool,X0,fFalse))) | X1 = X2) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_228)),
% 0.19/0.56 inference(forward_demodulation,[],[f3056,f1005])).
% 0.19/0.56 tff(f3056,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),bot_bot(fun(X0,bool)))) | X1 = X2) ) | (~spl39_16 | ~spl39_208 | ~spl39_228)),
% 0.19/0.56 inference(forward_demodulation,[],[f3054,f2781])).
% 0.19/0.56 tff(f3054,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) ) | ~spl39_228),
% 0.19/0.56 inference(avatar_component_clause,[],[f3053])).
% 0.19/0.56 tff(f3055,plain,(
% 0.19/0.56 spl39_228),
% 0.19/0.56 inference(avatar_split_clause,[],[f635,f3053])).
% 0.19/0.56 tff(f635,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f510,f491,f491])).
% 0.19/0.56 tff(f510,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | insert(X0,X1,bot_bot(fun(X0,bool))) != insert(X0,X2,bot_bot(fun(X0,bool)))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f285])).
% 0.19/0.56 tff(f285,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = X2 | insert(X0,X1,bot_bot(fun(X0,bool))) != insert(X0,X2,bot_bot(fun(X0,bool))))),
% 0.19/0.56 inference(ennf_transformation,[],[f197])).
% 0.19/0.56 tff(f197,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : X0,X2 : X0] : (insert(X0,X1,bot_bot(fun(X0,bool))) = insert(X0,X2,bot_bot(fun(X0,bool))) => X1 = X2)),
% 0.19/0.56 inference(rectify,[],[f29])).
% 0.19/0.56 tff(f29,axiom,(
% 0.19/0.56 ! [X1 : $tType,X16 : X1,X17 : X1] : (insert(X1,X17,bot_bot(fun(X1,bool))) = insert(X1,X16,bot_bot(fun(X1,bool))) => X16 = X17)),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_singleton__inject)).
% 0.19/0.56 tff(f3016,plain,(
% 0.19/0.56 spl39_227 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_225),
% 0.19/0.56 inference(avatar_split_clause,[],[f3008,f3004,f2777,f1004,f901,f3014])).
% 0.19/0.56 tff(f3014,plain,(
% 0.19/0.56 spl39_227 <=> ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))),combk(bool,hoare_28830079triple(X0),fFalse))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_227])])).
% 0.19/0.56 tff(f3004,plain,(
% 0.19/0.56 spl39_225 <=> ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_225])])).
% 0.19/0.56 tff(f3008,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1)))),combk(bool,hoare_28830079triple(X0),fFalse))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4)))) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_225)),
% 0.19/0.56 inference(forward_demodulation,[],[f3007,f1005])).
% 0.19/0.56 tff(f3007,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fimplies,combb(bool,bool,hoare_28830079triple(X0),fNot,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(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,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4)))) ) | (~spl39_16 | ~spl39_208 | ~spl39_225)),
% 0.19/0.56 inference(forward_demodulation,[],[f3005,f2781])).
% 0.19/0.56 tff(f3005,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4)))) ) | ~spl39_225),
% 0.19/0.56 inference(avatar_component_clause,[],[f3004])).
% 0.19/0.56 tff(f3012,plain,(
% 0.19/0.56 spl39_226 | ~spl39_90 | ~spl39_194),
% 0.19/0.56 inference(avatar_split_clause,[],[f2628,f2624,f1316,f3010])).
% 0.19/0.56 tff(f1316,plain,(
% 0.19/0.56 spl39_90 <=> ! [X2 : fun(a,fun(state,bool)),X5 : a,X3 : fun(a,fun(state,bool))] : (~hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)))),combk(bool,hoare_28830079triple(a),fFalse))) | ~pp(aa(a,bool,combc(a,state,bool,X2,sK4),X5)) | pp(aa(a,bool,combc(a,state,bool,X3,sK5(X2,X3)),X5)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_90])])).
% 0.19/0.56 tff(f2624,plain,(
% 0.19/0.56 spl39_194 <=> hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,p1,c,q1)))),combk(bool,hoare_28830079triple(a),fFalse)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_194])])).
% 0.19/0.56 tff(f2628,plain,(
% 0.19/0.56 ( ! [X0 : a] : (~pp(aa(a,bool,combc(a,state,bool,p1,sK4),X0)) | pp(aa(a,bool,combc(a,state,bool,q1,sK5(p1,q1)),X0))) ) | (~spl39_90 | ~spl39_194)),
% 0.19/0.56 inference(resolution,[],[f2626,f1317])).
% 0.19/0.56 tff(f1317,plain,(
% 0.19/0.56 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool)),X5 : a] : (~hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)))),combk(bool,hoare_28830079triple(a),fFalse))) | ~pp(aa(a,bool,combc(a,state,bool,X2,sK4),X5)) | pp(aa(a,bool,combc(a,state,bool,X3,sK5(X2,X3)),X5))) ) | ~spl39_90),
% 0.19/0.56 inference(avatar_component_clause,[],[f1316])).
% 0.19/0.56 tff(f2626,plain,(
% 0.19/0.56 hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,p1,c,q1)))),combk(bool,hoare_28830079triple(a),fFalse))) | ~spl39_194),
% 0.19/0.56 inference(avatar_component_clause,[],[f2624])).
% 0.19/0.56 tff(f3006,plain,(
% 0.19/0.56 spl39_225),
% 0.19/0.56 inference(avatar_split_clause,[],[f809,f3004])).
% 0.19/0.56 tff(f809,plain,(
% 0.19/0.56 ( ! [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,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4)))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f683,f439])).
% 0.19/0.56 tff(f683,plain,(
% 0.19/0.56 ( ! [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,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X4,X2,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool)))))) | pp(aa(state,bool,aa(X0,fun(state,bool),X4,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4)))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f583,f491])).
% 0.19/0.56 tff(f583,plain,(
% 0.19/0.56 ( ! [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,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,sK33(X0,X1,X2,X3,X4)),sK34(X0,X1,X2,X3,X4)))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f405])).
% 0.19/0.56 tff(f2973,plain,(
% 0.19/0.56 spl39_224 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_223),
% 0.19/0.56 inference(avatar_split_clause,[],[f2969,f2964,f2777,f1004,f901,f2971])).
% 0.19/0.56 tff(f2971,plain,(
% 0.19/0.56 spl39_224 <=> ! [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,minus_minus(fun(X0,bool),sK21(X0,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK20(X0,X1)))),combk(bool,X0,fFalse))))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_224])])).
% 0.19/0.56 tff(f2964,plain,(
% 0.19/0.56 spl39_223 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),sK21(X0,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK20(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) | pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_223])])).
% 0.19/0.56 tff(f2969,plain,(
% 0.19/0.56 ( ! [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,minus_minus(fun(X0,bool),sK21(X0,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK20(X0,X1)))),combk(bool,X0,fFalse))))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_223)),
% 0.19/0.56 inference(forward_demodulation,[],[f2968,f1005])).
% 0.19/0.56 tff(f2968,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),sK21(X0,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK20(X0,X1)))),combk(bool,X0,fFalse))))) | pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_223)),
% 0.19/0.56 inference(forward_demodulation,[],[f2967,f1005])).
% 0.19/0.56 tff(f2967,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),sK21(X0,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK20(X0,X1)))),bot_bot(fun(X0,bool)))))) | pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_16 | ~spl39_208 | ~spl39_223)),
% 0.19/0.56 inference(forward_demodulation,[],[f2965,f2781])).
% 0.19/0.56 tff(f2965,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),sK21(X0,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK20(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) | pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | ~spl39_223),
% 0.19/0.56 inference(avatar_component_clause,[],[f2964])).
% 0.19/0.56 tff(f2966,plain,(
% 0.19/0.56 spl39_223),
% 0.19/0.56 inference(avatar_split_clause,[],[f741,f2964])).
% 0.19/0.56 tff(f741,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),sK21(X0,X1),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK20(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))))) | pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f632,f439])).
% 0.19/0.56 tff(f632,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),sK21(X0,X1),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK20(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) )),
% 0.19/0.56 inference(definition_unfolding,[],[f501,f491])).
% 0.19/0.56 tff(f501,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),sK21(X0,X1),insert(X0,sK20(X0,X1),bot_bot(fun(X0,bool)))))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) )),
% 0.19/0.56 inference(cnf_transformation,[],[f366])).
% 0.19/0.56 tff(f366,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | (~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),sK21(X0,X1),insert(X0,sK20(X0,X1),bot_bot(fun(X0,bool)))))) & pp(aa(fun(X0,bool),bool,X1,sK21(X0,X1))) & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK20(X0,X1)),sK21(X0,X1))) & finite_finite1(X0,sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 0.19/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f279,f365])).
% 0.19/0.56 tff(f365,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (? [X3 : X0,X4 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),X4,insert(X0,X3,bot_bot(fun(X0,bool)))))) & 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,minus_minus(fun(X0,bool),sK21(X0,X1),insert(X0,sK20(X0,X1),bot_bot(fun(X0,bool)))))) & pp(aa(fun(X0,bool),bool,X1,sK21(X0,X1))) & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK20(X0,X1)),sK21(X0,X1))) & finite_finite1(X0,sK21(X0,X1))))),
% 0.19/0.56 introduced(choice_axiom,[])).
% 0.19/0.56 tff(f279,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ? [X3 : X0,X4 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),X4,insert(X0,X3,bot_bot(fun(X0,bool)))))) & 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,X2)) | ~finite_finite1(X0,X2))),
% 0.19/0.56 inference(flattening,[],[f278])).
% 0.19/0.56 tff(f278,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (((pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ? [X3 : X0,X4 : fun(X0,bool)] : (((~pp(aa(fun(X0,bool),bool,X1,minus_minus(fun(X0,bool),X4,insert(X0,X3,bot_bot(fun(X0,bool)))))) & 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,X2))) | ~finite_finite1(X0,X2))),
% 0.19/0.56 inference(ennf_transformation,[],[f192])).
% 0.19/0.56 tff(f192,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool),X2 : fun(X0,bool)] : (finite_finite1(X0,X2) => (pp(aa(fun(X0,bool),bool,X1,X2)) => (! [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,minus_minus(fun(X0,bool),X4,insert(X0,X3,bot_bot(fun(X0,bool))))))))) => pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))))))),
% 0.19/0.56 inference(rectify,[],[f97])).
% 0.19/0.56 tff(f97,axiom,(
% 0.19/0.56 ! [X1 : $tType,X20 : fun(fun(X1,bool),bool),X14 : fun(X1,bool)] : (finite_finite1(X1,X14) => (pp(aa(fun(X1,bool),bool,X20,X14)) => (! [X61 : X1,X62 : fun(X1,bool)] : (finite_finite1(X1,X62) => (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X61),X62)) => (pp(aa(fun(X1,bool),bool,X20,X62)) => pp(aa(fun(X1,bool),bool,X20,minus_minus(fun(X1,bool),X62,insert(X1,X61,bot_bot(fun(X1,bool))))))))) => pp(aa(fun(X1,bool),bool,X20,bot_bot(fun(X1,bool)))))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_finite__empty__induct)).
% 0.19/0.56 tff(f2961,plain,(
% 0.19/0.56 spl39_222),
% 0.19/0.56 inference(avatar_split_clause,[],[f830,f2959])).
% 0.19/0.56 tff(f2959,plain,(
% 0.19/0.56 spl39_222 <=> ! [X1 : $tType,X0 : $tType,X5 : fun(X0,bool),X3 : X1,X4 : fun(X0,fun(X1,X1)),X6 : X0,X2 : X1] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X5),X6)) | finite_fold_graph(X0,X1,X4,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X6)),combc(X0,fun(X0,bool),bool,member(X0),X5)),aa(X1,X1,aa(X0,fun(X1,X1),X4,X6),X2)) | ~finite_fold_graph(X0,X1,X4,X3,X5,X2))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_222])])).
% 0.19/0.56 tff(f830,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X1,X6 : X0,X4 : fun(X0,fun(X1,X1)),X5 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X5),X6)) | finite_fold_graph(X0,X1,X4,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X6)),combc(X0,fun(X0,bool),bool,member(X0),X5)),aa(X1,X1,aa(X0,fun(X1,X1),X4,X6),X2)) | ~finite_fold_graph(X0,X1,X4,X3,X5,X2)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f829,f595])).
% 0.19/0.56 tff(f595,plain,(
% 0.19/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : (aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)) )),
% 0.19/0.56 inference(cnf_transformation,[],[f244])).
% 0.19/0.56 tff(f244,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)),
% 0.19/0.56 inference(rectify,[],[f112])).
% 0.19/0.56 tff(f112,axiom,(
% 0.19/0.56 ! [X0 : $tType,X2 : $tType,X1 : $tType,X73 : X0,X74 : X1,X72 : fun(X0,fun(X1,X2))] : aa(X0,X2,combc(X0,X1,X2,X72,X74),X73) = aa(X1,X2,aa(X0,fun(X1,X2),X72,X73),X74)),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U)).
% 0.19/0.56 tff(f829,plain,(
% 0.19/0.56 ( ! [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,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X6)),combc(X0,fun(X0,bool),bool,member(X0),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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f689,f439])).
% 0.19/0.56 tff(f689,plain,(
% 0.19/0.56 ( ! [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,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X6)),combc(X0,fun(X0,bool),bool,member(X0),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))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f609,f491])).
% 0.19/0.56 tff(f609,plain,(
% 0.19/0.56 ( ! [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,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))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f321])).
% 0.19/0.56 tff(f321,plain,(
% 0.19/0.56 ! [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,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)))),
% 0.19/0.56 inference(flattening,[],[f320])).
% 0.19/0.56 tff(f320,plain,(
% 0.19/0.56 ! [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,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)))),
% 0.19/0.56 inference(ennf_transformation,[],[f251])).
% 0.19/0.56 tff(f251,plain,(
% 0.19/0.56 ! [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,insert(X0,X6,X5),aa(X1,X1,aa(X0,fun(X1,X1),X4,X6),X2))))),
% 0.19/0.56 inference(rectify,[],[f72])).
% 0.19/0.56 tff(f72,axiom,(
% 0.19/0.56 ! [X1 : $tType,X2 : $tType,X24 : X2,X57 : X2,X47 : fun(X1,fun(X2,X2)),X14 : fun(X1,bool),X15 : X1] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X14)) => (finite_fold_graph(X1,X2,X47,X57,X14,X24) => finite_fold_graph(X1,X2,X47,X57,insert(X1,X15,X14),aa(X2,X2,aa(X1,fun(X2,X2),X47,X15),X24))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_fold__graph_OinsertI)).
% 0.19/0.56 tff(f2937,plain,(
% 0.19/0.56 spl39_221 | ~spl39_16 | ~spl39_208 | ~spl39_220),
% 0.19/0.56 inference(avatar_split_clause,[],[f2933,f2930,f2777,f901,f2935])).
% 0.19/0.56 tff(f2935,plain,(
% 0.19/0.56 spl39_221 <=> ! [X3 : $tType,X2 : $tType,X7 : fun(X3,bool),X8 : X2,X0 : X2,X6 : X3,X1 : fun(X3,fun(X2,X2))] : (sP2(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fimplies,combb(bool,bool,X3,fNot,combc(X3,X3,bool,fequal(X3),X6))),X7)) | pp(aa(X3,bool,combc(X3,fun(X3,bool),bool,member(X3),X7),X6)) | ~finite_fold_graph(X3,X2,X1,X0,X7,X8))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_221])])).
% 0.19/0.56 tff(f2930,plain,(
% 0.19/0.56 spl39_220 <=> ! [X3 : $tType,X2 : $tType,X7 : fun(X3,bool),X8 : X2,X0 : X2,X6 : X3,X1 : fun(X3,fun(X2,X2))] : (pp(aa(X3,bool,combc(X3,fun(X3,bool),bool,member(X3),X7),X6)) | sP2(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),X6)),combc(X3,fun(X3,bool),bool,member(X3),X7))) | ~finite_fold_graph(X3,X2,X1,X0,X7,X8))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_220])])).
% 0.19/0.56 tff(f2933,plain,(
% 0.19/0.56 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X8 : X2,X6 : X3,X7 : fun(X3,bool)] : (sP2(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fimplies,combb(bool,bool,X3,fNot,combc(X3,X3,bool,fequal(X3),X6))),X7)) | pp(aa(X3,bool,combc(X3,fun(X3,bool),bool,member(X3),X7),X6)) | ~finite_fold_graph(X3,X2,X1,X0,X7,X8)) ) | (~spl39_16 | ~spl39_208 | ~spl39_220)),
% 0.19/0.56 inference(forward_demodulation,[],[f2931,f2781])).
% 0.19/0.56 tff(f2931,plain,(
% 0.19/0.56 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X8 : X2,X6 : X3,X7 : fun(X3,bool)] : (pp(aa(X3,bool,combc(X3,fun(X3,bool),bool,member(X3),X7),X6)) | sP2(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),X6)),combc(X3,fun(X3,bool),bool,member(X3),X7))) | ~finite_fold_graph(X3,X2,X1,X0,X7,X8)) ) | ~spl39_220),
% 0.19/0.56 inference(avatar_component_clause,[],[f2930])).
% 0.19/0.56 tff(f2932,plain,(
% 0.19/0.56 spl39_220),
% 0.19/0.56 inference(avatar_split_clause,[],[f823,f2930])).
% 0.19/0.56 tff(f823,plain,(
% 0.19/0.56 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X8 : X2,X6 : X3,X7 : fun(X3,bool)] : (pp(aa(X3,bool,combc(X3,fun(X3,bool),bool,member(X3),X7),X6)) | sP2(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),X6)),combc(X3,fun(X3,bool),bool,member(X3),X7))) | ~finite_fold_graph(X3,X2,X1,X0,X7,X8)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f822,f595])).
% 0.19/0.56 tff(f822,plain,(
% 0.19/0.56 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X8 : X2,X6 : X3,X7 : fun(X3,bool)] : (sP2(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),X6)),combc(X3,fun(X3,bool),bool,member(X3),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))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f718,f439])).
% 0.19/0.56 tff(f718,plain,(
% 0.19/0.56 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X8 : X2,X6 : X3,X7 : fun(X3,bool)] : (sP2(X2,X3,X0,X1,aa(X2,X2,aa(X3,fun(X2,X2),X1,X6),X8),collect(X3,combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),X6)),combc(X3,fun(X3,bool),bool,member(X3),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))) )),
% 0.19/0.56 inference(equality_resolution,[],[f717])).
% 0.19/0.56 tff(f717,plain,(
% 0.19/0.56 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X8 : X2,X6 : X3,X7 : fun(X3,bool),X5 : fun(X3,bool)] : (sP2(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)) | collect(X3,combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),X6)),combc(X3,fun(X3,bool),bool,member(X3),X7))) != X5) )),
% 0.19/0.56 inference(equality_resolution,[],[f686])).
% 0.19/0.56 tff(f686,plain,(
% 0.19/0.56 ( ! [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)] : (sP2(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 | collect(X3,combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),X6)),combc(X3,fun(X3,bool),bool,member(X3),X7))) != X5) )),
% 0.19/0.56 inference(definition_unfolding,[],[f603,f491])).
% 0.19/0.56 tff(f603,plain,(
% 0.19/0.56 ( ! [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)] : (sP2(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 | insert(X3,X6,X7) != X5) )),
% 0.19/0.56 inference(cnf_transformation,[],[f413])).
% 0.19/0.56 tff(f413,plain,(
% 0.19/0.56 ! [X0 : X2,X1 : fun(X3,fun(X2,X2)),X2 : $tType,X3 : $tType,X4 : X2,X5 : fun(X3,bool)] : ((sP2(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 | insert(X3,X6,X7) != X5)) & ((finite_fold_graph(X3,X2,X1,X0,sK37(X2,X3,X0,X1,X4,X5),sK38(X2,X3,X0,X1,X4,X5)) & ~pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),sK36(X2,X3,X0,X1,X4,X5)),sK37(X2,X3,X0,X1,X4,X5))) & aa(X2,X2,aa(X3,fun(X2,X2),X1,sK36(X2,X3,X0,X1,X4,X5)),sK38(X2,X3,X0,X1,X4,X5)) = X4 & insert(X3,sK36(X2,X3,X0,X1,X4,X5),sK37(X2,X3,X0,X1,X4,X5)) = X5) | ~sP2(X2,X3,X0,X1,X4,X5)))),
% 0.19/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37,sK38])],[f411,f412])).
% 0.19/0.56 tff(f412,plain,(
% 0.19/0.56 ! [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 & insert(X3,X9,X10) = X5) => (finite_fold_graph(X3,X2,X1,X0,sK37(X2,X3,X0,X1,X4,X5),sK38(X2,X3,X0,X1,X4,X5)) & ~pp(aa(fun(X3,bool),bool,aa(X3,fun(fun(X3,bool),bool),member(X3),sK36(X2,X3,X0,X1,X4,X5)),sK37(X2,X3,X0,X1,X4,X5))) & aa(X2,X2,aa(X3,fun(X2,X2),X1,sK36(X2,X3,X0,X1,X4,X5)),sK38(X2,X3,X0,X1,X4,X5)) = X4 & insert(X3,sK36(X2,X3,X0,X1,X4,X5),sK37(X2,X3,X0,X1,X4,X5)) = X5))),
% 0.19/0.56 introduced(choice_axiom,[])).
% 0.19/0.56 tff(f411,plain,(
% 0.19/0.56 ! [X0 : X2,X1 : fun(X3,fun(X2,X2)),X2 : $tType,X3 : $tType,X4 : X2,X5 : fun(X3,bool)] : ((sP2(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 | 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 & insert(X3,X9,X10) = X5) | ~sP2(X2,X3,X0,X1,X4,X5)))),
% 0.19/0.56 inference(rectify,[],[f410])).
% 0.19/0.56 tff(f410,plain,(
% 0.19/0.56 ! [X4 : X1,X5 : fun(X0,fun(X1,X1)),X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool)] : ((sP2(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 | 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 & insert(X0,X6,X7) = X3) | ~sP2(X1,X0,X4,X5,X2,X3)))),
% 0.19/0.56 inference(nnf_transformation,[],[f326])).
% 0.19/0.56 tff(f326,plain,(
% 0.19/0.56 ! [X4 : X1,X5 : fun(X0,fun(X1,X1)),X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool)] : (sP2(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 & insert(X0,X6,X7) = X3))),
% 0.19/0.56 introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])])).
% 0.19/0.56 tff(f2913,plain,(
% 0.19/0.56 spl39_219 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_218),
% 0.19/0.56 inference(avatar_split_clause,[],[f2901,f2896,f2777,f1420,f901,f2911])).
% 0.19/0.56 tff(f2911,plain,(
% 0.19/0.56 spl39_219 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)) | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)),X3)) | X2 = X3)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_219])])).
% 0.19/0.56 tff(f2896,plain,(
% 0.19/0.56 spl39_218 <=> ! [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),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | X2 = X3)),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_218])])).
% 0.19/0.56 tff(f2901,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)) | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)),X3)) | X2 = X3) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_218)),
% 0.19/0.56 inference(forward_demodulation,[],[f2900,f1421])).
% 0.19/0.56 tff(f2900,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X2))),X1)),X3)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | X2 = X3) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_218)),
% 0.19/0.56 inference(forward_demodulation,[],[f2899,f2781])).
% 0.19/0.56 tff(f2899,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))),X3)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | X2 = X3) ) | (~spl39_104 | ~spl39_218)),
% 0.19/0.56 inference(forward_demodulation,[],[f2897,f1421])).
% 0.19/0.56 tff(f2897,plain,(
% 0.19/0.56 ( ! [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),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | X2 = X3) ) | ~spl39_218),
% 0.19/0.56 inference(avatar_component_clause,[],[f2896])).
% 0.19/0.56 tff(f2898,plain,(
% 0.19/0.56 spl39_218),
% 0.19/0.56 inference(avatar_split_clause,[],[f772,f2896])).
% 0.19/0.56 tff(f772,plain,(
% 0.19/0.56 ( ! [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),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) | X2 = X3) )),
% 0.19/0.56 inference(forward_demodulation,[],[f655,f439])).
% 0.19/0.56 tff(f655,plain,(
% 0.19/0.56 ( ! [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),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f539,f491])).
% 0.19/0.56 tff(f539,plain,(
% 0.19/0.56 ( ! [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),insert(X0,X2,X1)))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f304])).
% 0.19/0.56 tff(f304,plain,(
% 0.19/0.56 ! [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),insert(X0,X2,X1))))),
% 0.19/0.56 inference(flattening,[],[f303])).
% 0.19/0.56 tff(f303,plain,(
% 0.19/0.56 ! [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),insert(X0,X2,X1))))),
% 0.19/0.56 inference(ennf_transformation,[],[f221])).
% 0.19/0.56 tff(f221,plain,(
% 0.19/0.56 ! [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),insert(X0,X2,X1))) => (X2 != X3 => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))))),
% 0.19/0.56 inference(rectify,[],[f7])).
% 0.19/0.56 tff(f7,axiom,(
% 0.19/0.56 ! [X1 : $tType,X14 : fun(X1,bool),X16 : X1,X17 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),insert(X1,X16,X14))) => (X16 != X17 => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),X14))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_insertE)).
% 0.19/0.56 tff(f2873,plain,(
% 0.19/0.56 spl39_217 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_216),
% 0.19/0.56 inference(avatar_split_clause,[],[f2869,f2864,f2777,f1420,f901,f2871])).
% 0.19/0.56 tff(f2871,plain,(
% 0.19/0.56 spl39_217 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),X2)),X3)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_217])])).
% 0.19/0.56 tff(f2864,plain,(
% 0.19/0.56 spl39_216 <=> ! [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),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),X2)))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_216])])).
% 0.19/0.56 tff(f2869,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),X2)),X3))) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_216)),
% 0.19/0.56 inference(forward_demodulation,[],[f2868,f1421])).
% 0.19/0.56 tff(f2868,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X1))),X2)),X3)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_216)),
% 0.19/0.56 inference(forward_demodulation,[],[f2867,f2781])).
% 0.19/0.56 tff(f2867,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X3)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | (~spl39_104 | ~spl39_216)),
% 0.19/0.56 inference(forward_demodulation,[],[f2865,f1421])).
% 0.19/0.56 tff(f2865,plain,(
% 0.19/0.56 ( ! [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),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),X2)))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | ~spl39_216),
% 0.19/0.56 inference(avatar_component_clause,[],[f2864])).
% 0.19/0.56 tff(f2866,plain,(
% 0.19/0.56 spl39_216),
% 0.19/0.56 inference(avatar_split_clause,[],[f771,f2864])).
% 0.19/0.56 tff(f771,plain,(
% 0.19/0.56 ( ! [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),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),X2)))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f654,f439])).
% 0.19/0.56 tff(f654,plain,(
% 0.19/0.56 ( ! [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),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),X2))))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f537,f491])).
% 0.19/0.56 tff(f537,plain,(
% 0.19/0.56 ( ! [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),insert(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f300])).
% 0.19/0.56 tff(f300,plain,(
% 0.19/0.56 ! [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),insert(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 0.19/0.56 inference(ennf_transformation,[],[f219])).
% 0.19/0.56 tff(f219,plain,(
% 0.19/0.56 ! [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),insert(X0,X1,X2))))),
% 0.19/0.56 inference(rectify,[],[f21])).
% 0.19/0.56 tff(f21,axiom,(
% 0.19/0.56 ! [X1 : $tType,X16 : X1,X18 : fun(X1,bool),X17 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),X18)) => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),insert(X1,X16,X18))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_insertI2)).
% 0.19/0.56 tff(f2837,plain,(
% 0.19/0.56 spl39_215 | ~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_214),
% 0.19/0.56 inference(avatar_split_clause,[],[f2833,f2829,f2777,f1004,f901,f2835])).
% 0.19/0.56 tff(f2835,plain,(
% 0.19/0.56 spl39_215 <=> ! [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,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK22(X0,X1)))),sK23(X0,X1)))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_215])])).
% 0.19/0.56 tff(f2829,plain,(
% 0.19/0.56 spl39_214 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK22(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK23(X0,X1))))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_214])])).
% 0.19/0.56 tff(f2833,plain,(
% 0.19/0.56 ( ! [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,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK22(X0,X1)))),sK23(X0,X1)))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_16 | ~spl39_37 | ~spl39_208 | ~spl39_214)),
% 0.19/0.56 inference(forward_demodulation,[],[f2832,f1005])).
% 0.19/0.56 tff(f2832,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),sK22(X0,X1)))),sK23(X0,X1)))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | (~spl39_16 | ~spl39_208 | ~spl39_214)),
% 0.19/0.56 inference(forward_demodulation,[],[f2830,f2781])).
% 0.19/0.56 tff(f2830,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK22(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK23(X0,X1))))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | ~spl39_214),
% 0.19/0.56 inference(avatar_component_clause,[],[f2829])).
% 0.19/0.56 tff(f2831,plain,(
% 0.19/0.56 spl39_214),
% 0.19/0.56 inference(avatar_split_clause,[],[f742,f2829])).
% 0.19/0.56 tff(f742,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(fun(X0,bool),bool,X1,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK22(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK23(X0,X1))))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 0.19/0.56 inference(forward_demodulation,[],[f633,f439])).
% 0.19/0.56 tff(f633,plain,(
% 0.19/0.56 ( ! [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,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK22(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK23(X0,X1)))))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 0.19/0.56 inference(definition_unfolding,[],[f505,f491])).
% 0.19/0.56 tff(f505,plain,(
% 0.19/0.56 ( ! [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,insert(X0,sK22(X0,X1),sK23(X0,X1)))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 0.19/0.56 inference(cnf_transformation,[],[f368])).
% 0.19/0.56 tff(f368,plain,(
% 0.19/0.56 ! [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,insert(X0,sK22(X0,X1),sK23(X0,X1)))) & pp(aa(fun(X0,bool),bool,X1,sK23(X0,X1))) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK22(X0,X1)),sK23(X0,X1))) & finite_finite1(X0,sK23(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 0.19/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f281,f367])).
% 0.19/0.56 tff(f367,plain,(
% 0.19/0.56 ! [X0 : $tType,X1 : fun(fun(X0,bool),bool)] : (? [X3 : X0,X4 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,X1,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,insert(X0,sK22(X0,X1),sK23(X0,X1)))) & pp(aa(fun(X0,bool),bool,X1,sK23(X0,X1))) & ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK22(X0,X1)),sK23(X0,X1))) & finite_finite1(X0,sK23(X0,X1))))),
% 0.19/0.56 introduced(choice_axiom,[])).
% 0.19/0.56 tff(f281,plain,(
% 0.19/0.56 ! [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,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))),
% 0.19/0.56 inference(flattening,[],[f280])).
% 0.19/0.56 tff(f280,plain,(
% 0.19/0.56 ! [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,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))),
% 0.19/0.56 inference(ennf_transformation,[],[f193])).
% 0.19/0.56 tff(f193,plain,(
% 0.19/0.56 ! [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,insert(X0,X3,X4)))))) => pp(aa(fun(X0,bool),bool,X1,X2)))))),
% 0.19/0.56 inference(rectify,[],[f100])).
% 0.19/0.56 tff(f100,axiom,(
% 0.19/0.56 ! [X1 : $tType,X20 : fun(fun(X1,bool),bool),X55 : fun(X1,bool)] : (finite_finite1(X1,X55) => (pp(aa(fun(X1,bool),bool,X20,bot_bot(fun(X1,bool)))) => (! [X59 : X1,X69 : fun(X1,bool)] : (finite_finite1(X1,X69) => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X59),X69)) => (pp(aa(fun(X1,bool),bool,X20,X69)) => pp(aa(fun(X1,bool),bool,X20,insert(X1,X59,X69)))))) => pp(aa(fun(X1,bool),bool,X20,X55)))))),
% 0.19/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_finite__induct)).
% 0.19/0.56 tff(f2826,plain,(
% 0.19/0.56 spl39_213 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_212),
% 0.19/0.56 inference(avatar_split_clause,[],[f2822,f2818,f2777,f1420,f901,f2824])).
% 0.19/0.56 tff(f2824,plain,(
% 0.19/0.56 spl39_213 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,X0)),X3 : X0,X2 : fun(X0,bool),X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK31(X0,X1,X2,X3,X4)),sK30(X0,X1,X2,X3,X4))) | ~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2),X1))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_213])])).
% 0.19/0.56 tff(f2818,plain,(
% 0.19/0.56 spl39_212 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,X0)),X3 : X0,X2 : fun(X0,bool),X1 : X0] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK30(X0,X1,X2,X3,X4)),sK31(X0,X1,X2,X3,X4))))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_212])])).
% 0.19/0.56 tff(f2822,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK31(X0,X1,X2,X3,X4)),sK30(X0,X1,X2,X3,X4))) | ~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2),X1)) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_212)),
% 0.19/0.56 inference(forward_demodulation,[],[f2821,f1421])).
% 0.19/0.56 tff(f2821,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X2),X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK30(X0,X1,X2,X3,X4)),sK31(X0,X1,X2,X3,X4)))) ) | (~spl39_16 | ~spl39_208 | ~spl39_212)),
% 0.19/0.56 inference(forward_demodulation,[],[f2819,f2781])).
% 0.19/0.56 tff(f2819,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK30(X0,X1,X2,X3,X4)),sK31(X0,X1,X2,X3,X4)))) ) | ~spl39_212),
% 0.19/0.56 inference(avatar_component_clause,[],[f2818])).
% 0.19/0.56 tff(f2820,plain,(
% 0.19/0.56 spl39_212),
% 0.19/0.56 inference(avatar_split_clause,[],[f788,f2818])).
% 0.19/0.56 tff(f788,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK30(X0,X1,X2,X3,X4)),sK31(X0,X1,X2,X3,X4)))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f671,f439])).
% 0.19/0.56 tff(f671,plain,(
% 0.19/0.56 ( ! [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),sK30(X0,X1,X2,X3,X4)),sK31(X0,X1,X2,X3,X4))) | ~finite_fold1Set(X0,X4,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X1)) )),
% 0.19/0.56 inference(definition_unfolding,[],[f571,f491])).
% 0.19/0.56 tff(f571,plain,(
% 0.19/0.56 ( ! [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),sK30(X0,X1,X2,X3,X4)),sK31(X0,X1,X2,X3,X4))) | ~finite_fold1Set(X0,X4,insert(X0,X3,X2),X1)) )),
% 0.19/0.56 inference(cnf_transformation,[],[f395])).
% 0.19/0.56 tff(f2816,plain,(
% 0.19/0.56 spl39_211 | ~spl39_111 | spl39_197),
% 0.19/0.56 inference(avatar_split_clause,[],[f2735,f2669,f1473,f2813])).
% 0.19/0.56 tff(f1473,plain,(
% 0.19/0.56 spl39_111 <=> ! [X0 : state] : (q(sK3,X0) | fTrue = aa(a,bool,combc(a,state,bool,p1,sK4),sK6(sK4,X0)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_111])])).
% 0.19/0.56 tff(f2735,plain,(
% 0.19/0.56 fTrue = aa(a,bool,combc(a,state,bool,p1,sK4),sK6(sK4,sK5(p1,q1))) | (~spl39_111 | spl39_197)),
% 0.19/0.56 inference(resolution,[],[f2671,f1474])).
% 0.19/0.56 tff(f1474,plain,(
% 0.19/0.56 ( ! [X0 : state] : (q(sK3,X0) | fTrue = aa(a,bool,combc(a,state,bool,p1,sK4),sK6(sK4,X0))) ) | ~spl39_111),
% 0.19/0.56 inference(avatar_component_clause,[],[f1473])).
% 0.19/0.56 tff(f2794,plain,(
% 0.19/0.56 spl39_210 | ~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_209),
% 0.19/0.56 inference(avatar_split_clause,[],[f2790,f2786,f2777,f1420,f901,f2792])).
% 0.19/0.56 tff(f2786,plain,(
% 0.19/0.56 spl39_209 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)),X2) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_209])])).
% 0.19/0.56 tff(f2790,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1),X2)) ) | (~spl39_16 | ~spl39_104 | ~spl39_208 | ~spl39_209)),
% 0.19/0.56 inference(forward_demodulation,[],[f2789,f1421])).
% 0.19/0.56 tff(f2789,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fimplies,combb(bool,bool,X0,fNot,combc(X0,X0,bool,fequal(X0),X3))),X1),X2) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | (~spl39_16 | ~spl39_208 | ~spl39_209)),
% 0.19/0.56 inference(forward_demodulation,[],[f2787,f2781])).
% 0.19/0.56 tff(f2787,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)),X2) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | ~spl39_209),
% 0.19/0.56 inference(avatar_component_clause,[],[f2786])).
% 0.19/0.56 tff(f2788,plain,(
% 0.19/0.56 spl39_209),
% 0.19/0.56 inference(avatar_split_clause,[],[f765,f2786])).
% 0.19/0.56 tff(f765,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1)),X2) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(forward_demodulation,[],[f649,f439])).
% 0.19/0.56 tff(f649,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X1))),X2) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(definition_unfolding,[],[f529,f491])).
% 0.19/0.56 tff(f529,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,X2) = minus_minus(fun(X0,bool),insert(X0,X3,X1),X2) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f291])).
% 0.19/0.56 tff(f2779,plain,(
% 0.19/0.56 spl39_208),
% 0.19/0.56 inference(avatar_split_clause,[],[f739,f2777])).
% 0.19/0.56 tff(f2753,plain,(
% 0.19/0.56 spl39_207 | ~spl39_104 | ~spl39_206),
% 0.19/0.56 inference(avatar_split_clause,[],[f2749,f2744,f1420,f2751])).
% 0.19/0.56 tff(f2751,plain,(
% 0.19/0.56 spl39_207 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X2,X1)),X3)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_207])])).
% 0.19/0.56 tff(f2744,plain,(
% 0.19/0.56 spl39_206 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),minus_minus(fun(X0,bool),X2,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)))),
% 0.19/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_206])])).
% 0.19/0.56 tff(f2749,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X2,X1)),X3))) ) | (~spl39_104 | ~spl39_206)),
% 0.19/0.56 inference(forward_demodulation,[],[f2748,f1421])).
% 0.19/0.56 tff(f2748,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X2,X1)),X3)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))) ) | (~spl39_104 | ~spl39_206)),
% 0.19/0.56 inference(forward_demodulation,[],[f2747,f1421])).
% 0.19/0.56 tff(f2747,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X2,X1)),X3)) | 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))) ) | (~spl39_104 | ~spl39_206)),
% 0.19/0.56 inference(forward_demodulation,[],[f2745,f1421])).
% 0.19/0.56 tff(f2745,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),minus_minus(fun(X0,bool),X2,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))) ) | ~spl39_206),
% 0.19/0.56 inference(avatar_component_clause,[],[f2744])).
% 0.19/0.56 tff(f2746,plain,(
% 0.19/0.56 spl39_206),
% 0.19/0.56 inference(avatar_split_clause,[],[f538,f2744])).
% 0.19/0.56 tff(f538,plain,(
% 0.19/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),minus_minus(fun(X0,bool),X2,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))) )),
% 0.19/0.56 inference(cnf_transformation,[],[f302])).
% 0.19/0.56 tff(f302,plain,(
% 0.19/0.56 ! [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),minus_minus(fun(X0,bool),X2,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)))),
% 0.19/0.56 inference(flattening,[],[f301])).
% 0.19/0.56 tff(f301,plain,(
% 0.19/0.56 ! [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),minus_minus(fun(X0,bool),X2,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)))),
% 1.49/0.56 inference(ennf_transformation,[],[f220])).
% 1.49/0.56 tff(f220,plain,(
% 1.49/0.56 ! [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)) => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),minus_minus(fun(X0,bool),X2,X1)))))),
% 1.49/0.56 inference(rectify,[],[f59])).
% 1.49/0.56 tff(f59,axiom,(
% 1.49/0.56 ! [X1 : $tType,X18 : fun(X1,bool),X14 : fun(X1,bool),X21 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X21),X14)) => (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X21),X18)) => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X21),minus_minus(fun(X1,bool),X14,X18)))))),
% 1.49/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_DiffI)).
% 1.49/0.56 tff(f2739,plain,(
% 1.49/0.56 spl39_205 | ~spl39_104 | ~spl39_204),
% 1.49/0.56 inference(avatar_split_clause,[],[f2734,f2731,f1420,f2737])).
% 1.49/0.56 tff(f2737,plain,(
% 1.49/0.56 spl39_205 <=> ! [X0 : $tType,X5 : fun(X0,bool),X4 : X0,X6 : X0,X3 : fun(X0,fun(X0,X0))] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X5),X4)) | finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X5)),X6) | ~finite_fold_graph(X0,X0,X3,X4,X5,X6))),
% 1.49/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_205])])).
% 1.49/0.56 tff(f2731,plain,(
% 1.49/0.56 spl39_204 <=> ! [X0 : $tType,X5 : fun(X0,bool),X4 : X0,X6 : X0,X3 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),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))),
% 1.49/0.56 introduced(avatar_definition,[new_symbols(naming,[spl39_204])])).
% 1.49/0.57 tff(f2734,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X6 : X0,X4 : X0,X5 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X5),X4)) | finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X5)),X6) | ~finite_fold_graph(X0,X0,X3,X4,X5,X6)) ) | (~spl39_104 | ~spl39_204)),
% 1.49/0.57 inference(forward_demodulation,[],[f2732,f1421])).
% 1.49/0.57 tff(f2732,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X6 : X0,X4 : X0,X5 : fun(X0,bool)] : (finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),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)) ) | ~spl39_204),
% 1.49/0.57 inference(avatar_component_clause,[],[f2731])).
% 1.49/0.57 tff(f2733,plain,(
% 1.49/0.57 spl39_204),
% 1.49/0.57 inference(avatar_split_clause,[],[f775,f2731])).
% 1.49/0.57 tff(f775,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X6 : X0,X4 : X0,X5 : fun(X0,bool)] : (finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),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)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f702,f439])).
% 1.49/0.57 tff(f702,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X6 : X0,X4 : X0,X5 : fun(X0,bool)] : (finite_fold1Set(X0,X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),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)) )),
% 1.49/0.57 inference(equality_resolution,[],[f701])).
% 1.49/0.57 tff(f701,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X6 : X0,X4 : X0,X5 : fun(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) | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X5))) != X2) )),
% 1.49/0.57 inference(equality_resolution,[],[f658])).
% 1.49/0.57 tff(f658,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0,X6 : X0,X4 : X0,X5 : fun(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 | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X4)),combc(X0,fun(X0,bool),bool,member(X0),X5))) != X2) )),
% 1.49/0.57 inference(definition_unfolding,[],[f551,f491])).
% 1.49/0.57 tff(f551,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0,X6 : X0,X4 : X0,X5 : fun(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 | insert(X0,X4,X5) != X2) )),
% 1.49/0.57 inference(cnf_transformation,[],[f383])).
% 1.49/0.57 tff(f383,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0))] : ((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 | insert(X0,X4,X5) != X2)) & ((~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK27(X0,X1,X2,X3)),sK28(X0,X1,X2,X3))) & finite_fold_graph(X0,X0,X3,sK27(X0,X1,X2,X3),sK28(X0,X1,X2,X3),sK29(X0,X1,X2,X3)) & sK29(X0,X1,X2,X3) = X1 & insert(X0,sK27(X0,X1,X2,X3),sK28(X0,X1,X2,X3)) = X2) | ~finite_fold1Set(X0,X3,X2,X1)))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29])],[f381,f382])).
% 1.49/0.57 tff(f382,plain,(
% 1.49/0.57 ! [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 & insert(X0,X7,X8) = X2) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK27(X0,X1,X2,X3)),sK28(X0,X1,X2,X3))) & finite_fold_graph(X0,X0,X3,sK27(X0,X1,X2,X3),sK28(X0,X1,X2,X3),sK29(X0,X1,X2,X3)) & sK29(X0,X1,X2,X3) = X1 & insert(X0,sK27(X0,X1,X2,X3),sK28(X0,X1,X2,X3)) = X2))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f381,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0))] : ((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 | 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 & insert(X0,X7,X8) = X2) | ~finite_fold1Set(X0,X3,X2,X1)))),
% 1.49/0.57 inference(rectify,[],[f380])).
% 1.49/0.57 tff(f380,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0))] : ((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 | 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 & insert(X0,X4,X5) = X2) | ~finite_fold1Set(X0,X3,X2,X1)))),
% 1.49/0.57 inference(nnf_transformation,[],[f227])).
% 1.49/0.57 tff(f227,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0))] : (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 & insert(X0,X4,X5) = X2))),
% 1.49/0.57 inference(rectify,[],[f81])).
% 1.49/0.57 tff(f81,axiom,(
% 1.49/0.57 ! [X1 : $tType,X63 : X1,X64 : fun(X1,bool),X47 : fun(X1,fun(X1,X1))] : (finite_fold1Set(X1,X47,X64,X63) <=> ? [X65 : X1,X66 : fun(X1,bool),X19 : X1] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X65),X66)) & finite_fold_graph(X1,X1,X47,X65,X66,X19) & X19 = X63 & insert(X1,X65,X66) = X64))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_fold1Set_Osimps)).
% 1.49/0.57 tff(f2714,plain,(
% 1.49/0.57 spl39_203 | ~spl39_104 | ~spl39_202),
% 1.49/0.57 inference(avatar_split_clause,[],[f2710,f2707,f1420,f2712])).
% 1.49/0.57 tff(f2712,plain,(
% 1.49/0.57 spl39_203 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK25(X0,X1,X2))) = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_203])])).
% 1.49/0.57 tff(f2707,plain,(
% 1.49/0.57 spl39_202 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK25(X0,X1,X2))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_202])])).
% 1.49/0.57 tff(f2710,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK25(X0,X1,X2))) = X1) ) | (~spl39_104 | ~spl39_202)),
% 1.49/0.57 inference(forward_demodulation,[],[f2708,f1421])).
% 1.49/0.57 tff(f2708,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK25(X0,X1,X2))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | ~spl39_202),
% 1.49/0.57 inference(avatar_component_clause,[],[f2707])).
% 1.49/0.57 tff(f2709,plain,(
% 1.49/0.57 spl39_202),
% 1.49/0.57 inference(avatar_split_clause,[],[f749,f2707])).
% 1.49/0.57 tff(f749,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK25(X0,X1,X2))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f639,f439])).
% 1.49/0.57 tff(f639,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK25(X0,X1,X2)))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f515,f491])).
% 1.49/0.57 tff(f515,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : 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))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f373])).
% 1.49/0.57 tff(f373,plain,(
% 1.49/0.57 ! [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))) & 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)))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f289,f372])).
% 1.49/0.57 tff(f372,plain,(
% 1.49/0.57 ! [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)) & 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))) & insert(X0,X2,sK25(X0,X1,X2)) = X1))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f289,plain,(
% 1.49/0.57 ! [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)) & insert(X0,X2,X3) = X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 1.49/0.57 inference(ennf_transformation,[],[f201])).
% 1.49/0.57 tff(f201,plain,(
% 1.49/0.57 ! [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)) & insert(X0,X2,X3) = X1))),
% 1.49/0.57 inference(rectify,[],[f41])).
% 1.49/0.57 tff(f41,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool),X17 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),X14)) => ? [X32 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),X32)) & insert(X1,X17,X32) = X14))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_mk__disjoint__insert)).
% 1.49/0.57 tff(f2690,plain,(
% 1.49/0.57 spl39_201 | ~spl39_104 | ~spl39_200),
% 1.49/0.57 inference(avatar_split_clause,[],[f2686,f2683,f1420,f2688])).
% 1.49/0.57 tff(f2688,plain,(
% 1.49/0.57 spl39_201 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK24(X0,X1,X2))) = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_201])])).
% 1.49/0.57 tff(f2683,plain,(
% 1.49/0.57 spl39_200 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK24(X0,X1,X2))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_200])])).
% 1.49/0.57 tff(f2686,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK24(X0,X1,X2))) = X1) ) | (~spl39_104 | ~spl39_200)),
% 1.49/0.57 inference(forward_demodulation,[],[f2684,f1421])).
% 1.49/0.57 tff(f2684,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK24(X0,X1,X2))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | ~spl39_200),
% 1.49/0.57 inference(avatar_component_clause,[],[f2683])).
% 1.49/0.57 tff(f2685,plain,(
% 1.49/0.57 spl39_200),
% 1.49/0.57 inference(avatar_split_clause,[],[f748,f2683])).
% 1.49/0.57 tff(f748,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK24(X0,X1,X2))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f638,f439])).
% 1.49/0.57 tff(f638,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),sK24(X0,X1,X2)))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f513,f491])).
% 1.49/0.57 tff(f513,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (insert(X0,X2,sK24(X0,X1,X2)) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f371])).
% 1.49/0.57 tff(f371,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : ((~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK24(X0,X1,X2))) & insert(X0,X2,sK24(X0,X1,X2)) = X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f288,f370])).
% 1.49/0.57 tff(f370,plain,(
% 1.49/0.57 ! [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)) & insert(X0,X2,X3) = X1) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK24(X0,X1,X2))) & insert(X0,X2,sK24(X0,X1,X2)) = X1))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f288,plain,(
% 1.49/0.57 ! [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)) & insert(X0,X2,X3) = X1) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 1.49/0.57 inference(ennf_transformation,[],[f200])).
% 1.49/0.57 tff(f200,plain,(
% 1.49/0.57 ! [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)] : (insert(X0,X2,X3) = X1 => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))))),
% 1.49/0.57 inference(rectify,[],[f40])).
% 1.49/0.57 tff(f40,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool),X15 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X14)) => ~! [X32 : fun(X1,bool)] : (insert(X1,X15,X32) = X14 => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X32))))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Set_Oset__insert)).
% 1.49/0.57 tff(f2680,plain,(
% 1.49/0.57 spl39_199),
% 1.49/0.57 inference(avatar_split_clause,[],[f728,f2678])).
% 1.49/0.57 tff(f2678,plain,(
% 1.49/0.57 spl39_199 <=> ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_199])])).
% 1.49/0.57 tff(f728,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3)) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f692,f439])).
% 1.49/0.57 tff(f692,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) | bot_bot(fun(X0,bool)) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3)))) )),
% 1.49/0.57 inference(equality_resolution,[],[f622])).
% 1.49/0.57 tff(f622,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),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),X2),X3)) | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X3))) != X1) )),
% 1.49/0.57 inference(definition_unfolding,[],[f470,f491])).
% 1.49/0.57 tff(f470,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),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),X2),X3)) | insert(X0,X2,X3) != X1) )),
% 1.49/0.57 inference(cnf_transformation,[],[f343])).
% 1.49/0.57 tff(f343,plain,(
% 1.49/0.57 ! [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)) | insert(X0,X2,X3) != X1)) & ((~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK10(X0,X1)),sK11(X0,X1))) & insert(X0,sK10(X0,X1),sK11(X0,X1)) = X1) | bot_bot(fun(X0,bool)) = X1))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f341,f342])).
% 1.49/0.57 tff(f342,plain,(
% 1.49/0.57 ! [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)) & insert(X0,X4,X5) = X1) => (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK10(X0,X1)),sK11(X0,X1))) & insert(X0,sK10(X0,X1),sK11(X0,X1)) = X1))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f341,plain,(
% 1.49/0.57 ! [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)) | 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)) & insert(X0,X4,X5) = X1) | bot_bot(fun(X0,bool)) = X1))),
% 1.49/0.57 inference(rectify,[],[f340])).
% 1.49/0.57 tff(f340,plain,(
% 1.49/0.57 ! [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)) | 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)) & insert(X0,X2,X3) = X1) | bot_bot(fun(X0,bool)) = X1))),
% 1.49/0.57 inference(nnf_transformation,[],[f169])).
% 1.49/0.57 tff(f169,plain,(
% 1.49/0.57 ! [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)) & insert(X0,X2,X3) = X1))),
% 1.49/0.57 inference(rectify,[],[f47])).
% 1.49/0.57 tff(f47,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool)] : (bot_bot(fun(X1,bool)) != X14 <=> ? [X19 : X1,X46 : fun(X1,bool)] : (~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X19),X46)) & insert(X1,X19,X46) = X14))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_nonempty__iff)).
% 1.49/0.57 tff(f2676,plain,(
% 1.49/0.57 spl39_198),
% 1.49/0.57 inference(avatar_split_clause,[],[f825,f2674])).
% 1.49/0.57 tff(f2674,plain,(
% 1.49/0.57 spl39_198 <=> ! [X3 : $tType,X2 : $tType,X4 : X2,X0 : X2,X5 : fun(X3,bool),X1 : fun(X3,fun(X2,X2))] : (combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),sK36(X2,X3,X0,X1,X4,X5))),combc(X3,fun(X3,bool),bool,member(X3),sK37(X2,X3,X0,X1,X4,X5))) = X5 | ~sP2(X2,X3,X0,X1,X4,X5))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_198])])).
% 1.49/0.57 tff(f825,plain,(
% 1.49/0.57 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),sK36(X2,X3,X0,X1,X4,X5))),combc(X3,fun(X3,bool),bool,member(X3),sK37(X2,X3,X0,X1,X4,X5))) = X5 | ~sP2(X2,X3,X0,X1,X4,X5)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f687,f439])).
% 1.49/0.57 tff(f687,plain,(
% 1.49/0.57 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (collect(X3,combs(X3,bool,bool,combb(bool,fun(bool,bool),X3,fdisj,combc(X3,X3,bool,fequal(X3),sK36(X2,X3,X0,X1,X4,X5))),combc(X3,fun(X3,bool),bool,member(X3),sK37(X2,X3,X0,X1,X4,X5)))) = X5 | ~sP2(X2,X3,X0,X1,X4,X5)) )),
% 1.49/0.57 inference(definition_unfolding,[],[f599,f491])).
% 1.49/0.57 tff(f599,plain,(
% 1.49/0.57 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (insert(X3,sK36(X2,X3,X0,X1,X4,X5),sK37(X2,X3,X0,X1,X4,X5)) = X5 | ~sP2(X2,X3,X0,X1,X4,X5)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f413])).
% 1.49/0.57 tff(f2672,plain,(
% 1.49/0.57 ~spl39_197 | ~spl39_51 | ~spl39_194),
% 1.49/0.57 inference(avatar_split_clause,[],[f2629,f2624,f1082,f2669])).
% 1.49/0.57 tff(f1082,plain,(
% 1.49/0.57 spl39_51 <=> ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (~hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)))),combk(bool,hoare_28830079triple(a),fFalse))) | ~q(sK3,sK5(X2,X3)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_51])])).
% 1.49/0.57 tff(f2629,plain,(
% 1.49/0.57 ~q(sK3,sK5(p1,q1)) | (~spl39_51 | ~spl39_194)),
% 1.49/0.57 inference(resolution,[],[f2626,f1083])).
% 1.49/0.57 tff(f1083,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (~hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)))),combk(bool,hoare_28830079triple(a),fFalse))) | ~q(sK3,sK5(X2,X3))) ) | ~spl39_51),
% 1.49/0.57 inference(avatar_component_clause,[],[f1082])).
% 1.49/0.57 tff(f2646,plain,(
% 1.49/0.57 spl39_196 | ~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_104 | ~spl39_195),
% 1.49/0.57 inference(avatar_split_clause,[],[f2642,f2637,f1420,f1380,f1271,f1004,f2644])).
% 1.49/0.57 tff(f2644,plain,(
% 1.49/0.57 spl39_196 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combk(bool,X0,fFalse))),X2)) | X1 = X2)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_196])])).
% 1.49/0.57 tff(f1271,plain,(
% 1.49/0.57 spl39_86 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK12(X0,X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_86])])).
% 1.49/0.57 tff(f1380,plain,(
% 1.49/0.57 spl39_101 <=> ! [X0 : $tType,X1 : X0] : ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_101])])).
% 1.49/0.57 tff(f2637,plain,(
% 1.49/0.57 spl39_195 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) | X1 = X2)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_195])])).
% 1.49/0.57 tff(f2642,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combk(bool,X0,fFalse))),X2)) | X1 = X2) ) | (~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_104 | ~spl39_195)),
% 1.49/0.57 inference(forward_demodulation,[],[f2641,f1383])).
% 1.49/0.57 tff(f1383,plain,(
% 1.49/0.57 ( ! [X0 : $tType] : (combk(bool,X0,fFalse) = combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse))) ) | (~spl39_86 | ~spl39_101)),
% 1.49/0.57 inference(resolution,[],[f1381,f1272])).
% 1.49/0.57 tff(f1272,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,sK12(X0,X1))) | combk(bool,X0,fFalse) = X1) ) | ~spl39_86),
% 1.49/0.57 inference(avatar_component_clause,[],[f1271])).
% 1.49/0.57 tff(f1381,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1))) ) | ~spl39_101),
% 1.49/0.57 inference(avatar_component_clause,[],[f1380])).
% 1.49/0.57 tff(f2641,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)))),X2)) | X1 = X2) ) | (~spl39_37 | ~spl39_104 | ~spl39_195)),
% 1.49/0.57 inference(forward_demodulation,[],[f2640,f1005])).
% 1.49/0.57 tff(f2640,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))),X2)) | X1 = X2) ) | (~spl39_104 | ~spl39_195)),
% 1.49/0.57 inference(forward_demodulation,[],[f2638,f1421])).
% 1.49/0.57 tff(f2638,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) | X1 = X2) ) | ~spl39_195),
% 1.49/0.57 inference(avatar_component_clause,[],[f2637])).
% 1.49/0.57 tff(f2639,plain,(
% 1.49/0.57 spl39_195),
% 1.49/0.57 inference(avatar_split_clause,[],[f750,f2637])).
% 1.49/0.57 tff(f750,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) | X1 = X2) )),
% 1.49/0.57 inference(forward_demodulation,[],[f640,f439])).
% 1.49/0.57 tff(f640,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f517,f491])).
% 1.49/0.57 tff(f517,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),insert(X0,X1,bot_bot(fun(X0,bool)))))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f290])).
% 1.49/0.57 tff(f290,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = X2 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),insert(X0,X1,bot_bot(fun(X0,bool))))))),
% 1.49/0.57 inference(ennf_transformation,[],[f202])).
% 1.49/0.57 tff(f202,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : X0] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),insert(X0,X1,bot_bot(fun(X0,bool))))) => X1 = X2)),
% 1.49/0.57 inference(rectify,[],[f30])).
% 1.49/0.57 tff(f30,axiom,(
% 1.49/0.57 ! [X1 : $tType,X17 : X1,X16 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X16),insert(X1,X17,bot_bot(fun(X1,bool))))) => X16 = X17)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_singletonE)).
% 1.49/0.57 tff(f2627,plain,(
% 1.49/0.57 spl39_194 | ~spl39_37 | ~spl39_193),
% 1.49/0.57 inference(avatar_split_clause,[],[f2622,f2617,f1004,f2624])).
% 1.49/0.57 tff(f2617,plain,(
% 1.49/0.57 spl39_193 <=> hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,p1,c,q1))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_193])])).
% 1.49/0.57 tff(f2622,plain,(
% 1.49/0.57 hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,p1,c,q1)))),combk(bool,hoare_28830079triple(a),fFalse))) | (~spl39_37 | ~spl39_193)),
% 1.49/0.57 inference(forward_demodulation,[],[f2621,f1005])).
% 1.49/0.57 tff(f2621,plain,(
% 1.49/0.57 hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,p1,c,q1)))),bot_bot(fun(hoare_28830079triple(a),bool)))) | ~spl39_193),
% 1.49/0.57 inference(forward_demodulation,[],[f2619,f739])).
% 1.49/0.57 tff(f2619,plain,(
% 1.49/0.57 hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,p1,c,q1))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool)))))) | ~spl39_193),
% 1.49/0.57 inference(avatar_component_clause,[],[f2617])).
% 1.49/0.57 tff(f2620,plain,(
% 1.49/0.57 spl39_193),
% 1.49/0.57 inference(avatar_split_clause,[],[f618,f2617])).
% 1.49/0.57 tff(f618,plain,(
% 1.49/0.57 hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,p1,c,q1))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))))))),
% 1.49/0.57 inference(definition_unfolding,[],[f421,f491])).
% 1.49/0.57 tff(f421,plain,(
% 1.49/0.57 hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,p1,c,q1),bot_bot(fun(hoare_28830079triple(a),bool))))),
% 1.49/0.57 inference(cnf_transformation,[],[f128])).
% 1.49/0.57 tff(f128,axiom,(
% 1.49/0.57 hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,p1,c,q1),bot_bot(fun(hoare_28830079triple(a),bool))))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.49/0.57 tff(f2614,plain,(
% 1.49/0.57 spl39_192),
% 1.49/0.57 inference(avatar_split_clause,[],[f789,f2612])).
% 1.49/0.57 tff(f2612,plain,(
% 1.49/0.57 spl39_192 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,X0)),X3 : X0,X2 : fun(X0,bool),X1 : X0] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1) | finite_fold_graph(X0,X0,X4,sK30(X0,X1,X2,X3,X4),sK31(X0,X1,X2,X3,X4),X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_192])])).
% 1.49/0.57 tff(f789,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (~finite_fold1Set(X0,X4,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1) | finite_fold_graph(X0,X0,X4,sK30(X0,X1,X2,X3,X4),sK31(X0,X1,X2,X3,X4),X1)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f672,f439])).
% 1.49/0.57 tff(f672,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (finite_fold_graph(X0,X0,X4,sK30(X0,X1,X2,X3,X4),sK31(X0,X1,X2,X3,X4),X1) | ~finite_fold1Set(X0,X4,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X1)) )),
% 1.49/0.57 inference(definition_unfolding,[],[f570,f491])).
% 1.49/0.57 tff(f570,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0,X4 : fun(X0,fun(X0,X0))] : (finite_fold_graph(X0,X0,X4,sK30(X0,X1,X2,X3,X4),sK31(X0,X1,X2,X3,X4),X1) | ~finite_fold1Set(X0,X4,insert(X0,X3,X2),X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f395])).
% 1.49/0.57 tff(f2595,plain,(
% 1.49/0.57 spl39_191 | ~spl39_104 | ~spl39_189),
% 1.49/0.57 inference(avatar_split_clause,[],[f2587,f2584,f1420,f2593])).
% 1.49/0.57 tff(f2593,plain,(
% 1.49/0.57 spl39_191 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_191])])).
% 1.49/0.57 tff(f2584,plain,(
% 1.49/0.57 spl39_189 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_189])])).
% 1.49/0.57 tff(f2587,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = X1) ) | (~spl39_104 | ~spl39_189)),
% 1.49/0.57 inference(forward_demodulation,[],[f2585,f1421])).
% 1.49/0.57 tff(f2585,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | ~spl39_189),
% 1.49/0.57 inference(avatar_component_clause,[],[f2584])).
% 1.49/0.57 tff(f2591,plain,(
% 1.49/0.57 spl39_190 | ~spl39_24 | ~spl39_37),
% 1.49/0.57 inference(avatar_split_clause,[],[f1007,f1004,f936,f2589])).
% 1.49/0.57 tff(f2589,plain,(
% 1.49/0.57 spl39_190 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : fun(X0,fun(X1,X1))] : finite_fold_graph(X0,X1,X2,X3,combk(bool,X0,fFalse),X3)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_190])])).
% 1.49/0.57 tff(f936,plain,(
% 1.49/0.57 spl39_24 <=> ! [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)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_24])])).
% 1.49/0.57 tff(f1007,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X1)),X3 : X1] : (finite_fold_graph(X0,X1,X2,X3,combk(bool,X0,fFalse),X3)) ) | (~spl39_24 | ~spl39_37)),
% 1.49/0.57 inference(superposition,[],[f937,f1005])).
% 1.49/0.57 tff(f937,plain,(
% 1.49/0.57 ( ! [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)) ) | ~spl39_24),
% 1.49/0.57 inference(avatar_component_clause,[],[f936])).
% 1.49/0.57 tff(f2586,plain,(
% 1.49/0.57 spl39_189),
% 1.49/0.57 inference(avatar_split_clause,[],[f745,f2584])).
% 1.49/0.57 tff(f745,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f636,f439])).
% 1.49/0.57 tff(f636,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f511,f491])).
% 1.49/0.57 tff(f511,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : 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))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f286])).
% 1.49/0.57 tff(f286,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (insert(X0,X2,X1) = X1 | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 1.49/0.57 inference(ennf_transformation,[],[f198])).
% 1.49/0.57 tff(f198,plain,(
% 1.49/0.57 ! [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)) => insert(X0,X2,X1) = X1)),
% 1.49/0.57 inference(rectify,[],[f20])).
% 1.49/0.57 tff(f20,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool),X17 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),X14)) => insert(X1,X17,X14) = X14)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_insert__absorb)).
% 1.49/0.57 tff(f2574,plain,(
% 1.49/0.57 spl39_188 | ~spl39_37 | ~spl39_185),
% 1.49/0.57 inference(avatar_split_clause,[],[f2554,f2551,f1004,f2572])).
% 1.49/0.57 tff(f2572,plain,(
% 1.49/0.57 spl39_188 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK9(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK8(X0,X1))) = X1 | ~finite_finite1(X0,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_188])])).
% 1.49/0.57 tff(f2551,plain,(
% 1.49/0.57 spl39_185 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK9(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK8(X0,X1))) = X1 | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_185])])).
% 1.49/0.57 tff(f2554,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK9(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK8(X0,X1))) = X1 | ~finite_finite1(X0,X1)) ) | (~spl39_37 | ~spl39_185)),
% 1.49/0.57 inference(forward_demodulation,[],[f2552,f1005])).
% 1.49/0.57 tff(f2552,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK9(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK8(X0,X1))) = X1 | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) ) | ~spl39_185),
% 1.49/0.57 inference(avatar_component_clause,[],[f2551])).
% 1.49/0.57 tff(f2564,plain,(
% 1.49/0.57 spl39_187 | ~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_186),
% 1.49/0.57 inference(avatar_split_clause,[],[f2560,f2556,f1380,f1271,f1004,f2562])).
% 1.49/0.57 tff(f2562,plain,(
% 1.49/0.57 spl39_187 <=> ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : hoare_992312373derivs(X0,X2,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1))),combk(bool,hoare_28830079triple(X0),fFalse)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_187])])).
% 1.49/0.57 tff(f2556,plain,(
% 1.49/0.57 spl39_186 <=> ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : hoare_992312373derivs(X0,X2,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool)))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_186])])).
% 1.49/0.57 tff(f2560,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X2,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1))),combk(bool,hoare_28830079triple(X0),fFalse)))) ) | (~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_186)),
% 1.49/0.57 inference(forward_demodulation,[],[f2559,f1383])).
% 1.49/0.57 tff(f2559,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X2,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),combk(bool,hoare_28830079triple(X0),fFalse))))) ) | (~spl39_37 | ~spl39_186)),
% 1.49/0.57 inference(forward_demodulation,[],[f2557,f1005])).
% 1.49/0.57 tff(f2557,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X2,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool)))))) ) | ~spl39_186),
% 1.49/0.57 inference(avatar_component_clause,[],[f2556])).
% 1.49/0.57 tff(f2558,plain,(
% 1.49/0.57 spl39_186),
% 1.49/0.57 inference(avatar_split_clause,[],[f734,f2556])).
% 1.49/0.57 tff(f734,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X2,combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool)))))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f627,f439])).
% 1.49/0.57 tff(f627,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X2,collect(hoare_28830079triple(X0),combs(hoare_28830079triple(X0),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(X0),fdisj,combc(hoare_28830079triple(X0),hoare_28830079triple(X0),bool,fequal(hoare_28830079triple(X0)),hoare_1841697145triple(X0,X1,skip,X1))),combc(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),bool,member(hoare_28830079triple(X0)),bot_bot(fun(hoare_28830079triple(X0),bool))))))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f486,f491])).
% 1.49/0.57 tff(f486,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(hoare_28830079triple(X0),bool),X1 : fun(X0,fun(state,bool))] : (hoare_992312373derivs(X0,X2,insert(hoare_28830079triple(X0),hoare_1841697145triple(X0,X1,skip,X1),bot_bot(fun(hoare_28830079triple(X0),bool))))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f180])).
% 1.49/0.57 tff(f180,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,fun(state,bool)),X2 : fun(hoare_28830079triple(X0),bool)] : hoare_992312373derivs(X0,X2,insert(hoare_28830079triple(X0),hoare_1841697145triple(X0,X1,skip,X1),bot_bot(fun(hoare_28830079triple(X0),bool))))),
% 1.49/0.57 inference(rectify,[],[f37])).
% 1.49/0.57 tff(f37,axiom,(
% 1.49/0.57 ! [X1 : $tType,X20 : fun(X1,fun(state,bool)),X10 : fun(hoare_28830079triple(X1),bool)] : hoare_992312373derivs(X1,X10,insert(hoare_28830079triple(X1),hoare_1841697145triple(X1,X20,skip,X20),bot_bot(fun(hoare_28830079triple(X1),bool))))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_hoare__derivs_OSkip)).
% 1.49/0.57 tff(f2553,plain,(
% 1.49/0.57 spl39_185),
% 1.49/0.57 inference(avatar_split_clause,[],[f727,f2551])).
% 1.49/0.57 tff(f727,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK9(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK8(X0,X1))) = X1 | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f621,f439])).
% 1.49/0.57 tff(f621,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK9(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK8(X0,X1)))) = X1 | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) )),
% 1.49/0.57 inference(definition_unfolding,[],[f464,f491])).
% 1.49/0.57 tff(f464,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (insert(X0,sK9(X0,X1),sK8(X0,X1)) = X1 | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f339])).
% 1.49/0.57 tff(f339,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : ((finite_finite1(X0,X1) | (! [X2 : fun(X0,bool),X3 : X0] : (~finite_finite1(X0,X2) | insert(X0,X3,X2) != X1) & bot_bot(fun(X0,bool)) != X1)) & ((finite_finite1(X0,sK8(X0,X1)) & insert(X0,sK9(X0,X1),sK8(X0,X1)) = X1) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f337,f338])).
% 1.49/0.57 tff(f338,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X4 : fun(X0,bool),X5 : X0] : (finite_finite1(X0,X4) & insert(X0,X5,X4) = X1) => (finite_finite1(X0,sK8(X0,X1)) & insert(X0,sK9(X0,X1),sK8(X0,X1)) = X1))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f337,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : ((finite_finite1(X0,X1) | (! [X2 : fun(X0,bool),X3 : X0] : (~finite_finite1(X0,X2) | insert(X0,X3,X2) != X1) & bot_bot(fun(X0,bool)) != X1)) & (? [X4 : fun(X0,bool),X5 : X0] : (finite_finite1(X0,X4) & insert(X0,X5,X4) = X1) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)))),
% 1.49/0.57 inference(rectify,[],[f336])).
% 1.49/0.57 tff(f336,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : ((finite_finite1(X0,X1) | (! [X2 : fun(X0,bool),X3 : X0] : (~finite_finite1(X0,X2) | insert(X0,X3,X2) != X1) & bot_bot(fun(X0,bool)) != X1)) & (? [X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,X2) & insert(X0,X3,X2) = X1) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)))),
% 1.49/0.57 inference(flattening,[],[f335])).
% 1.49/0.57 tff(f335,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : ((finite_finite1(X0,X1) | (! [X2 : fun(X0,bool),X3 : X0] : (~finite_finite1(X0,X2) | insert(X0,X3,X2) != X1) & bot_bot(fun(X0,bool)) != X1)) & ((? [X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,X2) & insert(X0,X3,X2) = X1) | bot_bot(fun(X0,bool)) = X1) | ~finite_finite1(X0,X1)))),
% 1.49/0.57 inference(nnf_transformation,[],[f168])).
% 1.49/0.57 tff(f168,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) <=> (? [X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,X2) & insert(X0,X3,X2) = X1) | bot_bot(fun(X0,bool)) = X1))),
% 1.49/0.57 inference(rectify,[],[f99])).
% 1.49/0.57 tff(f99,axiom,(
% 1.49/0.57 ! [X1 : $tType,X17 : fun(X1,bool)] : (finite_finite1(X1,X17) <=> (? [X66 : fun(X1,bool),X65 : X1] : (finite_finite1(X1,X66) & insert(X1,X65,X66) = X17) | bot_bot(fun(X1,bool)) = X17))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite_Osimps)).
% 1.49/0.57 tff(f2539,plain,(
% 1.49/0.57 spl39_184 | ~spl39_37 | ~spl39_181),
% 1.49/0.57 inference(avatar_split_clause,[],[f2497,f2494,f1004,f2537])).
% 1.49/0.57 tff(f2537,plain,(
% 1.49/0.57 spl39_184 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK10(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK11(X0,X1)))) = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_184])])).
% 1.49/0.57 tff(f2494,plain,(
% 1.49/0.57 spl39_181 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK10(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK11(X0,X1)))) = X1 | bot_bot(fun(X0,bool)) = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_181])])).
% 1.49/0.57 tff(f2497,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK10(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK11(X0,X1)))) = X1) ) | (~spl39_37 | ~spl39_181)),
% 1.49/0.57 inference(forward_demodulation,[],[f2495,f1005])).
% 1.49/0.57 tff(f2495,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK10(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK11(X0,X1)))) = X1 | bot_bot(fun(X0,bool)) = X1) ) | ~spl39_181),
% 1.49/0.57 inference(avatar_component_clause,[],[f2494])).
% 1.49/0.57 tff(f2505,plain,(
% 1.49/0.57 spl39_183),
% 1.49/0.57 inference(avatar_split_clause,[],[f796,f2503])).
% 1.49/0.57 tff(f2503,plain,(
% 1.49/0.57 spl39_183 <=> ! [X1 : $tType,X4 : fun(X1,bool),X0 : X1,X3 : X1,X2 : fun(X1,bool)] : (combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4))) = X4 | X0 = X3 | ~sP0(X1,X0,X2,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_183])])).
% 1.49/0.57 tff(f796,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4))) = X4 | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f676,f439])).
% 1.49/0.57 tff(f676,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X3)),combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4)))) = X4 | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) )),
% 1.49/0.57 inference(definition_unfolding,[],[f573,f491])).
% 1.49/0.57 tff(f573,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (insert(X1,X3,sK32(X1,X0,X2,X3,X4)) = X4 | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f400])).
% 1.49/0.57 tff(f2501,plain,(
% 1.49/0.57 spl39_182),
% 1.49/0.57 inference(avatar_split_clause,[],[f795,f2499])).
% 1.49/0.57 tff(f2499,plain,(
% 1.49/0.57 spl39_182 <=> ! [X1 : $tType,X4 : fun(X1,bool),X0 : X1,X3 : X1,X2 : fun(X1,bool)] : (combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4))) = X2 | X0 = X3 | ~sP0(X1,X0,X2,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_182])])).
% 1.49/0.57 tff(f795,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4))) = X2 | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f675,f439])).
% 1.49/0.57 tff(f675,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fdisj,combc(X1,X1,bool,fequal(X1),X0)),combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4)))) = X2 | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) )),
% 1.49/0.57 inference(definition_unfolding,[],[f575,f491])).
% 1.49/0.57 tff(f575,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (insert(X1,X0,sK32(X1,X0,X2,X3,X4)) = X2 | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f400])).
% 1.49/0.57 tff(f2496,plain,(
% 1.49/0.57 spl39_181),
% 1.49/0.57 inference(avatar_split_clause,[],[f623,f2494])).
% 1.49/0.57 tff(f623,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK10(X0,X1))),combc(X0,fun(X0,bool),bool,member(X0),sK11(X0,X1)))) = X1 | bot_bot(fun(X0,bool)) = X1) )),
% 1.49/0.57 inference(definition_unfolding,[],[f468,f491])).
% 1.49/0.57 tff(f468,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (insert(X0,sK10(X0,X1),sK11(X0,X1)) = X1 | bot_bot(fun(X0,bool)) = X1) )),
% 1.49/0.57 inference(cnf_transformation,[],[f343])).
% 1.49/0.57 tff(f2492,plain,(
% 1.49/0.57 spl39_180),
% 1.49/0.57 inference(avatar_split_clause,[],[f598,f2490])).
% 1.49/0.57 tff(f2490,plain,(
% 1.49/0.57 spl39_180 <=> ! [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))] : 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_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_180])])).
% 1.49/0.57 tff(f598,plain,(
% 1.49/0.57 ( ! [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_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f247])).
% 1.49/0.57 tff(f247,plain,(
% 1.49/0.57 ! [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_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))),
% 1.49/0.57 inference(rectify,[],[f15])).
% 1.49/0.57 tff(f15,axiom,(
% 1.49/0.57 ! [X1 : $tType,X2 : $tType,X7 : fun(X2,fun(state,bool)),X8 : com,X9 : fun(X2,fun(state,bool)),X22 : 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)),X22,X9),X8),X7) = hoare_376461865e_case(X2,X1,X22,hoare_1841697145triple(X2,X9,X8,X7))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_triple_Osimps_I2_J)).
% 1.49/0.57 tff(f2482,plain,(
% 1.49/0.57 spl39_179 | ~spl39_178),
% 1.49/0.57 inference(avatar_split_clause,[],[f2478,f2475,f2480])).
% 1.49/0.57 tff(f2480,plain,(
% 1.49/0.57 spl39_179 <=> ! [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_678420151le_rec(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2)) = hoare_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_179])])).
% 1.49/0.57 tff(f2475,plain,(
% 1.49/0.57 spl39_178 <=> ! [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_678420151le_rec(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)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_178])])).
% 1.49/0.57 tff(f2478,plain,(
% 1.49/0.57 ( ! [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_678420151le_rec(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2)) = hoare_376461865e_case(X1,X0,X5,hoare_1841697145triple(X1,X4,X3,X2))) ) | ~spl39_178),
% 1.49/0.57 inference(forward_demodulation,[],[f2476,f598])).
% 1.49/0.57 tff(f2476,plain,(
% 1.49/0.57 ( ! [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_678420151le_rec(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)) ) | ~spl39_178),
% 1.49/0.57 inference(avatar_component_clause,[],[f2475])).
% 1.49/0.57 tff(f2477,plain,(
% 1.49/0.57 spl39_178),
% 1.49/0.57 inference(avatar_split_clause,[],[f597,f2475])).
% 1.49/0.57 tff(f597,plain,(
% 1.49/0.57 ( ! [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_678420151le_rec(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)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f246])).
% 1.49/0.57 tff(f246,plain,(
% 1.49/0.57 ! [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_678420151le_rec(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)),
% 1.49/0.57 inference(rectify,[],[f14])).
% 1.49/0.57 tff(f14,axiom,(
% 1.49/0.57 ! [X1 : $tType,X2 : $tType,X7 : fun(X2,fun(state,bool)),X8 : com,X9 : fun(X2,fun(state,bool)),X22 : fun(fun(X2,fun(state,bool)),fun(com,fun(fun(X2,fun(state,bool)),X1)))] : hoare_678420151le_rec(X2,X1,X22,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)),X22,X9),X8),X7)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_triple_Orecs)).
% 1.49/0.57 tff(f2460,plain,(
% 1.49/0.57 spl39_177),
% 1.49/0.57 inference(avatar_split_clause,[],[f492,f2458])).
% 1.49/0.57 tff(f2458,plain,(
% 1.49/0.57 spl39_177 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : minus_minus(fun(X0,bool),X2,X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,combc(X0,fun(X0,bool),bool,member(X0),X2)),combb(bool,bool,X0,fNot,combc(X0,fun(X0,bool),bool,member(X0),X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_177])])).
% 1.49/0.57 tff(f492,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X2,X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,combc(X0,fun(X0,bool),bool,member(X0),X2)),combb(bool,bool,X0,fNot,combc(X0,fun(X0,bool),bool,member(X0),X1))))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f186])).
% 1.49/0.57 tff(f186,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : minus_minus(fun(X0,bool),X2,X1) = collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,combc(X0,fun(X0,bool),bool,member(X0),X2)),combb(bool,bool,X0,fNot,combc(X0,fun(X0,bool),bool,member(X0),X1))))),
% 1.49/0.57 inference(rectify,[],[f69])).
% 1.49/0.57 tff(f69,axiom,(
% 1.49/0.57 ! [X1 : $tType,X18 : fun(X1,bool),X14 : fun(X1,bool)] : minus_minus(fun(X1,bool),X14,X18) = collect(X1,combs(X1,bool,bool,combb(bool,fun(bool,bool),X1,fconj,combc(X1,fun(X1,bool),bool,member(X1),X14)),combb(bool,bool,X1,fNot,combc(X1,fun(X1,bool),bool,member(X1),X18))))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_set__diff__eq)).
% 1.49/0.57 tff(f2454,plain,(
% 1.49/0.57 spl39_176),
% 1.49/0.57 inference(avatar_split_clause,[],[f776,f2452])).
% 1.49/0.57 tff(f2452,plain,(
% 1.49/0.57 spl39_176 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool),X1 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK27(X0,X1,X2,X3))),combc(X0,fun(X0,bool),bool,member(X0),sK28(X0,X1,X2,X3))) = X2 | ~finite_fold1Set(X0,X3,X2,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_176])])).
% 1.49/0.57 tff(f776,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK27(X0,X1,X2,X3))),combc(X0,fun(X0,bool),bool,member(X0),sK28(X0,X1,X2,X3))) = X2 | ~finite_fold1Set(X0,X3,X2,X1)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f659,f439])).
% 1.49/0.57 tff(f659,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),sK27(X0,X1,X2,X3))),combc(X0,fun(X0,bool),bool,member(X0),sK28(X0,X1,X2,X3)))) = X2 | ~finite_fold1Set(X0,X3,X2,X1)) )),
% 1.49/0.57 inference(definition_unfolding,[],[f547,f491])).
% 1.49/0.57 tff(f547,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (insert(X0,sK27(X0,X1,X2,X3),sK28(X0,X1,X2,X3)) = X2 | ~finite_fold1Set(X0,X3,X2,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f383])).
% 1.49/0.57 tff(f2437,plain,(
% 1.49/0.57 spl39_175 | ~spl39_104 | ~spl39_174),
% 1.49/0.57 inference(avatar_split_clause,[],[f2433,f2430,f1420,f2435])).
% 1.49/0.57 tff(f2430,plain,(
% 1.49/0.57 spl39_174 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_174])])).
% 1.49/0.57 tff(f2433,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))),X2))) ) | (~spl39_104 | ~spl39_174)),
% 1.49/0.57 inference(forward_demodulation,[],[f2431,f1421])).
% 1.49/0.57 tff(f2431,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))))) ) | ~spl39_174),
% 1.49/0.57 inference(avatar_component_clause,[],[f2430])).
% 1.49/0.57 tff(f2432,plain,(
% 1.49/0.57 spl39_174),
% 1.49/0.57 inference(avatar_split_clause,[],[f735,f2430])).
% 1.49/0.57 tff(f735,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f628,f439])).
% 1.49/0.57 tff(f628,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f488,f491])).
% 1.49/0.57 tff(f488,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),insert(X0,X2,X1)))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f182])).
% 1.49/0.57 tff(f182,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),insert(X0,X2,X1)))),
% 1.49/0.57 inference(rectify,[],[f28])).
% 1.49/0.57 tff(f28,axiom,(
% 1.49/0.57 ! [X1 : $tType,X18 : fun(X1,bool),X17 : X1] : pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),insert(X1,X17,X18)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_insertI1)).
% 1.49/0.57 tff(f2415,plain,(
% 1.49/0.57 spl39_173 | ~spl39_37 | ~spl39_104 | ~spl39_172),
% 1.49/0.57 inference(avatar_split_clause,[],[f2411,f2407,f1420,f1004,f2413])).
% 1.49/0.57 tff(f2413,plain,(
% 1.49/0.57 spl39_173 <=> ! [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(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK23(X0,X1)),sK22(X0,X1))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_173])])).
% 1.49/0.57 tff(f2407,plain,(
% 1.49/0.57 spl39_172 <=> ! [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),sK22(X0,X1)),sK23(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_172])])).
% 1.49/0.57 tff(f2411,plain,(
% 1.49/0.57 ( ! [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(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK23(X0,X1)),sK22(X0,X1))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_37 | ~spl39_104 | ~spl39_172)),
% 1.49/0.57 inference(forward_demodulation,[],[f2410,f1005])).
% 1.49/0.57 tff(f2410,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK23(X0,X1)),sK22(X0,X1))) | pp(aa(fun(X0,bool),bool,X1,X2)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | (~spl39_104 | ~spl39_172)),
% 1.49/0.57 inference(forward_demodulation,[],[f2408,f1421])).
% 1.49/0.57 tff(f2408,plain,(
% 1.49/0.57 ( ! [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),sK22(X0,X1)),sK23(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | ~spl39_172),
% 1.49/0.57 inference(avatar_component_clause,[],[f2407])).
% 1.49/0.57 tff(f2409,plain,(
% 1.49/0.57 spl39_172),
% 1.49/0.57 inference(avatar_split_clause,[],[f503,f2407])).
% 1.49/0.57 tff(f503,plain,(
% 1.49/0.57 ( ! [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),sK22(X0,X1)),sK23(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f368])).
% 1.49/0.57 tff(f2382,plain,(
% 1.49/0.57 spl39_171 | spl39_2 | ~spl39_150),
% 1.49/0.57 inference(avatar_split_clause,[],[f2287,f2159,f837,f2379])).
% 1.49/0.57 tff(f2379,plain,(
% 1.49/0.57 spl39_171 <=> fTrue = aa(bool,bool,fNot,fFalse)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_171])])).
% 1.49/0.57 tff(f837,plain,(
% 1.49/0.57 spl39_2 <=> pp(fFalse)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_2])])).
% 1.49/0.57 tff(f2159,plain,(
% 1.49/0.57 spl39_150 <=> ! [X0 : bool] : (fTrue = aa(bool,bool,fNot,X0) | pp(X0))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_150])])).
% 1.49/0.57 tff(f2287,plain,(
% 1.49/0.57 fTrue = aa(bool,bool,fNot,fFalse) | (spl39_2 | ~spl39_150)),
% 1.49/0.57 inference(resolution,[],[f2160,f839])).
% 1.49/0.57 tff(f839,plain,(
% 1.49/0.57 ~pp(fFalse) | spl39_2),
% 1.49/0.57 inference(avatar_component_clause,[],[f837])).
% 1.49/0.57 tff(f2160,plain,(
% 1.49/0.57 ( ! [X0 : bool] : (pp(X0) | fTrue = aa(bool,bool,fNot,X0)) ) | ~spl39_150),
% 1.49/0.57 inference(avatar_component_clause,[],[f2159])).
% 1.49/0.57 tff(f2377,plain,(
% 1.49/0.57 spl39_170 | ~spl39_37 | ~spl39_104 | ~spl39_169),
% 1.49/0.57 inference(avatar_split_clause,[],[f2373,f2369,f1420,f1004,f2375])).
% 1.49/0.57 tff(f2375,plain,(
% 1.49/0.57 spl39_170 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK21(X0,X1)),sK20(X0,X1))) | pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_170])])).
% 1.49/0.57 tff(f2369,plain,(
% 1.49/0.57 spl39_169 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK20(X0,X1)),sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_169])])).
% 1.49/0.57 tff(f2373,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK21(X0,X1)),sK20(X0,X1))) | pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_37 | ~spl39_104 | ~spl39_169)),
% 1.49/0.57 inference(forward_demodulation,[],[f2372,f1421])).
% 1.49/0.57 tff(f2372,plain,(
% 1.49/0.57 ( ! [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,aa(X0,fun(fun(X0,bool),bool),member(X0),sK20(X0,X1)),sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_37 | ~spl39_169)),
% 1.49/0.57 inference(forward_demodulation,[],[f2370,f1005])).
% 1.49/0.57 tff(f2370,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK20(X0,X1)),sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | ~spl39_169),
% 1.49/0.57 inference(avatar_component_clause,[],[f2369])).
% 1.49/0.57 tff(f2371,plain,(
% 1.49/0.57 spl39_169),
% 1.49/0.57 inference(avatar_split_clause,[],[f499,f2369])).
% 1.49/0.57 tff(f499,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK20(X0,X1)),sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f366])).
% 1.49/0.57 tff(f2357,plain,(
% 1.49/0.57 spl39_168),
% 1.49/0.57 inference(avatar_split_clause,[],[f781,f2355])).
% 1.49/0.57 tff(f2355,plain,(
% 1.49/0.57 spl39_168 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : fun(X0,bool)] : (~finite_finite1(X0,minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) | finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_168])])).
% 1.49/0.57 tff(f781,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (~finite_finite1(X0,minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) | finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f664,f439])).
% 1.49/0.57 tff(f664,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1)) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f558,f491])).
% 1.49/0.57 tff(f558,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1)) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X3,insert(X0,X2,X1)))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f388])).
% 1.49/0.57 tff(f388,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : ((finite_finite1(X0,minus_minus(fun(X0,bool),X3,insert(X0,X2,X1))) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1))) & (finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1)) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X3,insert(X0,X2,X1)))))),
% 1.49/0.57 inference(nnf_transformation,[],[f230])).
% 1.49/0.57 tff(f230,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0,X3 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X3,insert(X0,X2,X1))) <=> finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1)))),
% 1.49/0.57 inference(rectify,[],[f91])).
% 1.49/0.57 tff(f91,axiom,(
% 1.49/0.57 ! [X1 : $tType,X18 : fun(X1,bool),X17 : X1,X14 : fun(X1,bool)] : (finite_finite1(X1,minus_minus(fun(X1,bool),X14,insert(X1,X17,X18))) <=> finite_finite1(X1,minus_minus(fun(X1,bool),X14,X18)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_finite__Diff__insert)).
% 1.49/0.57 tff(f2353,plain,(
% 1.49/0.57 spl39_167),
% 1.49/0.57 inference(avatar_split_clause,[],[f780,f2351])).
% 1.49/0.57 tff(f2351,plain,(
% 1.49/0.57 spl39_167 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_167])])).
% 1.49/0.57 tff(f780,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f663,f439])).
% 1.49/0.57 tff(f663,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))))) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f559,f491])).
% 1.49/0.57 tff(f559,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X3,insert(X0,X2,X1))) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X3,X1))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f388])).
% 1.49/0.57 tff(f2337,plain,(
% 1.49/0.57 spl39_166),
% 1.49/0.57 inference(avatar_split_clause,[],[f779,f2335])).
% 1.49/0.57 tff(f2335,plain,(
% 1.49/0.57 spl39_166 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : X0] : (~pp(aa(X0,bool,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1)) | pp(aa(X0,bool,X2,X1)) | X1 = X3)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_166])])).
% 1.49/0.57 tff(f779,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (~pp(aa(X0,bool,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1)) | pp(aa(X0,bool,X2,X1)) | X1 = X3) )),
% 1.49/0.57 inference(forward_demodulation,[],[f662,f439])).
% 1.49/0.57 tff(f662,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,X2,X1)) | X1 = X3 | ~pp(aa(X0,bool,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X1))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f555,f491])).
% 1.49/0.57 tff(f555,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,X2,X1)) | X1 = X3 | ~pp(aa(X0,bool,insert(X0,X3,X2),X1))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f387])).
% 1.49/0.57 tff(f387,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0] : ((pp(aa(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,insert(X0,X3,X2),X1))))),
% 1.49/0.57 inference(flattening,[],[f386])).
% 1.49/0.57 tff(f386,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0] : ((pp(aa(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,insert(X0,X3,X2),X1))))),
% 1.49/0.57 inference(nnf_transformation,[],[f229])).
% 1.49/0.57 tff(f229,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(X0,bool),X3 : X0] : (pp(aa(X0,bool,insert(X0,X3,X2),X1)) <=> (pp(aa(X0,bool,X2,X1)) | X1 = X3))),
% 1.49/0.57 inference(rectify,[],[f24])).
% 1.49/0.57 tff(f24,axiom,(
% 1.49/0.57 ! [X1 : $tType,X15 : X1,X14 : fun(X1,bool),X24 : X1] : (pp(aa(X1,bool,insert(X1,X24,X14),X15)) <=> (pp(aa(X1,bool,X14,X15)) | X15 = X24))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_insert__code)).
% 1.49/0.57 tff(f2315,plain,(
% 1.49/0.57 spl39_165 | ~spl39_104 | ~spl39_164),
% 1.49/0.57 inference(avatar_split_clause,[],[f2286,f2282,f1420,f2313])).
% 1.49/0.57 tff(f2313,plain,(
% 1.49/0.57 spl39_165 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X2,X1)),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_165])])).
% 1.49/0.57 tff(f2282,plain,(
% 1.49/0.57 spl39_164 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (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),minus_minus(fun(X0,bool),X2,X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_164])])).
% 1.49/0.57 tff(f2286,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X2,X1)),X3)) | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3))) ) | (~spl39_104 | ~spl39_164)),
% 1.49/0.57 inference(forward_demodulation,[],[f2285,f1421])).
% 1.49/0.57 tff(f2285,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),X3)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),minus_minus(fun(X0,bool),X2,X1)))) ) | (~spl39_104 | ~spl39_164)),
% 1.49/0.57 inference(forward_demodulation,[],[f2283,f1421])).
% 1.49/0.57 tff(f2283,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (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),minus_minus(fun(X0,bool),X2,X1)))) ) | ~spl39_164),
% 1.49/0.57 inference(avatar_component_clause,[],[f2282])).
% 1.49/0.57 tff(f2284,plain,(
% 1.49/0.57 spl39_164),
% 1.49/0.57 inference(avatar_split_clause,[],[f541,f2282])).
% 1.49/0.57 tff(f541,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (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),minus_minus(fun(X0,bool),X2,X1)))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f306])).
% 1.49/0.57 tff(f306,plain,(
% 1.49/0.57 ! [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),minus_minus(fun(X0,bool),X2,X1))))),
% 1.49/0.57 inference(ennf_transformation,[],[f223])).
% 1.49/0.57 tff(f223,plain,(
% 1.49/0.57 ! [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),minus_minus(fun(X0,bool),X2,X1))) => pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))),
% 1.49/0.57 inference(rectify,[],[f68])).
% 1.49/0.57 tff(f68,axiom,(
% 1.49/0.57 ! [X1 : $tType,X18 : fun(X1,bool),X14 : fun(X1,bool),X21 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X21),minus_minus(fun(X1,bool),X14,X18))) => pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X21),X14)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_DiffD1)).
% 1.49/0.57 tff(f2263,plain,(
% 1.49/0.57 spl39_163 | ~spl39_104 | ~spl39_162),
% 1.49/0.57 inference(avatar_split_clause,[],[f2259,f2255,f1420,f2261])).
% 1.49/0.57 tff(f2261,plain,(
% 1.49/0.57 spl39_163 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X2,X1)),X3)) | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_163])])).
% 1.49/0.57 tff(f2255,plain,(
% 1.49/0.57 spl39_162 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (~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),minus_minus(fun(X0,bool),X2,X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_162])])).
% 1.49/0.57 tff(f2259,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),minus_minus(fun(X0,bool),X2,X1)),X3)) | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3))) ) | (~spl39_104 | ~spl39_162)),
% 1.49/0.57 inference(forward_demodulation,[],[f2258,f1421])).
% 1.49/0.57 tff(f2258,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X3)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),minus_minus(fun(X0,bool),X2,X1)))) ) | (~spl39_104 | ~spl39_162)),
% 1.49/0.57 inference(forward_demodulation,[],[f2256,f1421])).
% 1.49/0.57 tff(f2256,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (~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),minus_minus(fun(X0,bool),X2,X1)))) ) | ~spl39_162),
% 1.49/0.57 inference(avatar_component_clause,[],[f2255])).
% 1.49/0.57 tff(f2257,plain,(
% 1.49/0.57 spl39_162),
% 1.49/0.57 inference(avatar_split_clause,[],[f540,f2255])).
% 1.49/0.57 tff(f540,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (~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),minus_minus(fun(X0,bool),X2,X1)))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f305])).
% 1.49/0.57 tff(f305,plain,(
% 1.49/0.57 ! [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),X1)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),minus_minus(fun(X0,bool),X2,X1))))),
% 1.49/0.57 inference(ennf_transformation,[],[f222])).
% 1.49/0.57 tff(f222,plain,(
% 1.49/0.57 ! [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),minus_minus(fun(X0,bool),X2,X1))) => ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)))),
% 1.49/0.57 inference(rectify,[],[f67])).
% 1.49/0.57 tff(f67,axiom,(
% 1.49/0.57 ! [X1 : $tType,X18 : fun(X1,bool),X14 : fun(X1,bool),X21 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X21),minus_minus(fun(X1,bool),X14,X18))) => ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X21),X18)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_DiffD2)).
% 1.49/0.57 tff(f2242,plain,(
% 1.49/0.57 spl39_161),
% 1.49/0.57 inference(avatar_split_clause,[],[f777,f2240])).
% 1.49/0.57 tff(f2240,plain,(
% 1.49/0.57 spl39_161 <=> ! [X0 : $tType,X3 : X0,X2 : fun(X0,bool),X1 : X0] : (pp(aa(X0,bool,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1)) | ~pp(aa(X0,bool,X2,X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_161])])).
% 1.49/0.57 tff(f777,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X1)) | ~pp(aa(X0,bool,X2,X1))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f660,f439])).
% 1.49/0.57 tff(f660,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X1)) | ~pp(aa(X0,bool,X2,X1))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f557,f491])).
% 1.49/0.57 tff(f557,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,insert(X0,X3,X2),X1)) | ~pp(aa(X0,bool,X2,X1))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f387])).
% 1.49/0.57 tff(f2231,plain,(
% 1.49/0.57 spl39_160 | ~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_159),
% 1.49/0.57 inference(avatar_split_clause,[],[f2227,f2223,f1380,f1271,f1004,f2229])).
% 1.49/0.57 tff(f2229,plain,(
% 1.49/0.57 spl39_160 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : X0,X1 : X0] : (~finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combk(bool,X0,fFalse)),X1) | X1 = X2)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_160])])).
% 1.49/0.57 tff(f2223,plain,(
% 1.49/0.57 spl39_159 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : X0,X1 : X0] : (~finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))),X1) | X1 = X2)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_159])])).
% 1.49/0.57 tff(f2227,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combk(bool,X0,fFalse)),X1) | X1 = X2) ) | (~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_159)),
% 1.49/0.57 inference(forward_demodulation,[],[f2226,f1383])).
% 1.49/0.57 tff(f2226,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse))),X1) | X1 = X2) ) | (~spl39_37 | ~spl39_159)),
% 1.49/0.57 inference(forward_demodulation,[],[f2224,f1005])).
% 1.49/0.57 tff(f2224,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))),X1) | X1 = X2) ) | ~spl39_159),
% 1.49/0.57 inference(avatar_component_clause,[],[f2223])).
% 1.49/0.57 tff(f2225,plain,(
% 1.49/0.57 spl39_159),
% 1.49/0.57 inference(avatar_split_clause,[],[f783,f2223])).
% 1.49/0.57 tff(f783,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))),X1) | X1 = X2) )),
% 1.49/0.57 inference(forward_demodulation,[],[f666,f439])).
% 1.49/0.57 tff(f666,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (X1 = X2 | ~finite_fold1Set(X0,X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))),X1)) )),
% 1.49/0.57 inference(definition_unfolding,[],[f560,f491])).
% 1.49/0.57 tff(f560,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (X1 = X2 | ~finite_fold1Set(X0,X3,insert(X0,X2,bot_bot(fun(X0,bool))),X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f389])).
% 1.49/0.57 tff(f389,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : fun(X0,fun(X0,X0))] : ((finite_fold1Set(X0,X3,insert(X0,X2,bot_bot(fun(X0,bool))),X1) | X1 != X2) & (X1 = X2 | ~finite_fold1Set(X0,X3,insert(X0,X2,bot_bot(fun(X0,bool))),X1)))),
% 1.49/0.57 inference(nnf_transformation,[],[f231])).
% 1.49/0.57 tff(f231,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X3,insert(X0,X2,bot_bot(fun(X0,bool))),X1) <=> X1 = X2)),
% 1.49/0.57 inference(rectify,[],[f49])).
% 1.49/0.57 tff(f49,axiom,(
% 1.49/0.57 ! [X1 : $tType,X16 : X1,X17 : X1,X47 : fun(X1,fun(X1,X1))] : (finite_fold1Set(X1,X47,insert(X1,X17,bot_bot(fun(X1,bool))),X16) <=> X16 = X17)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_fold1Set__sing)).
% 1.49/0.57 tff(f2213,plain,(
% 1.49/0.57 spl39_158 | ~spl39_10 | ~spl39_45),
% 1.49/0.57 inference(avatar_split_clause,[],[f1150,f1044,f874,f2211])).
% 1.49/0.57 tff(f2211,plain,(
% 1.49/0.57 spl39_158 <=> ! [X1 : $tType,X0 : bool] : (finite_finite1(X1,combk(bool,X1,X0)) | fTrue = X0)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_158])])).
% 1.49/0.57 tff(f874,plain,(
% 1.49/0.57 spl39_10 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_10])])).
% 1.49/0.57 tff(f1044,plain,(
% 1.49/0.57 spl39_45 <=> ! [X0 : $tType] : finite_finite1(X0,combk(bool,X0,fFalse))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_45])])).
% 1.49/0.57 tff(f1150,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : bool] : (finite_finite1(X1,combk(bool,X1,X0)) | fTrue = X0) ) | (~spl39_10 | ~spl39_45)),
% 1.49/0.57 inference(superposition,[],[f1045,f875])).
% 1.49/0.57 tff(f875,plain,(
% 1.49/0.57 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) ) | ~spl39_10),
% 1.49/0.57 inference(avatar_component_clause,[],[f874])).
% 1.49/0.57 tff(f1045,plain,(
% 1.49/0.57 ( ! [X0 : $tType] : (finite_finite1(X0,combk(bool,X0,fFalse))) ) | ~spl39_45),
% 1.49/0.57 inference(avatar_component_clause,[],[f1044])).
% 1.49/0.57 tff(f2209,plain,(
% 1.49/0.57 spl39_157 | ~spl39_104 | ~spl39_156),
% 1.49/0.57 inference(avatar_split_clause,[],[f2205,f2201,f1420,f2207])).
% 1.49/0.57 tff(f2207,plain,(
% 1.49/0.57 spl39_157 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK25(X0,X1,X2)),X2)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_157])])).
% 1.49/0.57 tff(f2201,plain,(
% 1.49/0.57 spl39_156 <=> ! [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)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_156])])).
% 1.49/0.57 tff(f2205,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK25(X0,X1,X2)),X2))) ) | (~spl39_104 | ~spl39_156)),
% 1.49/0.57 inference(forward_demodulation,[],[f2204,f1421])).
% 1.49/0.57 tff(f2204,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK25(X0,X1,X2)),X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | (~spl39_104 | ~spl39_156)),
% 1.49/0.57 inference(forward_demodulation,[],[f2202,f1421])).
% 1.49/0.57 tff(f2202,plain,(
% 1.49/0.57 ( ! [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))) ) | ~spl39_156),
% 1.49/0.57 inference(avatar_component_clause,[],[f2201])).
% 1.49/0.57 tff(f2203,plain,(
% 1.49/0.57 spl39_156),
% 1.49/0.57 inference(avatar_split_clause,[],[f516,f2201])).
% 1.49/0.57 tff(f516,plain,(
% 1.49/0.57 ( ! [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))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f373])).
% 1.49/0.57 tff(f2191,plain,(
% 1.49/0.57 spl39_155 | ~spl39_104 | ~spl39_154),
% 1.49/0.57 inference(avatar_split_clause,[],[f2187,f2183,f1420,f2189])).
% 1.49/0.57 tff(f2189,plain,(
% 1.49/0.57 spl39_155 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK24(X0,X1,X2)),X2)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_155])])).
% 1.49/0.57 tff(f2183,plain,(
% 1.49/0.57 spl39_154 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK24(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_154])])).
% 1.49/0.57 tff(f2187,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK24(X0,X1,X2)),X2))) ) | (~spl39_104 | ~spl39_154)),
% 1.49/0.57 inference(forward_demodulation,[],[f2186,f1421])).
% 1.49/0.57 tff(f2186,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK24(X0,X1,X2)),X2)) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | (~spl39_104 | ~spl39_154)),
% 1.49/0.57 inference(forward_demodulation,[],[f2184,f1421])).
% 1.49/0.57 tff(f2184,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK24(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) ) | ~spl39_154),
% 1.49/0.57 inference(avatar_component_clause,[],[f2183])).
% 1.49/0.57 tff(f2185,plain,(
% 1.49/0.57 spl39_154),
% 1.49/0.57 inference(avatar_split_clause,[],[f514,f2183])).
% 1.49/0.57 tff(f514,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),sK24(X0,X1,X2))) | ~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f371])).
% 1.49/0.57 tff(f2180,plain,(
% 1.49/0.57 spl39_153 | ~spl39_37 | ~spl39_152),
% 1.49/0.57 inference(avatar_split_clause,[],[f2176,f2173,f1004,f2178])).
% 1.49/0.57 tff(f2178,plain,(
% 1.49/0.57 spl39_153 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : combk(bool,X0,fFalse) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_153])])).
% 1.49/0.57 tff(f2173,plain,(
% 1.49/0.57 spl39_152 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : bot_bot(fun(X0,bool)) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_152])])).
% 1.49/0.57 tff(f2176,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) ) | (~spl39_37 | ~spl39_152)),
% 1.49/0.57 inference(forward_demodulation,[],[f2174,f1005])).
% 1.49/0.57 tff(f2174,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) ) | ~spl39_152),
% 1.49/0.57 inference(avatar_component_clause,[],[f2173])).
% 1.49/0.57 tff(f2175,plain,(
% 1.49/0.57 spl39_152),
% 1.49/0.57 inference(avatar_split_clause,[],[f624,f2173])).
% 1.49/0.57 tff(f624,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1)))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f483,f491])).
% 1.49/0.57 tff(f483,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != insert(X0,X2,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f177])).
% 1.49/0.57 tff(f177,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : bot_bot(fun(X0,bool)) != insert(X0,X2,X1)),
% 1.49/0.57 inference(rectify,[],[f33])).
% 1.49/0.57 tff(f33,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool),X17 : X1] : bot_bot(fun(X1,bool)) != insert(X1,X17,X14)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insert__not__empty)).
% 1.49/0.57 tff(f2165,plain,(
% 1.49/0.57 spl39_151 | ~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_149),
% 1.49/0.57 inference(avatar_split_clause,[],[f2157,f2153,f1380,f1271,f1004,f2163])).
% 1.49/0.57 tff(f2163,plain,(
% 1.49/0.57 spl39_151 <=> ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combk(bool,X0,fFalse)),X2)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_151])])).
% 1.49/0.57 tff(f2153,plain,(
% 1.49/0.57 spl39_149 <=> ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))),X2)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_149])])).
% 1.49/0.57 tff(f2157,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combk(bool,X0,fFalse)),X2)) ) | (~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_149)),
% 1.49/0.57 inference(forward_demodulation,[],[f2156,f1383])).
% 1.49/0.57 tff(f2156,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse))),X2)) ) | (~spl39_37 | ~spl39_149)),
% 1.49/0.57 inference(forward_demodulation,[],[f2154,f1005])).
% 1.49/0.57 tff(f2154,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))),X2)) ) | ~spl39_149),
% 1.49/0.57 inference(avatar_component_clause,[],[f2153])).
% 1.49/0.57 tff(f2161,plain,(
% 1.49/0.57 spl39_150 | ~spl39_17 | ~spl39_19),
% 1.49/0.57 inference(avatar_split_clause,[],[f940,f913,f905,f2159])).
% 1.49/0.57 tff(f905,plain,(
% 1.49/0.57 spl39_17 <=> ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_17])])).
% 1.49/0.57 tff(f913,plain,(
% 1.49/0.57 spl39_19 <=> ! [X0 : bool] : (~pp(X0) | fTrue = X0)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_19])])).
% 1.49/0.57 tff(f940,plain,(
% 1.49/0.57 ( ! [X0 : bool] : (fTrue = aa(bool,bool,fNot,X0) | pp(X0)) ) | (~spl39_17 | ~spl39_19)),
% 1.49/0.57 inference(resolution,[],[f914,f906])).
% 1.49/0.57 tff(f906,plain,(
% 1.49/0.57 ( ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0)) ) | ~spl39_17),
% 1.49/0.57 inference(avatar_component_clause,[],[f905])).
% 1.49/0.57 tff(f914,plain,(
% 1.49/0.57 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | ~spl39_19),
% 1.49/0.57 inference(avatar_component_clause,[],[f913])).
% 1.49/0.57 tff(f2155,plain,(
% 1.49/0.57 spl39_149),
% 1.49/0.57 inference(avatar_split_clause,[],[f782,f2153])).
% 1.49/0.57 tff(f782,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X3,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))),X2)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f706,f439])).
% 1.49/0.57 tff(f706,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))),X2)) )),
% 1.49/0.57 inference(equality_resolution,[],[f665])).
% 1.49/0.57 tff(f665,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (finite_fold1Set(X0,X3,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))),X1) | X1 != X2) )),
% 1.49/0.57 inference(definition_unfolding,[],[f561,f491])).
% 1.49/0.57 tff(f561,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,fun(X0,X0)),X1 : X0] : (finite_fold1Set(X0,X3,insert(X0,X2,bot_bot(fun(X0,bool))),X1) | X1 != X2) )),
% 1.49/0.57 inference(cnf_transformation,[],[f389])).
% 1.49/0.57 tff(f2141,plain,(
% 1.49/0.57 spl39_148 | ~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_147),
% 1.49/0.57 inference(avatar_split_clause,[],[f2137,f2133,f1380,f1271,f1004,f2139])).
% 1.49/0.57 tff(f2139,plain,(
% 1.49/0.57 spl39_148 <=> ! [X0 : $tType,X1 : X0] : the_elem(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combk(bool,X0,fFalse))) = X1),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_148])])).
% 1.49/0.57 tff(f2133,plain,(
% 1.49/0.57 spl39_147 <=> ! [X0 : $tType,X1 : X0] : the_elem(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = X1),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_147])])).
% 1.49/0.57 tff(f2137,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (the_elem(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combk(bool,X0,fFalse))) = X1) ) | (~spl39_37 | ~spl39_86 | ~spl39_101 | ~spl39_147)),
% 1.49/0.57 inference(forward_demodulation,[],[f2136,f1383])).
% 1.49/0.57 tff(f2136,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (the_elem(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)))) = X1) ) | (~spl39_37 | ~spl39_147)),
% 1.49/0.57 inference(forward_demodulation,[],[f2134,f1005])).
% 1.49/0.57 tff(f2134,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (the_elem(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = X1) ) | ~spl39_147),
% 1.49/0.57 inference(avatar_component_clause,[],[f2133])).
% 1.49/0.57 tff(f2135,plain,(
% 1.49/0.57 spl39_147),
% 1.49/0.57 inference(avatar_split_clause,[],[f725,f2133])).
% 1.49/0.57 tff(f725,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (the_elem(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))))) = X1) )),
% 1.49/0.57 inference(forward_demodulation,[],[f619,f439])).
% 1.49/0.57 tff(f619,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (the_elem(X0,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X1)),combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool)))))) = X1) )),
% 1.49/0.57 inference(definition_unfolding,[],[f441,f491])).
% 1.49/0.57 tff(f441,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (the_elem(X0,insert(X0,X1,bot_bot(fun(X0,bool)))) = X1) )),
% 1.49/0.57 inference(cnf_transformation,[],[f145])).
% 1.49/0.57 tff(f145,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0] : the_elem(X0,insert(X0,X1,bot_bot(fun(X0,bool)))) = X1),
% 1.49/0.57 inference(rectify,[],[f34])).
% 1.49/0.57 tff(f34,axiom,(
% 1.49/0.57 ! [X1 : $tType,X15 : X1] : the_elem(X1,insert(X1,X15,bot_bot(fun(X1,bool)))) = X15),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_the__elem__eq)).
% 1.49/0.57 tff(f2119,plain,(
% 1.49/0.57 spl39_146),
% 1.49/0.57 inference(avatar_split_clause,[],[f824,f2117])).
% 1.49/0.57 tff(f2117,plain,(
% 1.49/0.57 spl39_146 <=> ! [X3 : $tType,X2 : $tType,X4 : X2,X0 : X2,X5 : fun(X3,bool),X1 : fun(X3,fun(X2,X2))] : (~pp(aa(X3,bool,combc(X3,fun(X3,bool),bool,member(X3),sK37(X2,X3,X0,X1,X4,X5)),sK36(X2,X3,X0,X1,X4,X5))) | ~sP2(X2,X3,X0,X1,X4,X5))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_146])])).
% 1.49/0.57 tff(f824,plain,(
% 1.49/0.57 ( ! [X3 : $tType,X2 : $tType,X0 : X2,X1 : fun(X3,fun(X2,X2)),X4 : X2,X5 : fun(X3,bool)] : (~pp(aa(X3,bool,combc(X3,fun(X3,bool),bool,member(X3),sK37(X2,X3,X0,X1,X4,X5)),sK36(X2,X3,X0,X1,X4,X5))) | ~sP2(X2,X3,X0,X1,X4,X5)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f601,f595])).
% 1.49/0.57 tff(f601,plain,(
% 1.49/0.57 ( ! [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),sK36(X2,X3,X0,X1,X4,X5)),sK37(X2,X3,X0,X1,X4,X5))) | ~sP2(X2,X3,X0,X1,X4,X5)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f413])).
% 1.49/0.57 tff(f2046,plain,(
% 1.49/0.57 spl39_145 | ~spl39_37 | ~spl39_139),
% 1.49/0.57 inference(avatar_split_clause,[],[f2022,f2019,f1004,f2044])).
% 1.49/0.57 tff(f2044,plain,(
% 1.49/0.57 spl39_145 <=> ! [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,sK23(X0,X1))) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_145])])).
% 1.49/0.57 tff(f2019,plain,(
% 1.49/0.57 spl39_139 <=> ! [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,sK23(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_139])])).
% 1.49/0.57 tff(f2022,plain,(
% 1.49/0.57 ( ! [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,sK23(X0,X1))) | ~finite_finite1(X0,X2)) ) | (~spl39_37 | ~spl39_139)),
% 1.49/0.57 inference(forward_demodulation,[],[f2020,f1005])).
% 1.49/0.57 tff(f2020,plain,(
% 1.49/0.57 ( ! [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,sK23(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | ~spl39_139),
% 1.49/0.57 inference(avatar_component_clause,[],[f2019])).
% 1.49/0.57 tff(f2042,plain,(
% 1.49/0.57 spl39_144 | ~spl39_37 | ~spl39_138),
% 1.49/0.57 inference(avatar_split_clause,[],[f2017,f2014,f1004,f2040])).
% 1.49/0.57 tff(f2040,plain,(
% 1.49/0.57 spl39_144 <=> ! [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,sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_144])])).
% 1.49/0.57 tff(f2014,plain,(
% 1.49/0.57 spl39_138 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | pp(aa(fun(X0,bool),bool,X1,sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_138])])).
% 1.49/0.57 tff(f2017,plain,(
% 1.49/0.57 ( ! [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,sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_37 | ~spl39_138)),
% 1.49/0.57 inference(forward_demodulation,[],[f2015,f1005])).
% 1.49/0.57 tff(f2015,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | pp(aa(fun(X0,bool),bool,X1,sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | ~spl39_138),
% 1.49/0.57 inference(avatar_component_clause,[],[f2014])).
% 1.49/0.57 tff(f2038,plain,(
% 1.49/0.57 spl39_143),
% 1.49/0.57 inference(avatar_split_clause,[],[f778,f2036])).
% 1.49/0.57 tff(f2036,plain,(
% 1.49/0.57 spl39_143 <=> ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : pp(aa(X0,bool,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X3))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_143])])).
% 1.49/0.57 tff(f778,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (pp(aa(X0,bool,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)),X3))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f705,f439])).
% 1.49/0.57 tff(f705,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (pp(aa(X0,bool,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X3))) )),
% 1.49/0.57 inference(equality_resolution,[],[f661])).
% 1.49/0.57 tff(f661,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))),X1)) | X1 != X3) )),
% 1.49/0.57 inference(definition_unfolding,[],[f556,f491])).
% 1.49/0.57 tff(f556,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : X0] : (pp(aa(X0,bool,insert(X0,X3,X2),X1)) | X1 != X3) )),
% 1.49/0.57 inference(cnf_transformation,[],[f387])).
% 1.49/0.57 tff(f2034,plain,(
% 1.49/0.57 spl39_142),
% 1.49/0.57 inference(avatar_split_clause,[],[f752,f2032])).
% 1.49/0.57 tff(f2032,plain,(
% 1.49/0.57 spl39_142 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~finite_finite1(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) | finite_finite1(X0,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_142])])).
% 1.49/0.57 tff(f752,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~finite_finite1(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))) | finite_finite1(X0,X1)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f642,f439])).
% 1.49/0.57 tff(f642,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X2)),combc(X0,fun(X0,bool),bool,member(X0),X1))))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f518,f491])).
% 1.49/0.57 tff(f518,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,insert(X0,X2,X1))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f374])).
% 1.49/0.57 tff(f374,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : ((finite_finite1(X0,insert(X0,X2,X1)) | ~finite_finite1(X0,X1)) & (finite_finite1(X0,X1) | ~finite_finite1(X0,insert(X0,X2,X1))))),
% 1.49/0.57 inference(nnf_transformation,[],[f203])).
% 1.49/0.57 tff(f203,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (finite_finite1(X0,insert(X0,X2,X1)) <=> finite_finite1(X0,X1))),
% 1.49/0.57 inference(rectify,[],[f89])).
% 1.49/0.57 tff(f89,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool),X17 : X1] : (finite_finite1(X1,insert(X1,X17,X14)) <=> finite_finite1(X1,X14))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__insert)).
% 1.49/0.57 tff(f2030,plain,(
% 1.49/0.57 spl39_141),
% 1.49/0.57 inference(avatar_split_clause,[],[f726,f2028])).
% 1.49/0.57 tff(f2028,plain,(
% 1.49/0.57 spl39_141 <=> ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_141])])).
% 1.49/0.57 tff(f726,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(forward_demodulation,[],[f690,f439])).
% 1.49/0.57 tff(f690,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0] : (finite_finite1(X0,collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2)))) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(equality_resolution,[],[f620])).
% 1.49/0.57 tff(f620,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,X2) | collect(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combc(X0,X0,bool,fequal(X0),X3)),combc(X0,fun(X0,bool),bool,member(X0),X2))) != X1) )),
% 1.49/0.57 inference(definition_unfolding,[],[f467,f491])).
% 1.49/0.57 tff(f467,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : X0,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,X2) | insert(X0,X3,X2) != X1) )),
% 1.49/0.57 inference(cnf_transformation,[],[f339])).
% 1.49/0.57 tff(f2026,plain,(
% 1.49/0.57 spl39_140),
% 1.49/0.57 inference(avatar_split_clause,[],[f600,f2024])).
% 1.49/0.57 tff(f2024,plain,(
% 1.49/0.57 spl39_140 <=> ! [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,sK36(X2,X3,X0,X1,X4,X5)),sK38(X2,X3,X0,X1,X4,X5)) = X4 | ~sP2(X2,X3,X0,X1,X4,X5))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_140])])).
% 1.49/0.57 tff(f600,plain,(
% 1.49/0.57 ( ! [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,sK36(X2,X3,X0,X1,X4,X5)),sK38(X2,X3,X0,X1,X4,X5)) = X4 | ~sP2(X2,X3,X0,X1,X4,X5)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f413])).
% 1.49/0.57 tff(f2021,plain,(
% 1.49/0.57 spl39_139),
% 1.49/0.57 inference(avatar_split_clause,[],[f504,f2019])).
% 1.49/0.57 tff(f504,plain,(
% 1.49/0.57 ( ! [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,sK23(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f368])).
% 1.49/0.57 tff(f2016,plain,(
% 1.49/0.57 spl39_138),
% 1.49/0.57 inference(avatar_split_clause,[],[f500,f2014])).
% 1.49/0.57 tff(f500,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | pp(aa(fun(X0,bool),bool,X1,sK21(X0,X1))) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f366])).
% 1.49/0.57 tff(f2012,plain,(
% 1.49/0.57 spl39_137 | ~spl39_6 | ~spl39_123),
% 1.49/0.57 inference(avatar_split_clause,[],[f1798,f1602,f857,f2010])).
% 1.49/0.57 tff(f2010,plain,(
% 1.49/0.57 spl39_137 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | X0 = X1 | fTrue = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_137])])).
% 1.49/0.57 tff(f1602,plain,(
% 1.49/0.57 spl39_123 <=> ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_123])])).
% 1.49/0.57 tff(f1798,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X0) | X0 = X1 | fTrue = X1) ) | (~spl39_6 | ~spl39_123)),
% 1.49/0.57 inference(superposition,[],[f859,f1603])).
% 1.49/0.57 tff(f1603,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl39_123),
% 1.49/0.57 inference(avatar_component_clause,[],[f1602])).
% 1.49/0.57 tff(f859,plain,(
% 1.49/0.57 pp(fTrue) | ~spl39_6),
% 1.49/0.57 inference(avatar_component_clause,[],[f857])).
% 1.49/0.57 tff(f2001,plain,(
% 1.49/0.57 spl39_136 | ~spl39_104 | ~spl39_135),
% 1.49/0.57 inference(avatar_split_clause,[],[f1997,f1994,f1420,f1999])).
% 1.49/0.57 tff(f1999,plain,(
% 1.49/0.57 spl39_136 <=> ! [X1 : $tType,X4 : fun(X1,bool),X0 : X1,X3 : X1,X2 : fun(X1,bool)] : (~pp(aa(X1,bool,combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4)),X0)) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_136])])).
% 1.49/0.57 tff(f1994,plain,(
% 1.49/0.57 spl39_135 <=> ! [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),sK32(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_135])])).
% 1.49/0.57 tff(f1997,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (~pp(aa(X1,bool,combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4)),X0)) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) ) | (~spl39_104 | ~spl39_135)),
% 1.49/0.57 inference(forward_demodulation,[],[f1995,f1421])).
% 1.49/0.57 tff(f1995,plain,(
% 1.49/0.57 ( ! [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),sK32(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) ) | ~spl39_135),
% 1.49/0.57 inference(avatar_component_clause,[],[f1994])).
% 1.49/0.57 tff(f1996,plain,(
% 1.49/0.57 spl39_135),
% 1.49/0.57 inference(avatar_split_clause,[],[f576,f1994])).
% 1.49/0.57 tff(f576,plain,(
% 1.49/0.57 ( ! [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),sK32(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f400])).
% 1.49/0.57 tff(f1985,plain,(
% 1.49/0.57 spl39_134 | ~spl39_104 | ~spl39_133),
% 1.49/0.57 inference(avatar_split_clause,[],[f1981,f1978,f1420,f1983])).
% 1.49/0.57 tff(f1983,plain,(
% 1.49/0.57 spl39_134 <=> ! [X1 : $tType,X4 : fun(X1,bool),X0 : X1,X3 : X1,X2 : fun(X1,bool)] : (~pp(aa(X1,bool,combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4)),X3)) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_134])])).
% 1.49/0.57 tff(f1978,plain,(
% 1.49/0.57 spl39_133 <=> ! [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),sK32(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_133])])).
% 1.49/0.57 tff(f1981,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (~pp(aa(X1,bool,combc(X1,fun(X1,bool),bool,member(X1),sK32(X1,X0,X2,X3,X4)),X3)) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) ) | (~spl39_104 | ~spl39_133)),
% 1.49/0.57 inference(forward_demodulation,[],[f1979,f1421])).
% 1.49/0.57 tff(f1979,plain,(
% 1.49/0.57 ( ! [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),sK32(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) ) | ~spl39_133),
% 1.49/0.57 inference(avatar_component_clause,[],[f1978])).
% 1.49/0.57 tff(f1980,plain,(
% 1.49/0.57 spl39_133),
% 1.49/0.57 inference(avatar_split_clause,[],[f574,f1978])).
% 1.49/0.57 tff(f574,plain,(
% 1.49/0.57 ( ! [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),sK32(X1,X0,X2,X3,X4))) | X0 = X3 | ~sP0(X1,X0,X2,X3,X4)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f400])).
% 1.49/0.57 tff(f1965,plain,(
% 1.49/0.57 spl39_132 | ~spl39_104 | ~spl39_131),
% 1.49/0.57 inference(avatar_split_clause,[],[f1961,f1958,f1420,f1963])).
% 1.49/0.57 tff(f1963,plain,(
% 1.49/0.57 spl39_132 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool),X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK28(X0,X1,X2,X3)),sK27(X0,X1,X2,X3))) | ~finite_fold1Set(X0,X3,X2,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_132])])).
% 1.49/0.57 tff(f1958,plain,(
% 1.49/0.57 spl39_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),sK27(X0,X1,X2,X3)),sK28(X0,X1,X2,X3))) | ~finite_fold1Set(X0,X3,X2,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_131])])).
% 1.49/0.57 tff(f1961,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK28(X0,X1,X2,X3)),sK27(X0,X1,X2,X3))) | ~finite_fold1Set(X0,X3,X2,X1)) ) | (~spl39_104 | ~spl39_131)),
% 1.49/0.57 inference(forward_demodulation,[],[f1959,f1421])).
% 1.49/0.57 tff(f1959,plain,(
% 1.49/0.57 ( ! [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),sK27(X0,X1,X2,X3)),sK28(X0,X1,X2,X3))) | ~finite_fold1Set(X0,X3,X2,X1)) ) | ~spl39_131),
% 1.49/0.57 inference(avatar_component_clause,[],[f1958])).
% 1.49/0.57 tff(f1960,plain,(
% 1.49/0.57 spl39_131),
% 1.49/0.57 inference(avatar_split_clause,[],[f550,f1958])).
% 1.49/0.57 tff(f550,plain,(
% 1.49/0.57 ( ! [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),sK27(X0,X1,X2,X3)),sK28(X0,X1,X2,X3))) | ~finite_fold1Set(X0,X3,X2,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f383])).
% 1.49/0.57 tff(f1665,plain,(
% 1.49/0.57 spl39_130 | ~spl39_37 | ~spl39_104 | ~spl39_129),
% 1.49/0.57 inference(avatar_split_clause,[],[f1661,f1657,f1420,f1004,f1663])).
% 1.49/0.57 tff(f1663,plain,(
% 1.49/0.57 spl39_130 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK11(X0,X1)),sK10(X0,X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_130])])).
% 1.49/0.57 tff(f1657,plain,(
% 1.49/0.57 spl39_129 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK10(X0,X1)),sK11(X0,X1))) | bot_bot(fun(X0,bool)) = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_129])])).
% 1.49/0.57 tff(f1661,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | ~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK11(X0,X1)),sK10(X0,X1)))) ) | (~spl39_37 | ~spl39_104 | ~spl39_129)),
% 1.49/0.57 inference(forward_demodulation,[],[f1660,f1005])).
% 1.49/0.57 tff(f1660,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),sK11(X0,X1)),sK10(X0,X1))) | bot_bot(fun(X0,bool)) = X1) ) | (~spl39_104 | ~spl39_129)),
% 1.49/0.57 inference(forward_demodulation,[],[f1658,f1421])).
% 1.49/0.57 tff(f1658,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK10(X0,X1)),sK11(X0,X1))) | bot_bot(fun(X0,bool)) = X1) ) | ~spl39_129),
% 1.49/0.57 inference(avatar_component_clause,[],[f1657])).
% 1.49/0.57 tff(f1659,plain,(
% 1.49/0.57 spl39_129),
% 1.49/0.57 inference(avatar_split_clause,[],[f469,f1657])).
% 1.49/0.57 tff(f469,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (~pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK10(X0,X1)),sK11(X0,X1))) | bot_bot(fun(X0,bool)) = X1) )),
% 1.49/0.57 inference(cnf_transformation,[],[f343])).
% 1.49/0.57 tff(f1631,plain,(
% 1.49/0.57 spl39_128 | ~spl39_37 | ~spl39_126),
% 1.49/0.57 inference(avatar_split_clause,[],[f1623,f1620,f1004,f1629])).
% 1.49/0.57 tff(f1629,plain,(
% 1.49/0.57 spl39_128 <=> ! [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,sK23(X0,X1)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_128])])).
% 1.49/0.57 tff(f1620,plain,(
% 1.49/0.57 spl39_126 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | finite_finite1(X0,sK23(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_126])])).
% 1.49/0.57 tff(f1623,plain,(
% 1.49/0.57 ( ! [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,sK23(X0,X1)) | ~finite_finite1(X0,X2)) ) | (~spl39_37 | ~spl39_126)),
% 1.49/0.57 inference(forward_demodulation,[],[f1621,f1005])).
% 1.49/0.57 tff(f1621,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | finite_finite1(X0,sK23(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) ) | ~spl39_126),
% 1.49/0.57 inference(avatar_component_clause,[],[f1620])).
% 1.49/0.57 tff(f1627,plain,(
% 1.49/0.57 spl39_127 | ~spl39_37 | ~spl39_125),
% 1.49/0.57 inference(avatar_split_clause,[],[f1618,f1615,f1004,f1625])).
% 1.49/0.57 tff(f1625,plain,(
% 1.49/0.57 spl39_127 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | finite_finite1(X0,sK21(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_127])])).
% 1.49/0.57 tff(f1615,plain,(
% 1.49/0.57 spl39_125 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | finite_finite1(X0,sK21(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_125])])).
% 1.49/0.57 tff(f1618,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,combk(bool,X0,fFalse))) | finite_finite1(X0,sK21(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_37 | ~spl39_125)),
% 1.49/0.57 inference(forward_demodulation,[],[f1616,f1005])).
% 1.49/0.57 tff(f1616,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | finite_finite1(X0,sK21(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) ) | ~spl39_125),
% 1.49/0.57 inference(avatar_component_clause,[],[f1615])).
% 1.49/0.57 tff(f1622,plain,(
% 1.49/0.57 spl39_126),
% 1.49/0.57 inference(avatar_split_clause,[],[f502,f1620])).
% 1.49/0.57 tff(f502,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,X2)) | finite_finite1(X0,sK23(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f368])).
% 1.49/0.57 tff(f1617,plain,(
% 1.49/0.57 spl39_125),
% 1.49/0.57 inference(avatar_split_clause,[],[f498,f1615])).
% 1.49/0.57 tff(f498,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(fun(X0,bool),bool)] : (pp(aa(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) | finite_finite1(X0,sK21(X0,X1)) | ~pp(aa(fun(X0,bool),bool,X1,X2)) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f366])).
% 1.49/0.57 tff(f1608,plain,(
% 1.49/0.57 spl39_124 | ~spl39_37 | ~spl39_104 | ~spl39_122),
% 1.49/0.57 inference(avatar_split_clause,[],[f1600,f1596,f1420,f1004,f1606])).
% 1.49/0.57 tff(f1606,plain,(
% 1.49/0.57 spl39_124 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK15(X0,X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_124])])).
% 1.49/0.57 tff(f1596,plain,(
% 1.49/0.57 spl39_122 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK15(X0,X1)),X1)) | bot_bot(fun(X0,bool)) = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_122])])).
% 1.49/0.57 tff(f1600,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK15(X0,X1)))) ) | (~spl39_37 | ~spl39_104 | ~spl39_122)),
% 1.49/0.57 inference(forward_demodulation,[],[f1599,f1005])).
% 1.49/0.57 tff(f1599,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK15(X0,X1))) | bot_bot(fun(X0,bool)) = X1) ) | (~spl39_104 | ~spl39_122)),
% 1.49/0.57 inference(forward_demodulation,[],[f1597,f1421])).
% 1.49/0.57 tff(f1597,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK15(X0,X1)),X1)) | bot_bot(fun(X0,bool)) = X1) ) | ~spl39_122),
% 1.49/0.57 inference(avatar_component_clause,[],[f1596])).
% 1.49/0.57 tff(f1604,plain,(
% 1.49/0.57 spl39_123 | ~spl39_10),
% 1.49/0.57 inference(avatar_split_clause,[],[f897,f874,f1602])).
% 1.49/0.57 tff(f897,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl39_10),
% 1.49/0.57 inference(superposition,[],[f875,f875])).
% 1.49/0.57 tff(f1598,plain,(
% 1.49/0.57 spl39_122),
% 1.49/0.57 inference(avatar_split_clause,[],[f480,f1596])).
% 1.49/0.57 tff(f480,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK15(X0,X1)),X1)) | bot_bot(fun(X0,bool)) = X1) )),
% 1.49/0.57 inference(cnf_transformation,[],[f360])).
% 1.49/0.57 tff(f360,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : ((pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK15(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))))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f358,f359])).
% 1.49/0.57 tff(f359,plain,(
% 1.49/0.57 ! [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),sK15(X0,X1)),X1)))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f358,plain,(
% 1.49/0.57 ! [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))))),
% 1.49/0.57 inference(rectify,[],[f357])).
% 1.49/0.57 tff(f357,plain,(
% 1.49/0.57 ! [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))))),
% 1.49/0.57 inference(nnf_transformation,[],[f174])).
% 1.49/0.57 tff(f174,plain,(
% 1.49/0.57 ! [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)),
% 1.49/0.57 inference(rectify,[],[f18])).
% 1.49/0.57 tff(f18,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool)] : (? [X19 : X1] : pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X19),X14)) <=> bot_bot(fun(X1,bool)) != X14)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_ex__in__conv)).
% 1.49/0.57 tff(f1589,plain,(
% 1.49/0.57 spl39_121 | ~spl39_37 | ~spl39_104 | ~spl39_120),
% 1.49/0.57 inference(avatar_split_clause,[],[f1585,f1581,f1420,f1004,f1587])).
% 1.49/0.57 tff(f1587,plain,(
% 1.49/0.57 spl39_121 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK14(X0,X1))) | combk(bool,X0,fFalse) = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_121])])).
% 1.49/0.57 tff(f1581,plain,(
% 1.49/0.57 spl39_120 <=> ! [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),sK14(X0,X1)),X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_120])])).
% 1.49/0.57 tff(f1585,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK14(X0,X1))) | combk(bool,X0,fFalse) = X1) ) | (~spl39_37 | ~spl39_104 | ~spl39_120)),
% 1.49/0.57 inference(forward_demodulation,[],[f1584,f1421])).
% 1.49/0.57 tff(f1584,plain,(
% 1.49/0.57 ( ! [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),sK14(X0,X1)),X1))) ) | (~spl39_37 | ~spl39_120)),
% 1.49/0.57 inference(forward_demodulation,[],[f1582,f1005])).
% 1.49/0.57 tff(f1582,plain,(
% 1.49/0.57 ( ! [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),sK14(X0,X1)),X1))) ) | ~spl39_120),
% 1.49/0.57 inference(avatar_component_clause,[],[f1581])).
% 1.49/0.57 tff(f1583,plain,(
% 1.49/0.57 spl39_120),
% 1.49/0.57 inference(avatar_split_clause,[],[f477,f1581])).
% 1.49/0.57 tff(f477,plain,(
% 1.49/0.57 ( ! [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),sK14(X0,X1)),X1))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f356])).
% 1.49/0.57 tff(f356,plain,(
% 1.49/0.57 ! [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),sK14(X0,X1)),X1))))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f354,f355])).
% 1.49/0.57 tff(f355,plain,(
% 1.49/0.57 ! [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),sK14(X0,X1)),X1)))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f354,plain,(
% 1.49/0.57 ! [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))))),
% 1.49/0.57 inference(rectify,[],[f353])).
% 1.49/0.57 tff(f353,plain,(
% 1.49/0.57 ! [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))))),
% 1.49/0.57 inference(nnf_transformation,[],[f173])).
% 1.49/0.57 tff(f173,plain,(
% 1.49/0.57 ! [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)),
% 1.49/0.57 inference(rectify,[],[f9])).
% 1.49/0.57 tff(f9,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool)] : (! [X19 : X1] : ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X19),X14)) <=> bot_bot(fun(X1,bool)) = X14)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_all__not__in__conv)).
% 1.49/0.57 tff(f1574,plain,(
% 1.49/0.57 spl39_119 | ~spl39_37 | ~spl39_104 | ~spl39_118),
% 1.49/0.57 inference(avatar_split_clause,[],[f1570,f1566,f1420,f1004,f1572])).
% 1.49/0.57 tff(f1572,plain,(
% 1.49/0.57 spl39_119 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK7(X0,X1))) | combk(bool,X0,fFalse) = X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_119])])).
% 1.49/0.57 tff(f1566,plain,(
% 1.49/0.57 spl39_118 <=> ! [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),sK7(X0,X1)),X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_118])])).
% 1.49/0.57 tff(f1570,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK7(X0,X1))) | combk(bool,X0,fFalse) = X1) ) | (~spl39_37 | ~spl39_104 | ~spl39_118)),
% 1.49/0.57 inference(forward_demodulation,[],[f1569,f1421])).
% 1.49/0.57 tff(f1569,plain,(
% 1.49/0.57 ( ! [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),sK7(X0,X1)),X1))) ) | (~spl39_37 | ~spl39_118)),
% 1.49/0.57 inference(forward_demodulation,[],[f1567,f1005])).
% 1.49/0.57 tff(f1567,plain,(
% 1.49/0.57 ( ! [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),sK7(X0,X1)),X1))) ) | ~spl39_118),
% 1.49/0.57 inference(avatar_component_clause,[],[f1566])).
% 1.49/0.57 tff(f1568,plain,(
% 1.49/0.57 spl39_118),
% 1.49/0.57 inference(avatar_split_clause,[],[f463,f1566])).
% 1.49/0.57 tff(f463,plain,(
% 1.49/0.57 ( ! [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),sK7(X0,X1)),X1))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f334])).
% 1.49/0.57 tff(f334,plain,(
% 1.49/0.57 ! [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),sK7(X0,X1)),X1)))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f272,f333])).
% 1.49/0.57 tff(f333,plain,(
% 1.49/0.57 ! [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),sK7(X0,X1)),X1)))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f272,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(ennf_transformation,[],[f167])).
% 1.49/0.57 tff(f167,plain,(
% 1.49/0.57 ! [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)),
% 1.49/0.57 inference(rectify,[],[f45])).
% 1.49/0.57 tff(f45,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool)] : (! [X39 : X1] : ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X39),X14)) => bot_bot(fun(X1,bool)) = X14)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_equals0I)).
% 1.49/0.57 tff(f1536,plain,(
% 1.49/0.57 spl39_117),
% 1.49/0.57 inference(avatar_split_clause,[],[f602,f1534])).
% 1.49/0.57 tff(f1534,plain,(
% 1.49/0.57 spl39_117 <=> ! [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,sK37(X2,X3,X0,X1,X4,X5),sK38(X2,X3,X0,X1,X4,X5)) | ~sP2(X2,X3,X0,X1,X4,X5))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_117])])).
% 1.49/0.57 tff(f602,plain,(
% 1.49/0.57 ( ! [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,sK37(X2,X3,X0,X1,X4,X5),sK38(X2,X3,X0,X1,X4,X5)) | ~sP2(X2,X3,X0,X1,X4,X5)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f413])).
% 1.49/0.57 tff(f1532,plain,(
% 1.49/0.57 spl39_116),
% 1.49/0.57 inference(avatar_split_clause,[],[f596,f1530])).
% 1.49/0.57 tff(f1530,plain,(
% 1.49/0.57 spl39_116 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : fun(X2,fun(X1,X0)),X4 : fun(X2,X1),X3 : X2] : aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_116])])).
% 1.49/0.57 tff(f596,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : (aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f245])).
% 1.49/0.57 tff(f245,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))),
% 1.49/0.57 inference(rectify,[],[f114])).
% 1.49/0.57 tff(f114,axiom,(
% 1.49/0.57 ! [X2 : $tType,X1 : $tType,X0 : $tType,X73 : X0,X74 : fun(X0,X1),X72 : fun(X0,fun(X1,X2))] : aa(X0,X2,combs(X0,X1,X2,X72,X74),X73) = aa(X1,X2,aa(X0,fun(X1,X2),X72,X73),aa(X0,X1,X74,X73))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U)).
% 1.49/0.57 tff(f1513,plain,(
% 1.49/0.57 spl39_115),
% 1.49/0.57 inference(avatar_split_clause,[],[f615,f1511])).
% 1.49/0.57 tff(f1511,plain,(
% 1.49/0.57 spl39_115 <=> ! [X0 : $tType,X2 : com,X3 : fun(vname,fun(pname,fun(fun(state,nat),X0))),X10 : X0,X1 : com,X8 : fun(loc,fun(fun(state,nat),fun(com,X0))),X6 : fun(fun(state,bool),fun(com,fun(com,X0))),X9 : fun(vname,fun(fun(state,nat),X0)),X7 : fun(com,fun(com,X0)),X4 : fun(pname,X0),X5 : fun(fun(state,bool),fun(com,X0))] : com_case(X0,X10,X9,X8,X7,X6,X5,X4,X3,semi(X2,X1)) = aa(com,X0,aa(com,fun(com,X0),X7,X2),X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_115])])).
% 1.49/0.57 tff(f615,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : com,X3 : fun(vname,fun(pname,fun(fun(state,nat),X0))),X10 : X0,X1 : com,X8 : fun(loc,fun(fun(state,nat),fun(com,X0))),X6 : fun(fun(state,bool),fun(com,fun(com,X0))),X9 : fun(vname,fun(fun(state,nat),X0)),X7 : fun(com,fun(com,X0)),X4 : fun(pname,X0),X5 : fun(fun(state,bool),fun(com,X0))] : (com_case(X0,X10,X9,X8,X7,X6,X5,X4,X3,semi(X2,X1)) = aa(com,X0,aa(com,fun(com,X0),X7,X2),X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f254])).
% 1.49/0.57 tff(f254,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : com,X2 : com,X3 : fun(vname,fun(pname,fun(fun(state,nat),X0))),X4 : fun(pname,X0),X5 : fun(fun(state,bool),fun(com,X0)),X6 : fun(fun(state,bool),fun(com,fun(com,X0))),X7 : fun(com,fun(com,X0)),X8 : fun(loc,fun(fun(state,nat),fun(com,X0))),X9 : fun(vname,fun(fun(state,nat),X0)),X10 : X0] : com_case(X0,X10,X9,X8,X7,X6,X5,X4,X3,semi(X2,X1)) = aa(com,X0,aa(com,fun(com,X0),X7,X2),X1)),
% 1.49/0.57 inference(rectify,[],[f53])).
% 1.49/0.57 tff(f53,axiom,(
% 1.49/0.57 ! [X1 : $tType,X35 : com,X36 : com,X48 : fun(vname,fun(pname,fun(fun(state,nat),X1))),X49 : fun(pname,X1),X50 : fun(fun(state,bool),fun(com,X1)),X51 : fun(fun(state,bool),fun(com,fun(com,X1))),X52 : fun(com,fun(com,X1)),X53 : fun(loc,fun(fun(state,nat),fun(com,X1))),X54 : fun(vname,fun(fun(state,nat),X1)),X22 : X1] : com_case(X1,X22,X54,X53,X52,X51,X50,X49,X48,semi(X36,X35)) = aa(com,X1,aa(com,fun(com,X1),X52,X36),X35)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_com_Osimps_I67_J)).
% 1.49/0.57 tff(f1509,plain,(
% 1.49/0.57 spl39_114),
% 1.49/0.57 inference(avatar_split_clause,[],[f460,f1507])).
% 1.49/0.57 tff(f1507,plain,(
% 1.49/0.57 spl39_114 <=> ! [X1 : $tType,X0 : $tType,X4 : fun(X1,X0),X3 : fun(X1,X0),X2 : X1] : (aa(X1,X0,minus_minus(fun(X1,X0),X4,X3),X2) = minus_minus(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2)) | ~cl_Groups_Ominus(X0))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_114])])).
% 1.49/0.57 tff(f460,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X1,X0),X4 : fun(X1,X0)] : (aa(X1,X0,minus_minus(fun(X1,X0),X4,X3),X2) = minus_minus(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2)) | ~cl_Groups_Ominus(X0)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f268])).
% 1.49/0.57 tff(f268,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1,X3 : fun(X1,X0),X4 : fun(X1,X0)] : aa(X1,X0,minus_minus(fun(X1,X0),X4,X3),X2) = minus_minus(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2)) | ~cl_Groups_Ominus(X0))),
% 1.49/0.57 inference(ennf_transformation,[],[f164])).
% 1.49/0.57 tff(f164,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (cl_Groups_Ominus(X0) => ! [X2 : X1,X3 : fun(X1,X0),X4 : fun(X1,X0)] : aa(X1,X0,minus_minus(fun(X1,X0),X4,X3),X2) = minus_minus(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2)))),
% 1.49/0.57 inference(rectify,[],[f83])).
% 1.49/0.57 tff(f83,axiom,(
% 1.49/0.57 ! [X1 : $tType,X2 : $tType] : (cl_Groups_Ominus(X1) => ! [X15 : X2,X18 : fun(X2,X1),X14 : fun(X2,X1)] : aa(X2,X1,minus_minus(fun(X2,X1),X14,X18),X15) = minus_minus(X1,aa(X2,X1,X14,X15),aa(X2,X1,X18,X15)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_minus__apply)).
% 1.49/0.57 tff(f1489,plain,(
% 1.49/0.57 spl39_113),
% 1.49/0.57 inference(avatar_split_clause,[],[f549,f1487])).
% 1.49/0.57 tff(f1487,plain,(
% 1.49/0.57 spl39_113 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool),X1 : X0] : (finite_fold_graph(X0,X0,X3,sK27(X0,X1,X2,X3),sK28(X0,X1,X2,X3),sK29(X0,X1,X2,X3)) | ~finite_fold1Set(X0,X3,X2,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_113])])).
% 1.49/0.57 tff(f549,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (finite_fold_graph(X0,X0,X3,sK27(X0,X1,X2,X3),sK28(X0,X1,X2,X3),sK29(X0,X1,X2,X3)) | ~finite_fold1Set(X0,X3,X2,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f383])).
% 1.49/0.57 tff(f1485,plain,(
% 1.49/0.57 spl39_112),
% 1.49/0.57 inference(avatar_split_clause,[],[f546,f1483])).
% 1.49/0.57 tff(f1483,plain,(
% 1.49/0.57 spl39_112 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X1,X0),X2 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK26(X0,X1,X2,X3)) != aa(X1,X0,X2,sK26(X0,X1,X2,X3)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_112])])).
% 1.49/0.57 tff(f546,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK26(X0,X1,X2,X3)) != aa(X1,X0,X2,sK26(X0,X1,X2,X3))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f379])).
% 1.49/0.57 tff(f379,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK26(X0,X1,X2,X3)) != aa(X1,X0,X2,sK26(X0,X1,X2,X3)))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f309,f378])).
% 1.49/0.57 tff(f378,plain,(
% 1.49/0.57 ! [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,sK26(X0,X1,X2,X3)) != aa(X1,X0,X2,sK26(X0,X1,X2,X3)))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f309,plain,(
% 1.49/0.57 ! [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))),
% 1.49/0.57 inference(ennf_transformation,[],[f226])).
% 1.49/0.57 tff(f226,plain,(
% 1.49/0.57 ! [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)),
% 1.49/0.57 inference(rectify,[],[f76])).
% 1.49/0.57 tff(f76,axiom,(
% 1.49/0.57 ! [X2 : $tType,X1 : $tType,X58 : fun(X1,X2),X47 : fun(X1,X2)] : (! [X59 : X1] : aa(X1,X2,X47,X59) = aa(X1,X2,X58,X59) => X47 = X58)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext)).
% 1.49/0.57 tff(f1475,plain,(
% 1.49/0.57 spl39_111 | ~spl39_19 | ~spl39_97),
% 1.49/0.57 inference(avatar_split_clause,[],[f1417,f1360,f913,f1473])).
% 1.49/0.57 tff(f1360,plain,(
% 1.49/0.57 spl39_97 <=> ! [X0 : state] : (q(sK3,X0) | pp(aa(a,bool,combc(a,state,bool,p1,sK4),sK6(sK4,X0))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_97])])).
% 1.49/0.57 tff(f1417,plain,(
% 1.49/0.57 ( ! [X0 : state] : (q(sK3,X0) | fTrue = aa(a,bool,combc(a,state,bool,p1,sK4),sK6(sK4,X0))) ) | (~spl39_19 | ~spl39_97)),
% 1.49/0.57 inference(resolution,[],[f1361,f914])).
% 1.49/0.57 tff(f1361,plain,(
% 1.49/0.57 ( ! [X0 : state] : (pp(aa(a,bool,combc(a,state,bool,p1,sK4),sK6(sK4,X0))) | q(sK3,X0)) ) | ~spl39_97),
% 1.49/0.57 inference(avatar_component_clause,[],[f1360])).
% 1.49/0.57 tff(f1471,plain,(
% 1.49/0.57 spl39_110 | ~spl39_104 | ~spl39_109),
% 1.49/0.57 inference(avatar_split_clause,[],[f1467,f1464,f1420,f1469])).
% 1.49/0.57 tff(f1469,plain,(
% 1.49/0.57 spl39_110 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | ~pp(aa(X0,bool,X1,X2)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_110])])).
% 1.49/0.57 tff(f1464,plain,(
% 1.49/0.57 spl39_109 <=> ! [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)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_109])])).
% 1.49/0.57 tff(f1467,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | ~pp(aa(X0,bool,X1,X2))) ) | (~spl39_104 | ~spl39_109)),
% 1.49/0.57 inference(forward_demodulation,[],[f1465,f1421])).
% 1.49/0.57 tff(f1465,plain,(
% 1.49/0.57 ( ! [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))) ) | ~spl39_109),
% 1.49/0.57 inference(avatar_component_clause,[],[f1464])).
% 1.49/0.57 tff(f1466,plain,(
% 1.49/0.57 spl39_109),
% 1.49/0.57 inference(avatar_split_clause,[],[f521,f1464])).
% 1.49/0.57 tff(f521,plain,(
% 1.49/0.57 ( ! [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))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f375])).
% 1.49/0.57 tff(f375,plain,(
% 1.49/0.57 ! [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))))),
% 1.49/0.57 inference(nnf_transformation,[],[f204])).
% 1.49/0.57 tff(f204,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(rectify,[],[f77])).
% 1.49/0.57 tff(f77,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool),X15 : X1] : (pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X14)) <=> pp(aa(X1,bool,X14,X15)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def)).
% 1.49/0.57 tff(f1458,plain,(
% 1.49/0.57 spl39_108 | ~spl39_104 | ~spl39_107),
% 1.49/0.57 inference(avatar_split_clause,[],[f1454,f1451,f1420,f1456])).
% 1.49/0.57 tff(f1456,plain,(
% 1.49/0.57 spl39_108 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | pp(aa(X0,bool,X1,X2)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_108])])).
% 1.49/0.57 tff(f1451,plain,(
% 1.49/0.57 spl39_107 <=> ! [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)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_107])])).
% 1.49/0.57 tff(f1454,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) | pp(aa(X0,bool,X1,X2))) ) | (~spl39_104 | ~spl39_107)),
% 1.49/0.57 inference(forward_demodulation,[],[f1452,f1421])).
% 1.49/0.57 tff(f1452,plain,(
% 1.49/0.57 ( ! [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))) ) | ~spl39_107),
% 1.49/0.57 inference(avatar_component_clause,[],[f1451])).
% 1.49/0.57 tff(f1453,plain,(
% 1.49/0.57 spl39_107),
% 1.49/0.57 inference(avatar_split_clause,[],[f520,f1451])).
% 1.49/0.57 tff(f520,plain,(
% 1.49/0.57 ( ! [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))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f375])).
% 1.49/0.57 tff(f1448,plain,(
% 1.49/0.57 spl39_106 | ~spl39_37 | ~spl39_105),
% 1.49/0.57 inference(avatar_split_clause,[],[f1427,f1424,f1004,f1446])).
% 1.49/0.57 tff(f1446,plain,(
% 1.49/0.57 spl39_106 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1)),X2 : X1] : (combk(bool,X0,fFalse) = X3 | sP2(X1,X0,X4,X5,X2,X3) | ~finite_fold_graph(X0,X1,X5,X4,X3,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_106])])).
% 1.49/0.57 tff(f1424,plain,(
% 1.49/0.57 spl39_105 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1)),X2 : X1] : (sP2(X1,X0,X4,X5,X2,X3) | bot_bot(fun(X0,bool)) = X3 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_105])])).
% 1.49/0.57 tff(f1427,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (combk(bool,X0,fFalse) = X3 | sP2(X1,X0,X4,X5,X2,X3) | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)) ) | (~spl39_37 | ~spl39_105)),
% 1.49/0.57 inference(forward_demodulation,[],[f1425,f1005])).
% 1.49/0.57 tff(f1425,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (sP2(X1,X0,X4,X5,X2,X3) | bot_bot(fun(X0,bool)) = X3 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)) ) | ~spl39_105),
% 1.49/0.57 inference(avatar_component_clause,[],[f1424])).
% 1.49/0.57 tff(f1426,plain,(
% 1.49/0.57 spl39_105),
% 1.49/0.57 inference(avatar_split_clause,[],[f604,f1424])).
% 1.49/0.57 tff(f604,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (sP2(X1,X0,X4,X5,X2,X3) | bot_bot(fun(X0,bool)) = X3 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f415])).
% 1.49/0.57 tff(f415,plain,(
% 1.49/0.57 ! [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) | (~sP2(X1,X0,X4,X5,X2,X3) & (X2 != X4 | bot_bot(fun(X0,bool)) != X3))) & (sP2(X1,X0,X4,X5,X2,X3) | (X2 = X4 & bot_bot(fun(X0,bool)) = X3) | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)))),
% 1.49/0.57 inference(flattening,[],[f414])).
% 1.49/0.57 tff(f414,plain,(
% 1.49/0.57 ! [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) | (~sP2(X1,X0,X4,X5,X2,X3) & (X2 != X4 | bot_bot(fun(X0,bool)) != X3))) & ((sP2(X1,X0,X4,X5,X2,X3) | (X2 = X4 & bot_bot(fun(X0,bool)) = X3)) | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)))),
% 1.49/0.57 inference(nnf_transformation,[],[f327])).
% 1.49/0.57 tff(f327,plain,(
% 1.49/0.57 ! [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) <=> (sP2(X1,X0,X4,X5,X2,X3) | (X2 = X4 & bot_bot(fun(X0,bool)) = X3)))),
% 1.49/0.57 inference(definition_folding,[],[f249,f326])).
% 1.49/0.57 tff(f249,plain,(
% 1.49/0.57 ! [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 & insert(X0,X6,X7) = X3) | (X2 = X4 & bot_bot(fun(X0,bool)) = X3)))),
% 1.49/0.57 inference(rectify,[],[f84])).
% 1.49/0.57 tff(f84,axiom,(
% 1.49/0.57 ! [X1 : $tType,X2 : $tType,X63 : X2,X64 : fun(X1,bool),X57 : X2,X47 : fun(X1,fun(X2,X2))] : (finite_fold_graph(X1,X2,X47,X57,X64,X63) <=> (? [X19 : X1,X66 : fun(X1,bool),X67 : X2] : (finite_fold_graph(X1,X2,X47,X57,X66,X67) & ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X19),X66)) & aa(X2,X2,aa(X1,fun(X2,X2),X47,X19),X67) = X63 & insert(X1,X19,X66) = X64) | (X57 = X63 & bot_bot(fun(X1,bool)) = X64)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_fold__graph_Osimps)).
% 1.49/0.57 tff(f1422,plain,(
% 1.49/0.57 spl39_104),
% 1.49/0.57 inference(avatar_split_clause,[],[f595,f1420])).
% 1.49/0.57 tff(f1394,plain,(
% 1.49/0.57 spl39_103),
% 1.49/0.57 inference(avatar_split_clause,[],[f594,f1392])).
% 1.49/0.57 tff(f1392,plain,(
% 1.49/0.57 spl39_103 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : fun(X1,X0),X4 : fun(X2,X1),X3 : X2] : aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_103])])).
% 1.49/0.57 tff(f594,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : (aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f243])).
% 1.49/0.57 tff(f243,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 1.49/0.57 inference(rectify,[],[f111])).
% 1.49/0.57 tff(f111,axiom,(
% 1.49/0.57 ! [X2 : $tType,X1 : $tType,X0 : $tType,X73 : X0,X74 : fun(X0,X1),X72 : fun(X1,X2)] : aa(X0,X2,combb(X1,X2,X0,X72,X74),X73) = aa(X1,X2,X72,aa(X0,X1,X74,X73))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U)).
% 1.49/0.57 tff(f1390,plain,(
% 1.49/0.57 spl39_102),
% 1.49/0.57 inference(avatar_split_clause,[],[f487,f1388])).
% 1.49/0.57 tff(f1388,plain,(
% 1.49/0.57 spl39_102 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : minus_minus(fun(X0,bool),X2,X1) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X2,X1),X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_102])])).
% 1.49/0.57 tff(f487,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X2,X1) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X2,X1),X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f181])).
% 1.49/0.57 tff(f181,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : minus_minus(fun(X0,bool),X2,X1) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X2,X1),X1)),
% 1.49/0.57 inference(rectify,[],[f60])).
% 1.49/0.57 tff(f60,axiom,(
% 1.49/0.57 ! [X1 : $tType,X18 : fun(X1,bool),X14 : fun(X1,bool)] : minus_minus(fun(X1,bool),X14,X18) = minus_minus(fun(X1,bool),minus_minus(fun(X1,bool),X14,X18),X18)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Diff__idemp)).
% 1.49/0.57 tff(f1382,plain,(
% 1.49/0.57 spl39_101 | ~spl39_37 | ~spl39_100),
% 1.49/0.57 inference(avatar_split_clause,[],[f1378,f1374,f1004,f1380])).
% 1.49/0.57 tff(f1374,plain,(
% 1.49/0.57 spl39_100 <=> ! [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))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_100])])).
% 1.49/0.57 tff(f1378,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1))) ) | (~spl39_37 | ~spl39_100)),
% 1.49/0.57 inference(forward_demodulation,[],[f1377,f1005])).
% 1.49/0.57 tff(f1377,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (~pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))),X1))) ) | ~spl39_100),
% 1.49/0.57 inference(forward_demodulation,[],[f1375,f595])).
% 1.49/0.57 tff(f1375,plain,(
% 1.49/0.57 ( ! [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))))) ) | ~spl39_100),
% 1.49/0.57 inference(avatar_component_clause,[],[f1374])).
% 1.49/0.57 tff(f1376,plain,(
% 1.49/0.57 spl39_100),
% 1.49/0.57 inference(avatar_split_clause,[],[f445,f1374])).
% 1.49/0.57 tff(f445,plain,(
% 1.49/0.57 ( ! [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))))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f149])).
% 1.49/0.57 tff(f149,plain,(
% 1.49/0.57 ! [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))))),
% 1.49/0.57 inference(rectify,[],[f13])).
% 1.49/0.57 tff(f13,axiom,(
% 1.49/0.57 ! [X1 : $tType,X17 : X1] : ~pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X17),bot_bot(fun(X1,bool))))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_emptyE)).
% 1.49/0.57 tff(f1371,plain,(
% 1.49/0.57 spl39_99 | ~spl39_98),
% 1.49/0.57 inference(avatar_split_clause,[],[f1367,f1364,f1369])).
% 1.49/0.57 tff(f1364,plain,(
% 1.49/0.57 spl39_98 <=> ! [X2 : state,X0 : a,X1 : state] : (q(X0,X2) | ~pp(aa(state,bool,aa(a,fun(state,bool),q1,sK6(X1,X2)),X2)) | ~p(X0,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_98])])).
% 1.49/0.57 tff(f1367,plain,(
% 1.49/0.57 ( ! [X2 : state,X0 : a,X1 : state] : (~pp(aa(a,bool,combc(a,state,bool,q1,X2),sK6(X1,X2))) | q(X0,X2) | ~p(X0,X1)) ) | ~spl39_98),
% 1.49/0.57 inference(forward_demodulation,[],[f1365,f595])).
% 1.49/0.57 tff(f1365,plain,(
% 1.49/0.57 ( ! [X2 : state,X0 : a,X1 : state] : (q(X0,X2) | ~pp(aa(state,bool,aa(a,fun(state,bool),q1,sK6(X1,X2)),X2)) | ~p(X0,X1)) ) | ~spl39_98),
% 1.49/0.57 inference(avatar_component_clause,[],[f1364])).
% 1.49/0.57 tff(f1366,plain,(
% 1.49/0.57 spl39_98),
% 1.49/0.57 inference(avatar_split_clause,[],[f423,f1364])).
% 1.49/0.57 tff(f423,plain,(
% 1.49/0.57 ( ! [X2 : state,X0 : a,X1 : state] : (q(X0,X2) | ~pp(aa(state,bool,aa(a,fun(state,bool),q1,sK6(X1,X2)),X2)) | ~p(X0,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f332])).
% 1.49/0.57 tff(f332,plain,(
% 1.49/0.57 ! [X0 : a,X1 : state] : (! [X2 : state] : (q(X0,X2) | (~pp(aa(state,bool,aa(a,fun(state,bool),q1,sK6(X1,X2)),X2)) & pp(aa(state,bool,aa(a,fun(state,bool),p1,sK6(X1,X2)),X1)))) | ~p(X0,X1))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f261,f331])).
% 1.49/0.57 tff(f331,plain,(
% 1.49/0.57 ! [X1 : state,X2 : state] : (? [X3 : a] : (~pp(aa(state,bool,aa(a,fun(state,bool),q1,X3),X2)) & pp(aa(state,bool,aa(a,fun(state,bool),p1,X3),X1))) => (~pp(aa(state,bool,aa(a,fun(state,bool),q1,sK6(X1,X2)),X2)) & pp(aa(state,bool,aa(a,fun(state,bool),p1,sK6(X1,X2)),X1))))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f261,plain,(
% 1.49/0.57 ! [X0 : a,X1 : state] : (! [X2 : state] : (q(X0,X2) | ? [X3 : a] : (~pp(aa(state,bool,aa(a,fun(state,bool),q1,X3),X2)) & pp(aa(state,bool,aa(a,fun(state,bool),p1,X3),X1)))) | ~p(X0,X1))),
% 1.49/0.57 inference(ennf_transformation,[],[f133])).
% 1.49/0.57 tff(f133,plain,(
% 1.49/0.57 ! [X0 : a,X1 : state] : (p(X0,X1) => ! [X2 : state] : (! [X3 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),p1,X3),X1)) => pp(aa(state,bool,aa(a,fun(state,bool),q1,X3),X2))) => q(X0,X2)))),
% 1.49/0.57 inference(rectify,[],[f129])).
% 1.49/0.57 tff(f129,axiom,(
% 1.49/0.57 ! [X77 : a,X78 : state] : (p(X77,X78) => ! [X79 : state] : (! [X80 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),p1,X80),X78)) => pp(aa(state,bool,aa(a,fun(state,bool),q1,X80),X79))) => q(X77,X79)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 1.49/0.57 tff(f1362,plain,(
% 1.49/0.57 spl39_97 | ~spl39_1 | ~spl39_96),
% 1.49/0.57 inference(avatar_split_clause,[],[f1358,f1355,f832,f1360])).
% 1.49/0.57 tff(f1355,plain,(
% 1.49/0.57 spl39_96 <=> ! [X2 : state,X0 : a,X1 : state] : (pp(aa(a,bool,combc(a,state,bool,p1,X1),sK6(X1,X2))) | q(X0,X2) | ~p(X0,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_96])])).
% 1.49/0.57 tff(f1358,plain,(
% 1.49/0.57 ( ! [X0 : state] : (q(sK3,X0) | pp(aa(a,bool,combc(a,state,bool,p1,sK4),sK6(sK4,X0)))) ) | (~spl39_1 | ~spl39_96)),
% 1.49/0.57 inference(resolution,[],[f1356,f834])).
% 1.49/0.57 tff(f834,plain,(
% 1.49/0.57 p(sK3,sK4) | ~spl39_1),
% 1.49/0.57 inference(avatar_component_clause,[],[f832])).
% 1.49/0.57 tff(f1356,plain,(
% 1.49/0.57 ( ! [X2 : state,X0 : a,X1 : state] : (~p(X0,X1) | q(X0,X2) | pp(aa(a,bool,combc(a,state,bool,p1,X1),sK6(X1,X2)))) ) | ~spl39_96),
% 1.49/0.57 inference(avatar_component_clause,[],[f1355])).
% 1.49/0.57 tff(f1357,plain,(
% 1.49/0.57 spl39_96 | ~spl39_95),
% 1.49/0.57 inference(avatar_split_clause,[],[f1353,f1350,f1355])).
% 1.49/0.57 tff(f1350,plain,(
% 1.49/0.57 spl39_95 <=> ! [X2 : state,X0 : a,X1 : state] : (q(X0,X2) | pp(aa(state,bool,aa(a,fun(state,bool),p1,sK6(X1,X2)),X1)) | ~p(X0,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_95])])).
% 1.49/0.57 tff(f1353,plain,(
% 1.49/0.57 ( ! [X2 : state,X0 : a,X1 : state] : (pp(aa(a,bool,combc(a,state,bool,p1,X1),sK6(X1,X2))) | q(X0,X2) | ~p(X0,X1)) ) | ~spl39_95),
% 1.49/0.57 inference(forward_demodulation,[],[f1351,f595])).
% 1.49/0.57 tff(f1351,plain,(
% 1.49/0.57 ( ! [X2 : state,X0 : a,X1 : state] : (q(X0,X2) | pp(aa(state,bool,aa(a,fun(state,bool),p1,sK6(X1,X2)),X1)) | ~p(X0,X1)) ) | ~spl39_95),
% 1.49/0.57 inference(avatar_component_clause,[],[f1350])).
% 1.49/0.57 tff(f1352,plain,(
% 1.49/0.57 spl39_95),
% 1.49/0.57 inference(avatar_split_clause,[],[f422,f1350])).
% 1.49/0.57 tff(f422,plain,(
% 1.49/0.57 ( ! [X2 : state,X0 : a,X1 : state] : (q(X0,X2) | pp(aa(state,bool,aa(a,fun(state,bool),p1,sK6(X1,X2)),X1)) | ~p(X0,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f332])).
% 1.49/0.57 tff(f1338,plain,(
% 1.49/0.57 spl39_94 | ~spl39_37 | ~spl39_91),
% 1.49/0.57 inference(avatar_split_clause,[],[f1326,f1323,f1004,f1336])).
% 1.49/0.57 tff(f1336,plain,(
% 1.49/0.57 spl39_94 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = X2 | finite_fold1Set(X0,X1,X2,sK19(X0,X1,X2)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_94])])).
% 1.49/0.57 tff(f1323,plain,(
% 1.49/0.57 spl39_91 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X1,X2,sK19(X0,X1,X2)) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_91])])).
% 1.49/0.57 tff(f1326,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (combk(bool,X0,fFalse) = X2 | finite_fold1Set(X0,X1,X2,sK19(X0,X1,X2)) | ~finite_finite1(X0,X2)) ) | (~spl39_37 | ~spl39_91)),
% 1.49/0.57 inference(forward_demodulation,[],[f1324,f1005])).
% 1.49/0.57 tff(f1324,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X1,X2,sK19(X0,X1,X2)) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2)) ) | ~spl39_91),
% 1.49/0.57 inference(avatar_component_clause,[],[f1323])).
% 1.49/0.57 tff(f1334,plain,(
% 1.49/0.57 spl39_93),
% 1.49/0.57 inference(avatar_split_clause,[],[f612,f1332])).
% 1.49/0.57 tff(f1332,plain,(
% 1.49/0.57 spl39_93 <=> ! [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))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_93])])).
% 1.49/0.57 tff(f612,plain,(
% 1.49/0.57 ( ! [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)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f417])).
% 1.49/0.57 tff(f417,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(flattening,[],[f416])).
% 1.49/0.57 tff(f416,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(nnf_transformation,[],[f252])).
% 1.49/0.57 tff(f252,plain,(
% 1.49/0.57 ! [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))),
% 1.49/0.57 inference(rectify,[],[f1])).
% 1.49/0.57 tff(f1,axiom,(
% 1.49/0.57 ! [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))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_triple_Oinject)).
% 1.49/0.57 tff(f1330,plain,(
% 1.49/0.57 spl39_92),
% 1.49/0.57 inference(avatar_split_clause,[],[f610,f1328])).
% 1.49/0.57 tff(f1328,plain,(
% 1.49/0.57 spl39_92 <=> ! [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))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_92])])).
% 1.49/0.57 tff(f610,plain,(
% 1.49/0.57 ( ! [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)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f417])).
% 1.49/0.57 tff(f1325,plain,(
% 1.49/0.57 spl39_91),
% 1.49/0.57 inference(avatar_split_clause,[],[f497,f1323])).
% 1.49/0.57 tff(f497,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,fun(X0,X0))] : (finite_fold1Set(X0,X1,X2,sK19(X0,X1,X2)) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f364])).
% 1.49/0.57 tff(f364,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : (finite_fold1Set(X0,X1,X2,sK19(X0,X1,X2)) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f277,f363])).
% 1.49/0.57 tff(f363,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : (? [X3 : X0] : finite_fold1Set(X0,X1,X2,X3) => finite_fold1Set(X0,X1,X2,sK19(X0,X1,X2)))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f277,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : (? [X3 : X0] : finite_fold1Set(X0,X1,X2,X3) | bot_bot(fun(X0,bool)) = X2 | ~finite_finite1(X0,X2))),
% 1.49/0.57 inference(flattening,[],[f276])).
% 1.49/0.57 tff(f276,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : ((? [X3 : X0] : finite_fold1Set(X0,X1,X2,X3) | bot_bot(fun(X0,bool)) = X2) | ~finite_finite1(X0,X2))),
% 1.49/0.57 inference(ennf_transformation,[],[f191])).
% 1.49/0.57 tff(f191,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool)] : (finite_finite1(X0,X2) => (bot_bot(fun(X0,bool)) != X2 => ? [X3 : X0] : finite_fold1Set(X0,X1,X2,X3)))),
% 1.49/0.57 inference(rectify,[],[f98])).
% 1.49/0.57 tff(f98,axiom,(
% 1.49/0.57 ! [X1 : $tType,X47 : fun(X1,fun(X1,X1)),X14 : fun(X1,bool)] : (finite_finite1(X1,X14) => (bot_bot(fun(X1,bool)) != X14 => ? [X68 : X1] : finite_fold1Set(X1,X47,X14,X68)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_finite__nonempty__imp__fold1Set)).
% 1.49/0.57 tff(f1318,plain,(
% 1.49/0.57 spl39_90 | ~spl39_37 | ~spl39_89),
% 1.49/0.57 inference(avatar_split_clause,[],[f1314,f1308,f1004,f1316])).
% 1.49/0.57 tff(f1308,plain,(
% 1.49/0.57 spl39_89 <=> ! [X2 : fun(a,fun(state,bool)),X5 : a,X3 : fun(a,fun(state,bool))] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK5(X2,X3))) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4)) | ~hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool)))))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_89])])).
% 1.49/0.57 tff(f1314,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool)),X5 : a] : (~hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)))),combk(bool,hoare_28830079triple(a),fFalse))) | ~pp(aa(a,bool,combc(a,state,bool,X2,sK4),X5)) | pp(aa(a,bool,combc(a,state,bool,X3,sK5(X2,X3)),X5))) ) | (~spl39_37 | ~spl39_89)),
% 1.49/0.57 inference(forward_demodulation,[],[f1313,f1005])).
% 1.49/0.57 tff(f1313,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool)),X5 : a] : (~hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)))),bot_bot(fun(hoare_28830079triple(a),bool)))) | ~pp(aa(a,bool,combc(a,state,bool,X2,sK4),X5)) | pp(aa(a,bool,combc(a,state,bool,X3,sK5(X2,X3)),X5))) ) | ~spl39_89),
% 1.49/0.57 inference(forward_demodulation,[],[f1312,f739])).
% 1.49/0.57 tff(f1312,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool)),X5 : a] : (~pp(aa(a,bool,combc(a,state,bool,X2,sK4),X5)) | pp(aa(a,bool,combc(a,state,bool,X3,sK5(X2,X3)),X5)) | ~hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))))))) ) | ~spl39_89),
% 1.49/0.57 inference(forward_demodulation,[],[f1311,f595])).
% 1.49/0.57 tff(f1311,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool)),X5 : a] : (pp(aa(a,bool,combc(a,state,bool,X3,sK5(X2,X3)),X5)) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4)) | ~hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))))))) ) | ~spl39_89),
% 1.49/0.57 inference(forward_demodulation,[],[f1309,f595])).
% 1.49/0.57 tff(f1309,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool)),X5 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK5(X2,X3))) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4)) | ~hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))))))) ) | ~spl39_89),
% 1.49/0.57 inference(avatar_component_clause,[],[f1308])).
% 1.49/0.57 tff(f1310,plain,(
% 1.49/0.57 spl39_89),
% 1.49/0.57 inference(avatar_split_clause,[],[f617,f1308])).
% 1.49/0.57 tff(f617,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool)),X5 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK5(X2,X3))) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4)) | ~hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))))))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f419,f491])).
% 1.49/0.57 tff(f419,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool)),X5 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK5(X2,X3))) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4)) | ~hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f330])).
% 1.49/0.57 tff(f330,plain,(
% 1.49/0.57 ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : ((~q(sK3,sK5(X2,X3)) & ! [X5 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK5(X2,X3))) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4)))) | ~hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))) & p(sK3,sK4)),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f260,f329,f328])).
% 1.49/0.57 tff(f328,plain,(
% 1.49/0.57 ? [X0 : a,X1 : state] : (! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (? [X4 : state] : (~q(X0,X4) & ! [X5 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1)))) | ~hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))) & p(X0,X1)) => (! [X3 : fun(a,fun(state,bool)),X2 : fun(a,fun(state,bool))] : (? [X4 : state] : (~q(sK3,X4) & ! [X5 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4)))) | ~hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))) & p(sK3,sK4))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f329,plain,(
% 1.49/0.57 ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (? [X4 : state] : (~q(sK3,X4) & ! [X5 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4)))) => (~q(sK3,sK5(X2,X3)) & ! [X5 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK5(X2,X3))) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4)))))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f260,plain,(
% 1.49/0.57 ? [X0 : a,X1 : state] : (! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (? [X4 : state] : (~q(X0,X4) & ! [X5 : a] : (pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) | ~pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1)))) | ~hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))) & p(X0,X1))),
% 1.49/0.57 inference(ennf_transformation,[],[f132])).
% 1.49/0.57 tff(f132,plain,(
% 1.49/0.57 ~! [X0 : a,X1 : state] : (? [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (! [X4 : state] : (q(X0,X4) | ? [X5 : a] : (~pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) & pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1)))) & hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))) | ~p(X0,X1))),
% 1.49/0.57 inference(rectify,[],[f131])).
% 1.49/0.57 tff(f131,negated_conjecture,(
% 1.49/0.57 ~! [X40 : a,X41 : state] : (? [X42 : fun(a,fun(state,bool)),X43 : fun(a,fun(state,bool))] : (! [X44 : state] : (q(X40,X44) | ? [X45 : a] : (~pp(aa(state,bool,aa(a,fun(state,bool),X43,X45),X44)) & pp(aa(state,bool,aa(a,fun(state,bool),X42,X45),X41)))) & hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X42,c,X43),bot_bot(fun(hoare_28830079triple(a),bool))))) | ~p(X40,X41))),
% 1.49/0.57 inference(negated_conjecture,[],[f130])).
% 1.49/0.57 tff(f130,conjecture,(
% 1.49/0.57 ! [X40 : a,X41 : state] : (? [X42 : fun(a,fun(state,bool)),X43 : fun(a,fun(state,bool))] : (! [X44 : state] : (q(X40,X44) | ? [X45 : a] : (~pp(aa(state,bool,aa(a,fun(state,bool),X43,X45),X44)) & pp(aa(state,bool,aa(a,fun(state,bool),X42,X45),X41)))) & hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X42,c,X43),bot_bot(fun(hoare_28830079triple(a),bool))))) | ~p(X40,X41))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)).
% 1.49/0.57 tff(f1305,plain,(
% 1.49/0.57 spl39_88),
% 1.49/0.57 inference(avatar_split_clause,[],[f605,f1303])).
% 1.49/0.57 tff(f1303,plain,(
% 1.49/0.57 spl39_88 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1)),X2 : X1] : (sP2(X1,X0,X4,X5,X2,X3) | X2 = X4 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_88])])).
% 1.49/0.57 tff(f605,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,bool),X4 : X1,X5 : fun(X0,fun(X1,X1))] : (sP2(X1,X0,X4,X5,X2,X3) | X2 = X4 | ~finite_fold_graph(X0,X1,X5,X4,X3,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f415])).
% 1.49/0.57 tff(f1278,plain,(
% 1.49/0.57 spl39_87 | ~spl39_37 | ~spl39_83),
% 1.49/0.57 inference(avatar_split_clause,[],[f1261,f1258,f1004,f1276])).
% 1.49/0.57 tff(f1276,plain,(
% 1.49/0.57 spl39_87 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK13(X0,X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_87])])).
% 1.49/0.57 tff(f1258,plain,(
% 1.49/0.57 spl39_83 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK13(X0,X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_83])])).
% 1.49/0.57 tff(f1261,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK13(X0,X1)))) ) | (~spl39_37 | ~spl39_83)),
% 1.49/0.57 inference(forward_demodulation,[],[f1259,f1005])).
% 1.49/0.57 tff(f1259,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK13(X0,X1)))) ) | ~spl39_83),
% 1.49/0.57 inference(avatar_component_clause,[],[f1258])).
% 1.49/0.57 tff(f1273,plain,(
% 1.49/0.57 spl39_86 | ~spl39_37 | ~spl39_82),
% 1.49/0.57 inference(avatar_split_clause,[],[f1256,f1253,f1004,f1271])).
% 1.49/0.57 tff(f1253,plain,(
% 1.49/0.57 spl39_82 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK12(X0,X1))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_82])])).
% 1.49/0.57 tff(f1256,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | pp(aa(X0,bool,X1,sK12(X0,X1)))) ) | (~spl39_37 | ~spl39_82)),
% 1.49/0.57 inference(forward_demodulation,[],[f1254,f1005])).
% 1.49/0.57 tff(f1254,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK12(X0,X1)))) ) | ~spl39_82),
% 1.49/0.57 inference(avatar_component_clause,[],[f1253])).
% 1.49/0.57 tff(f1269,plain,(
% 1.49/0.57 spl39_85 | ~spl39_37 | ~spl39_79),
% 1.49/0.57 inference(avatar_split_clause,[],[f1240,f1237,f1004,f1267])).
% 1.49/0.57 tff(f1267,plain,(
% 1.49/0.57 spl39_85 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | finite_finite1(X0,sK8(X0,X1)) | ~finite_finite1(X0,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_85])])).
% 1.49/0.57 tff(f1237,plain,(
% 1.49/0.57 spl39_79 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,sK8(X0,X1)) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_79])])).
% 1.49/0.57 tff(f1240,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = X1 | finite_finite1(X0,sK8(X0,X1)) | ~finite_finite1(X0,X1)) ) | (~spl39_37 | ~spl39_79)),
% 1.49/0.57 inference(forward_demodulation,[],[f1238,f1005])).
% 1.49/0.57 tff(f1238,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,sK8(X0,X1)) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) ) | ~spl39_79),
% 1.49/0.57 inference(avatar_component_clause,[],[f1237])).
% 1.49/0.57 tff(f1265,plain,(
% 1.49/0.57 spl39_84 | ~spl39_37 | ~spl39_71),
% 1.49/0.57 inference(avatar_split_clause,[],[f1194,f1191,f1004,f1263])).
% 1.49/0.57 tff(f1263,plain,(
% 1.49/0.57 spl39_84 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),combk(bool,X0,fFalse),X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_84])])).
% 1.49/0.57 tff(f1191,plain,(
% 1.49/0.57 spl39_71 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),bot_bot(fun(X0,bool)),X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_71])])).
% 1.49/0.57 tff(f1194,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),combk(bool,X0,fFalse),X1)) ) | (~spl39_37 | ~spl39_71)),
% 1.49/0.57 inference(forward_demodulation,[],[f1192,f1005])).
% 1.49/0.57 tff(f1192,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),bot_bot(fun(X0,bool)),X1)) ) | ~spl39_71),
% 1.49/0.57 inference(avatar_component_clause,[],[f1191])).
% 1.49/0.57 tff(f1260,plain,(
% 1.49/0.57 spl39_83),
% 1.49/0.57 inference(avatar_split_clause,[],[f731,f1258])).
% 1.49/0.57 tff(f731,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK13(X0,X1)))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f476,f439])).
% 1.49/0.57 tff(f476,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = collect(X0,X1) | pp(aa(X0,bool,X1,sK13(X0,X1)))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f352])).
% 1.49/0.57 tff(f352,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,X1) | pp(aa(X0,bool,X1,sK13(X0,X1)))) & (! [X3 : X0] : ~pp(aa(X0,bool,X1,X3)) | bot_bot(fun(X0,bool)) != collect(X0,X1)))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f350,f351])).
% 1.49/0.57 tff(f351,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X2 : X0] : pp(aa(X0,bool,X1,X2)) => pp(aa(X0,bool,X1,sK13(X0,X1))))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f350,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(rectify,[],[f349])).
% 1.49/0.57 tff(f349,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(nnf_transformation,[],[f172])).
% 1.49/0.57 tff(f172,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = collect(X0,X1) <=> ! [X2 : X0] : ~pp(aa(X0,bool,X1,X2)))),
% 1.49/0.57 inference(rectify,[],[f12])).
% 1.49/0.57 tff(f12,axiom,(
% 1.49/0.57 ! [X1 : $tType,X20 : fun(X1,bool)] : (bot_bot(fun(X1,bool)) = collect(X1,X20) <=> ! [X19 : X1] : ~pp(aa(X1,bool,X20,X19)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Collect__empty__eq)).
% 1.49/0.57 tff(f1255,plain,(
% 1.49/0.57 spl39_82),
% 1.49/0.57 inference(avatar_split_clause,[],[f729,f1253])).
% 1.49/0.57 tff(f729,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = X1 | pp(aa(X0,bool,X1,sK12(X0,X1)))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f474,f439])).
% 1.49/0.57 tff(f474,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = collect(X0,X1) | pp(aa(X0,bool,X1,sK12(X0,X1)))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f348])).
% 1.49/0.57 tff(f348,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : ((bot_bot(fun(X0,bool)) = collect(X0,X1) | pp(aa(X0,bool,X1,sK12(X0,X1)))) & (! [X3 : X0] : ~pp(aa(X0,bool,X1,X3)) | bot_bot(fun(X0,bool)) != collect(X0,X1)))),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f346,f347])).
% 1.49/0.57 tff(f347,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : (? [X2 : X0] : pp(aa(X0,bool,X1,X2)) => pp(aa(X0,bool,X1,sK12(X0,X1))))),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f346,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(rectify,[],[f345])).
% 1.49/0.57 tff(f345,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(nnf_transformation,[],[f171])).
% 1.49/0.57 tff(f171,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = collect(X0,X1) <=> ! [X2 : X0] : ~pp(aa(X0,bool,X1,X2)))),
% 1.49/0.57 inference(rectify,[],[f10])).
% 1.49/0.57 tff(f10,axiom,(
% 1.49/0.57 ! [X1 : $tType,X20 : fun(X1,bool)] : (bot_bot(fun(X1,bool)) = collect(X1,X20) <=> ! [X19 : X1] : ~pp(aa(X1,bool,X20,X19)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_empty__Collect__eq)).
% 1.49/0.57 tff(f1249,plain,(
% 1.49/0.57 spl39_81 | ~spl39_80),
% 1.49/0.57 inference(avatar_split_clause,[],[f1245,f1242,f1247])).
% 1.49/0.57 tff(f1247,plain,(
% 1.49/0.57 spl39_81 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2)) | X1 = X2)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_81])])).
% 1.49/0.57 tff(f1242,plain,(
% 1.49/0.57 spl39_80 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_80])])).
% 1.49/0.57 tff(f1245,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (~pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2)) | X1 = X2) ) | ~spl39_80),
% 1.49/0.57 inference(forward_demodulation,[],[f1243,f595])).
% 1.49/0.57 tff(f1243,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))) ) | ~spl39_80),
% 1.49/0.57 inference(avatar_component_clause,[],[f1242])).
% 1.49/0.57 tff(f1244,plain,(
% 1.49/0.57 spl39_80),
% 1.49/0.57 inference(avatar_split_clause,[],[f494,f1242])).
% 1.49/0.57 tff(f494,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f188])).
% 1.49/0.57 tff(f188,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = X2 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)))),
% 1.49/0.57 inference(rectify,[],[f123])).
% 1.49/0.57 tff(f123,axiom,(
% 1.49/0.57 ! [X0 : $tType,X75 : X0,X76 : X0] : (X75 = X76 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X76),X75)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T)).
% 1.49/0.57 tff(f1239,plain,(
% 1.49/0.57 spl39_79),
% 1.49/0.57 inference(avatar_split_clause,[],[f465,f1237])).
% 1.49/0.57 tff(f465,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,sK8(X0,X1)) | bot_bot(fun(X0,bool)) = X1 | ~finite_finite1(X0,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f339])).
% 1.49/0.57 tff(f1232,plain,(
% 1.49/0.57 spl39_78 | ~spl39_20 | ~spl39_37),
% 1.49/0.57 inference(avatar_split_clause,[],[f1010,f1004,f917,f1230])).
% 1.49/0.57 tff(f1230,plain,(
% 1.49/0.57 spl39_78 <=> ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : hoare_992312373derivs(X0,X1,combk(bool,hoare_28830079triple(X0),fFalse))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_78])])).
% 1.49/0.57 tff(f917,plain,(
% 1.49/0.57 spl39_20 <=> ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : hoare_992312373derivs(X0,X1,bot_bot(fun(hoare_28830079triple(X0),bool)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_20])])).
% 1.49/0.57 tff(f1010,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,combk(bool,hoare_28830079triple(X0),fFalse))) ) | (~spl39_20 | ~spl39_37)),
% 1.49/0.57 inference(superposition,[],[f918,f1005])).
% 1.49/0.57 tff(f918,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,bot_bot(fun(hoare_28830079triple(X0),bool)))) ) | ~spl39_20),
% 1.49/0.57 inference(avatar_component_clause,[],[f917])).
% 1.49/0.57 tff(f1228,plain,(
% 1.49/0.57 spl39_77 | ~spl39_76),
% 1.49/0.57 inference(avatar_split_clause,[],[f1224,f1221,f1226])).
% 1.49/0.57 tff(f1226,plain,(
% 1.49/0.57 spl39_77 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fdisj,X0),X1)) | pp(X0) | pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_77])])).
% 1.49/0.57 tff(f1221,plain,(
% 1.49/0.57 spl39_76 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_76])])).
% 1.49/0.57 tff(f1224,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fdisj,X0),X1)) | pp(X0) | pp(X1)) ) | ~spl39_76),
% 1.49/0.57 inference(forward_demodulation,[],[f1222,f595])).
% 1.49/0.57 tff(f1222,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))) ) | ~spl39_76),
% 1.49/0.57 inference(avatar_component_clause,[],[f1221])).
% 1.49/0.57 tff(f1223,plain,(
% 1.49/0.57 spl39_76),
% 1.49/0.57 inference(avatar_split_clause,[],[f455,f1221])).
% 1.49/0.57 tff(f455,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f159])).
% 1.49/0.57 tff(f159,plain,(
% 1.49/0.57 ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)))),
% 1.49/0.57 inference(rectify,[],[f120])).
% 1.49/0.57 tff(f120,axiom,(
% 1.49/0.57 ! [X74 : bool,X72 : bool] : (pp(X74) | pp(X72) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X72),X74)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U)).
% 1.49/0.57 tff(f1216,plain,(
% 1.49/0.57 spl39_75 | ~spl39_74),
% 1.49/0.57 inference(avatar_split_clause,[],[f1212,f1209,f1214])).
% 1.49/0.57 tff(f1214,plain,(
% 1.49/0.57 spl39_75 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fimplies,X0),X1)) | pp(X0) | ~pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_75])])).
% 1.49/0.57 tff(f1209,plain,(
% 1.49/0.57 spl39_74 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_74])])).
% 1.49/0.57 tff(f1212,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fimplies,X0),X1)) | pp(X0) | ~pp(X1)) ) | ~spl39_74),
% 1.49/0.57 inference(forward_demodulation,[],[f1210,f595])).
% 1.49/0.57 tff(f1210,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))) ) | ~spl39_74),
% 1.49/0.57 inference(avatar_component_clause,[],[f1209])).
% 1.49/0.57 tff(f1211,plain,(
% 1.49/0.57 spl39_74),
% 1.49/0.57 inference(avatar_split_clause,[],[f452,f1209])).
% 1.49/0.57 tff(f452,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f156])).
% 1.49/0.57 tff(f156,plain,(
% 1.49/0.57 ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)))),
% 1.49/0.57 inference(rectify,[],[f127])).
% 1.49/0.57 tff(f127,axiom,(
% 1.49/0.57 ! [X74 : bool,X72 : bool] : (pp(X74) | ~pp(X72) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X72),X74)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U)).
% 1.49/0.57 tff(f1203,plain,(
% 1.49/0.57 spl39_73 | ~spl39_72),
% 1.49/0.57 inference(avatar_split_clause,[],[f1199,f1196,f1201])).
% 1.49/0.57 tff(f1201,plain,(
% 1.49/0.57 spl39_73 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_73])])).
% 1.49/0.57 tff(f1196,plain,(
% 1.49/0.57 spl39_72 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_72])])).
% 1.49/0.57 tff(f1199,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1)) ) | ~spl39_72),
% 1.49/0.57 inference(forward_demodulation,[],[f1197,f595])).
% 1.49/0.57 tff(f1197,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) ) | ~spl39_72),
% 1.49/0.57 inference(avatar_component_clause,[],[f1196])).
% 1.49/0.57 tff(f1198,plain,(
% 1.49/0.57 spl39_72),
% 1.49/0.57 inference(avatar_split_clause,[],[f447,f1196])).
% 1.49/0.57 tff(f447,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f151])).
% 1.49/0.57 tff(f151,plain,(
% 1.49/0.57 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 1.49/0.57 inference(rectify,[],[f115])).
% 1.49/0.57 tff(f115,axiom,(
% 1.49/0.57 ! [X74 : bool,X72 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X72),X74)) | ~pp(X74) | ~pp(X72))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U)).
% 1.49/0.57 tff(f1193,plain,(
% 1.49/0.57 spl39_71),
% 1.49/0.57 inference(avatar_split_clause,[],[f444,f1191])).
% 1.49/0.57 tff(f444,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),bot_bot(fun(X0,bool)),X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f148])).
% 1.49/0.57 tff(f148,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),bot_bot(fun(X0,bool)),X1)),
% 1.49/0.57 inference(rectify,[],[f62])).
% 1.49/0.57 tff(f62,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool)] : bot_bot(fun(X1,bool)) = minus_minus(fun(X1,bool),bot_bot(fun(X1,bool)),X14)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_empty__Diff)).
% 1.49/0.57 tff(f1186,plain,(
% 1.49/0.57 spl39_70 | ~spl39_22 | ~spl39_37),
% 1.49/0.57 inference(avatar_split_clause,[],[f1008,f1004,f925,f1184])).
% 1.49/0.57 tff(f1184,plain,(
% 1.49/0.57 spl39_70 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : ~finite_fold1Set(X0,X1,combk(bool,X0,fFalse),X2)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_70])])).
% 1.49/0.57 tff(f925,plain,(
% 1.49/0.57 spl39_22 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : ~finite_fold1Set(X0,X2,bot_bot(fun(X0,bool)),X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_22])])).
% 1.49/0.57 tff(f1008,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(X0,X0))] : (~finite_fold1Set(X0,X1,combk(bool,X0,fFalse),X2)) ) | (~spl39_22 | ~spl39_37)),
% 1.49/0.57 inference(superposition,[],[f926,f1005])).
% 1.49/0.57 tff(f926,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (~finite_fold1Set(X0,X2,bot_bot(fun(X0,bool)),X1)) ) | ~spl39_22),
% 1.49/0.57 inference(avatar_component_clause,[],[f925])).
% 1.49/0.57 tff(f1182,plain,(
% 1.49/0.57 spl39_69),
% 1.49/0.57 inference(avatar_split_clause,[],[f611,f1180])).
% 1.49/0.57 tff(f1180,plain,(
% 1.49/0.57 spl39_69 <=> ! [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))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_69])])).
% 1.49/0.57 tff(f611,plain,(
% 1.49/0.57 ( ! [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)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f417])).
% 1.49/0.57 tff(f1175,plain,(
% 1.49/0.57 spl39_68 | ~spl39_37 | ~spl39_67),
% 1.49/0.57 inference(avatar_split_clause,[],[f1167,f1164,f1004,f1173])).
% 1.49/0.57 tff(f1173,plain,(
% 1.49/0.57 spl39_68 <=> ! [X0 : $tType,X1 : fun(X0,bool),X3 : X0] : (combk(bool,X0,fFalse) != X1 | ~pp(aa(X0,bool,X1,X3)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_68])])).
% 1.49/0.57 tff(f1164,plain,(
% 1.49/0.57 spl39_67 <=> ! [X0 : $tType,X1 : fun(X0,bool),X3 : X0] : (bot_bot(fun(X0,bool)) != X1 | ~pp(aa(X0,bool,X1,X3)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_67])])).
% 1.49/0.57 tff(f1167,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X3 : X0,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) != X1 | ~pp(aa(X0,bool,X1,X3))) ) | (~spl39_37 | ~spl39_67)),
% 1.49/0.57 inference(forward_demodulation,[],[f1165,f1005])).
% 1.49/0.57 tff(f1165,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X3 : X0,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != X1 | ~pp(aa(X0,bool,X1,X3))) ) | ~spl39_67),
% 1.49/0.57 inference(avatar_component_clause,[],[f1164])).
% 1.49/0.57 tff(f1166,plain,(
% 1.49/0.57 spl39_67),
% 1.49/0.57 inference(avatar_split_clause,[],[f730,f1164])).
% 1.49/0.57 tff(f730,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X3 : X0,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) != X1 | ~pp(aa(X0,bool,X1,X3))) )),
% 1.49/0.57 inference(forward_demodulation,[],[f473,f439])).
% 1.49/0.57 tff(f473,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X3 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X3)) | bot_bot(fun(X0,bool)) != collect(X0,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f348])).
% 1.49/0.57 tff(f1162,plain,(
% 1.49/0.57 spl39_66),
% 1.49/0.57 inference(avatar_split_clause,[],[f607,f1160])).
% 1.49/0.57 tff(f1160,plain,(
% 1.49/0.57 spl39_66 <=> ! [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) | ~sP2(X1,X0,X4,X5,X2,X3))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_66])])).
% 1.49/0.57 tff(f607,plain,(
% 1.49/0.57 ( ! [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) | ~sP2(X1,X0,X4,X5,X2,X3)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f415])).
% 1.49/0.57 tff(f1158,plain,(
% 1.49/0.57 spl39_65),
% 1.49/0.57 inference(avatar_split_clause,[],[f506,f1156])).
% 1.49/0.57 tff(f1156,plain,(
% 1.49/0.57 spl39_65 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X1,X2)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_65])])).
% 1.49/0.57 tff(f506,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X1,X2)) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f369])).
% 1.49/0.57 tff(f369,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (((finite_finite1(X0,minus_minus(fun(X0,bool),X1,X2)) | ~finite_finite1(X0,X1)) & (finite_finite1(X0,X1) | ~finite_finite1(X0,minus_minus(fun(X0,bool),X1,X2)))) | ~finite_finite1(X0,X2))),
% 1.49/0.57 inference(nnf_transformation,[],[f282])).
% 1.49/0.57 tff(f282,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : ((finite_finite1(X0,minus_minus(fun(X0,bool),X1,X2)) <=> finite_finite1(X0,X1)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 inference(ennf_transformation,[],[f194])).
% 1.49/0.57 tff(f194,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (finite_finite1(X0,X2) => (finite_finite1(X0,minus_minus(fun(X0,bool),X1,X2)) <=> finite_finite1(X0,X1)))),
% 1.49/0.57 inference(rectify,[],[f92])).
% 1.49/0.57 tff(f92,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool),X18 : fun(X1,bool)] : (finite_finite1(X1,X18) => (finite_finite1(X1,minus_minus(fun(X1,bool),X14,X18)) <=> finite_finite1(X1,X14)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_finite__Diff2)).
% 1.49/0.57 tff(f1154,plain,(
% 1.49/0.57 spl39_64),
% 1.49/0.57 inference(avatar_split_clause,[],[f481,f1152])).
% 1.49/0.57 tff(f1152,plain,(
% 1.49/0.57 spl39_64 <=> ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : hoare_1841697145triple(X0,sK16(X0,X1),sK17(X0,X1),sK18(X0,X1)) = X1),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_64])])).
% 1.49/0.57 tff(f481,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : (hoare_1841697145triple(X0,sK16(X0,X1),sK17(X0,X1),sK18(X0,X1)) = X1) )),
% 1.49/0.57 inference(cnf_transformation,[],[f362])).
% 1.49/0.57 tff(f362,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : hoare_28830079triple(X0)] : hoare_1841697145triple(X0,sK16(X0,X1),sK17(X0,X1),sK18(X0,X1)) = X1),
% 1.49/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f273,f361])).
% 1.49/0.57 tff(f361,plain,(
% 1.49/0.57 ! [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,sK16(X0,X1),sK17(X0,X1),sK18(X0,X1)) = X1)),
% 1.49/0.57 introduced(choice_axiom,[])).
% 1.49/0.57 tff(f273,plain,(
% 1.49/0.57 ! [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),
% 1.49/0.57 inference(ennf_transformation,[],[f175])).
% 1.49/0.57 tff(f175,plain,(
% 1.49/0.57 ! [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),
% 1.49/0.57 inference(rectify,[],[f39])).
% 1.49/0.57 tff(f39,axiom,(
% 1.49/0.57 ! [X1 : $tType,X24 : hoare_28830079triple(X1)] : ~! [X29 : fun(X1,fun(state,bool)),X30 : com,X31 : fun(X1,fun(state,bool))] : hoare_1841697145triple(X1,X29,X30,X31) != X24),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_triple_Oexhaust)).
% 1.49/0.57 tff(f1148,plain,(
% 1.49/0.57 spl39_63 | ~spl39_62),
% 1.49/0.57 inference(avatar_split_clause,[],[f1144,f1141,f1146])).
% 1.49/0.57 tff(f1146,plain,(
% 1.49/0.57 spl39_63 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_63])])).
% 1.49/0.57 tff(f1141,plain,(
% 1.49/0.57 spl39_62 <=> ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_62])])).
% 1.49/0.57 tff(f1144,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X1)) ) | ~spl39_62),
% 1.49/0.57 inference(forward_demodulation,[],[f1142,f595])).
% 1.49/0.57 tff(f1142,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) ) | ~spl39_62),
% 1.49/0.57 inference(avatar_component_clause,[],[f1141])).
% 1.49/0.57 tff(f1143,plain,(
% 1.49/0.57 spl39_62),
% 1.49/0.57 inference(avatar_split_clause,[],[f454,f1141])).
% 1.49/0.57 tff(f454,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f158])).
% 1.49/0.57 tff(f158,plain,(
% 1.49/0.57 ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.49/0.57 inference(rectify,[],[f116])).
% 1.49/0.57 tff(f116,axiom,(
% 1.49/0.57 ! [X74 : bool,X72 : bool] : (pp(X72) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X72),X74)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U)).
% 1.49/0.57 tff(f1138,plain,(
% 1.49/0.57 spl39_61 | ~spl39_60),
% 1.49/0.57 inference(avatar_split_clause,[],[f1134,f1131,f1136])).
% 1.49/0.57 tff(f1136,plain,(
% 1.49/0.57 spl39_61 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_61])])).
% 1.49/0.57 tff(f1131,plain,(
% 1.49/0.57 spl39_60 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_60])])).
% 1.49/0.57 tff(f1134,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0)) ) | ~spl39_60),
% 1.49/0.57 inference(forward_demodulation,[],[f1132,f595])).
% 1.49/0.57 tff(f1132,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) ) | ~spl39_60),
% 1.49/0.57 inference(avatar_component_clause,[],[f1131])).
% 1.49/0.57 tff(f1133,plain,(
% 1.49/0.57 spl39_60),
% 1.49/0.57 inference(avatar_split_clause,[],[f453,f1131])).
% 1.49/0.57 tff(f453,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f157])).
% 1.49/0.57 tff(f157,plain,(
% 1.49/0.57 ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.49/0.57 inference(rectify,[],[f117])).
% 1.49/0.57 tff(f117,axiom,(
% 1.49/0.57 ! [X74 : bool,X72 : bool] : (pp(X74) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X72),X74)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U)).
% 1.49/0.57 tff(f1127,plain,(
% 1.49/0.57 spl39_59 | ~spl39_58),
% 1.49/0.57 inference(avatar_split_clause,[],[f1123,f1120,f1125])).
% 1.49/0.57 tff(f1125,plain,(
% 1.49/0.57 spl39_59 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fimplies,X0),X1)) | pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_59])])).
% 1.49/0.57 tff(f1120,plain,(
% 1.49/0.57 spl39_58 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) | pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_58])])).
% 1.49/0.57 tff(f1123,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fimplies,X0),X1)) | pp(X1)) ) | ~spl39_58),
% 1.49/0.57 inference(forward_demodulation,[],[f1121,f595])).
% 1.49/0.57 tff(f1121,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) | pp(X1)) ) | ~spl39_58),
% 1.49/0.57 inference(avatar_component_clause,[],[f1120])).
% 1.49/0.57 tff(f1122,plain,(
% 1.49/0.57 spl39_58),
% 1.49/0.57 inference(avatar_split_clause,[],[f451,f1120])).
% 1.49/0.57 tff(f451,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) | pp(X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f155])).
% 1.49/0.57 tff(f155,plain,(
% 1.49/0.57 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) | pp(X1))),
% 1.49/0.57 inference(rectify,[],[f125])).
% 1.49/0.57 tff(f125,axiom,(
% 1.49/0.57 ! [X74 : bool,X72 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X72),X74)) | pp(X72))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U)).
% 1.49/0.57 tff(f1116,plain,(
% 1.49/0.57 spl39_57 | ~spl39_56),
% 1.49/0.57 inference(avatar_split_clause,[],[f1112,f1109,f1114])).
% 1.49/0.57 tff(f1114,plain,(
% 1.49/0.57 spl39_57 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fimplies,X1),X0)) | ~pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_57])])).
% 1.49/0.57 tff(f1109,plain,(
% 1.49/0.57 spl39_56 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_56])])).
% 1.49/0.57 tff(f1112,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fimplies,X1),X0)) | ~pp(X1)) ) | ~spl39_56),
% 1.49/0.57 inference(forward_demodulation,[],[f1110,f595])).
% 1.49/0.57 tff(f1110,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X1)) ) | ~spl39_56),
% 1.49/0.57 inference(avatar_component_clause,[],[f1109])).
% 1.49/0.57 tff(f1111,plain,(
% 1.49/0.57 spl39_56),
% 1.49/0.57 inference(avatar_split_clause,[],[f450,f1109])).
% 1.49/0.57 tff(f450,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f154])).
% 1.49/0.57 tff(f154,plain,(
% 1.49/0.57 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1)) | ~pp(X1))),
% 1.49/0.57 inference(rectify,[],[f126])).
% 1.49/0.57 tff(f126,axiom,(
% 1.49/0.57 ! [X72 : bool,X74 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X72),X74)) | ~pp(X74))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U)).
% 1.49/0.57 tff(f1105,plain,(
% 1.49/0.57 spl39_55 | ~spl39_54),
% 1.49/0.57 inference(avatar_split_clause,[],[f1101,f1098,f1103])).
% 1.49/0.57 tff(f1103,plain,(
% 1.49/0.57 spl39_55 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fdisj,X1),X0)) | ~pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_55])])).
% 1.49/0.57 tff(f1098,plain,(
% 1.49/0.57 spl39_54 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_54])])).
% 1.49/0.57 tff(f1101,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fdisj,X1),X0)) | ~pp(X1)) ) | ~spl39_54),
% 1.49/0.57 inference(forward_demodulation,[],[f1099,f595])).
% 1.49/0.57 tff(f1099,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1)) ) | ~spl39_54),
% 1.49/0.57 inference(avatar_component_clause,[],[f1098])).
% 1.49/0.57 tff(f1100,plain,(
% 1.49/0.57 spl39_54),
% 1.49/0.57 inference(avatar_split_clause,[],[f449,f1098])).
% 1.49/0.57 tff(f449,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f153])).
% 1.49/0.57 tff(f153,plain,(
% 1.49/0.57 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1))),
% 1.49/0.57 inference(rectify,[],[f119])).
% 1.49/0.57 tff(f119,axiom,(
% 1.49/0.57 ! [X72 : bool,X74 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X72),X74)) | ~pp(X74))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U)).
% 1.49/0.57 tff(f1094,plain,(
% 1.49/0.57 spl39_53 | ~spl39_52),
% 1.49/0.57 inference(avatar_split_clause,[],[f1090,f1087,f1092])).
% 1.49/0.57 tff(f1092,plain,(
% 1.49/0.57 spl39_53 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fdisj,X0),X1)) | ~pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_53])])).
% 1.49/0.57 tff(f1087,plain,(
% 1.49/0.57 spl39_52 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_52])])).
% 1.49/0.57 tff(f1090,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fdisj,X0),X1)) | ~pp(X1)) ) | ~spl39_52),
% 1.49/0.57 inference(forward_demodulation,[],[f1088,f595])).
% 1.49/0.57 tff(f1088,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1)) ) | ~spl39_52),
% 1.49/0.57 inference(avatar_component_clause,[],[f1087])).
% 1.49/0.57 tff(f1089,plain,(
% 1.49/0.57 spl39_52),
% 1.49/0.57 inference(avatar_split_clause,[],[f448,f1087])).
% 1.49/0.57 tff(f448,plain,(
% 1.49/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f152])).
% 1.49/0.57 tff(f152,plain,(
% 1.49/0.57 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1))),
% 1.49/0.57 inference(rectify,[],[f118])).
% 1.49/0.57 tff(f118,axiom,(
% 1.49/0.57 ! [X74 : bool,X72 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X72),X74)) | ~pp(X72))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U)).
% 1.49/0.57 tff(f1084,plain,(
% 1.49/0.57 spl39_51 | ~spl39_37 | ~spl39_49),
% 1.49/0.57 inference(avatar_split_clause,[],[f1075,f1071,f1004,f1082])).
% 1.49/0.57 tff(f1071,plain,(
% 1.49/0.57 spl39_49 <=> ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (~q(sK3,sK5(X2,X3)) | ~hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool)))))))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_49])])).
% 1.49/0.57 tff(f1075,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (~hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)))),combk(bool,hoare_28830079triple(a),fFalse))) | ~q(sK3,sK5(X2,X3))) ) | (~spl39_37 | ~spl39_49)),
% 1.49/0.57 inference(forward_demodulation,[],[f1074,f1005])).
% 1.49/0.57 tff(f1074,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (~hoare_992312373derivs(a,g,combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fimplies,combb(bool,bool,hoare_28830079triple(a),fNot,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)))),bot_bot(fun(hoare_28830079triple(a),bool)))) | ~q(sK3,sK5(X2,X3))) ) | ~spl39_49),
% 1.49/0.57 inference(forward_demodulation,[],[f1072,f739])).
% 1.49/0.57 tff(f1072,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (~q(sK3,sK5(X2,X3)) | ~hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))))))) ) | ~spl39_49),
% 1.49/0.57 inference(avatar_component_clause,[],[f1071])).
% 1.49/0.57 tff(f1080,plain,(
% 1.49/0.57 spl39_50 | ~spl39_3 | ~spl39_23 | ~spl39_37 | ~spl39_40),
% 1.49/0.57 inference(avatar_split_clause,[],[f1060,f1022,f1004,f932,f842,f1077])).
% 1.49/0.57 tff(f1077,plain,(
% 1.49/0.57 spl39_50 <=> fFalse = bot_bot(bool)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_50])])).
% 1.49/0.57 tff(f842,plain,(
% 1.49/0.57 spl39_3 <=> bot(bool)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_3])])).
% 1.49/0.57 tff(f932,plain,(
% 1.49/0.57 spl39_23 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : X0] : aa(X0,X1,combk(X1,X0,X3),X2) = X3),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_23])])).
% 1.49/0.57 tff(f1022,plain,(
% 1.49/0.57 spl39_40 <=> ! [X1 : $tType,X0 : $tType,X2 : X0] : (bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) | ~bot(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_40])])).
% 1.49/0.57 tff(f1060,plain,(
% 1.49/0.57 fFalse = bot_bot(bool) | (~spl39_3 | ~spl39_23 | ~spl39_37 | ~spl39_40)),
% 1.49/0.57 inference(forward_demodulation,[],[f1059,f933])).
% 1.49/0.57 tff(f933,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (aa(X0,X1,combk(X1,X0,X3),X2) = X3) ) | ~spl39_23),
% 1.49/0.57 inference(avatar_component_clause,[],[f932])).
% 1.49/0.57 tff(f1059,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (bot_bot(bool) = aa(X0,bool,combk(bool,X0,fFalse),X1)) ) | (~spl39_3 | ~spl39_37 | ~spl39_40)),
% 1.49/0.57 inference(forward_demodulation,[],[f1057,f1005])).
% 1.49/0.57 tff(f1057,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : X0] : (aa(X0,bool,bot_bot(fun(X0,bool)),X1) = bot_bot(bool)) ) | (~spl39_3 | ~spl39_40)),
% 1.49/0.57 inference(resolution,[],[f1023,f844])).
% 1.49/0.57 tff(f844,plain,(
% 1.49/0.57 bot(bool) | ~spl39_3),
% 1.49/0.57 inference(avatar_component_clause,[],[f842])).
% 1.49/0.57 tff(f1023,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : X0] : (~bot(X1) | bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2)) ) | ~spl39_40),
% 1.49/0.57 inference(avatar_component_clause,[],[f1022])).
% 1.49/0.57 tff(f1073,plain,(
% 1.49/0.57 spl39_49),
% 1.49/0.57 inference(avatar_split_clause,[],[f616,f1071])).
% 1.49/0.57 tff(f616,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (~q(sK3,sK5(X2,X3)) | ~hoare_992312373derivs(a,g,collect(hoare_28830079triple(a),combs(hoare_28830079triple(a),bool,bool,combb(bool,fun(bool,bool),hoare_28830079triple(a),fdisj,combc(hoare_28830079triple(a),hoare_28830079triple(a),bool,fequal(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3))),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))))))) )),
% 1.49/0.57 inference(definition_unfolding,[],[f420,f491])).
% 1.49/0.57 tff(f420,plain,(
% 1.49/0.57 ( ! [X2 : fun(a,fun(state,bool)),X3 : fun(a,fun(state,bool))] : (~q(sK3,sK5(X2,X3)) | ~hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f330])).
% 1.49/0.57 tff(f1064,plain,(
% 1.49/0.57 spl39_48 | ~spl39_37 | ~spl39_41),
% 1.49/0.57 inference(avatar_split_clause,[],[f1029,f1026,f1004,f1062])).
% 1.49/0.57 tff(f1062,plain,(
% 1.49/0.57 spl39_48 <=> ! [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)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_48])])).
% 1.49/0.57 tff(f1026,plain,(
% 1.49/0.57 spl39_41 <=> ! [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))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_41])])).
% 1.49/0.57 tff(f1029,plain,(
% 1.49/0.57 ( ! [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) ) | (~spl39_37 | ~spl39_41)),
% 1.49/0.57 inference(forward_demodulation,[],[f1027,f1005])).
% 1.49/0.57 tff(f1027,plain,(
% 1.49/0.57 ( ! [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)) ) | ~spl39_41),
% 1.49/0.57 inference(avatar_component_clause,[],[f1026])).
% 1.49/0.57 tff(f1056,plain,(
% 1.49/0.57 spl39_47 | ~spl39_37 | ~spl39_39),
% 1.49/0.57 inference(avatar_split_clause,[],[f1020,f1017,f1004,f1054])).
% 1.49/0.57 tff(f1054,plain,(
% 1.49/0.57 spl39_47 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : minus_minus(fun(X0,bool),X1,combk(bool,X0,fFalse)) = X1),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_47])])).
% 1.49/0.57 tff(f1017,plain,(
% 1.49/0.57 spl39_39 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : minus_minus(fun(X0,bool),X1,bot_bot(fun(X0,bool))) = X1),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_39])])).
% 1.49/0.57 tff(f1020,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,combk(bool,X0,fFalse)) = X1) ) | (~spl39_37 | ~spl39_39)),
% 1.49/0.57 inference(forward_demodulation,[],[f1018,f1005])).
% 1.49/0.57 tff(f1018,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,bot_bot(fun(X0,bool))) = X1) ) | ~spl39_39),
% 1.49/0.57 inference(avatar_component_clause,[],[f1017])).
% 1.49/0.57 tff(f1052,plain,(
% 1.49/0.57 spl39_46 | ~spl39_37 | ~spl39_38),
% 1.49/0.57 inference(avatar_split_clause,[],[f1015,f1012,f1004,f1050])).
% 1.49/0.57 tff(f1050,plain,(
% 1.49/0.57 spl39_46 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),X1,X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_46])])).
% 1.49/0.57 tff(f1012,plain,(
% 1.49/0.57 spl39_38 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,X1)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_38])])).
% 1.49/0.57 tff(f1015,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),X1,X1)) ) | (~spl39_37 | ~spl39_38)),
% 1.49/0.57 inference(forward_demodulation,[],[f1013,f1005])).
% 1.49/0.57 tff(f1013,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,X1)) ) | ~spl39_38),
% 1.49/0.57 inference(avatar_component_clause,[],[f1012])).
% 1.49/0.57 tff(f1046,plain,(
% 1.49/0.57 spl39_45 | ~spl39_9 | ~spl39_37),
% 1.49/0.57 inference(avatar_split_clause,[],[f1009,f1004,f870,f1044])).
% 1.49/0.57 tff(f870,plain,(
% 1.49/0.57 spl39_9 <=> ! [X0 : $tType] : finite_finite1(X0,bot_bot(fun(X0,bool)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_9])])).
% 1.49/0.57 tff(f1009,plain,(
% 1.49/0.57 ( ! [X0 : $tType] : (finite_finite1(X0,combk(bool,X0,fFalse))) ) | (~spl39_9 | ~spl39_37)),
% 1.49/0.57 inference(superposition,[],[f871,f1005])).
% 1.49/0.57 tff(f871,plain,(
% 1.49/0.57 ( ! [X0 : $tType] : (finite_finite1(X0,bot_bot(fun(X0,bool)))) ) | ~spl39_9),
% 1.49/0.57 inference(avatar_component_clause,[],[f870])).
% 1.49/0.57 tff(f1042,plain,(
% 1.49/0.57 spl39_44 | ~spl39_43),
% 1.49/0.57 inference(avatar_split_clause,[],[f1038,f1035,f1040])).
% 1.49/0.57 tff(f1040,plain,(
% 1.49/0.57 spl39_44 <=> ! [X0 : $tType,X2 : X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_44])])).
% 1.49/0.57 tff(f1035,plain,(
% 1.49/0.57 spl39_43 <=> ! [X0 : $tType,X2 : X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_43])])).
% 1.49/0.57 tff(f1038,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0] : (pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))) ) | ~spl39_43),
% 1.49/0.57 inference(forward_demodulation,[],[f1036,f595])).
% 1.49/0.57 tff(f1036,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))) ) | ~spl39_43),
% 1.49/0.57 inference(avatar_component_clause,[],[f1035])).
% 1.49/0.57 tff(f1037,plain,(
% 1.49/0.57 spl39_43),
% 1.49/0.57 inference(avatar_split_clause,[],[f695,f1035])).
% 1.49/0.57 tff(f695,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))) )),
% 1.49/0.57 inference(equality_resolution,[],[f493])).
% 1.49/0.57 tff(f493,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) | X1 != X2) )),
% 1.49/0.57 inference(cnf_transformation,[],[f187])).
% 1.49/0.57 tff(f187,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) | X1 != X2)),
% 1.49/0.57 inference(rectify,[],[f124])).
% 1.49/0.57 tff(f124,axiom,(
% 1.49/0.57 ! [X0 : $tType,X75 : X0,X76 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X76),X75)) | X75 != X76)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T)).
% 1.49/0.57 tff(f1033,plain,(
% 1.49/0.57 spl39_42),
% 1.49/0.57 inference(avatar_split_clause,[],[f614,f1031])).
% 1.49/0.57 tff(f1031,plain,(
% 1.49/0.57 spl39_42 <=> ! [X0 : $tType,X5 : fun(com,fun(com,X0)),X6 : fun(loc,fun(fun(state,nat),fun(com,X0))),X4 : fun(fun(state,bool),fun(com,fun(com,X0))),X7 : fun(vname,fun(fun(state,nat),X0)),X8 : X0,X3 : fun(fun(state,bool),fun(com,X0)),X2 : fun(pname,X0),X1 : fun(vname,fun(pname,fun(fun(state,nat),X0)))] : com_case(X0,X8,X7,X6,X5,X4,X3,X2,X1,skip) = X8),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_42])])).
% 1.49/0.57 tff(f614,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(pname,X0),X3 : fun(fun(state,bool),fun(com,X0)),X1 : fun(vname,fun(pname,fun(fun(state,nat),X0))),X8 : X0,X6 : fun(loc,fun(fun(state,nat),fun(com,X0))),X7 : fun(vname,fun(fun(state,nat),X0)),X4 : fun(fun(state,bool),fun(com,fun(com,X0))),X5 : fun(com,fun(com,X0))] : (com_case(X0,X8,X7,X6,X5,X4,X3,X2,X1,skip) = X8) )),
% 1.49/0.57 inference(cnf_transformation,[],[f253])).
% 1.49/0.57 tff(f253,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(vname,fun(pname,fun(fun(state,nat),X0))),X2 : fun(pname,X0),X3 : fun(fun(state,bool),fun(com,X0)),X4 : fun(fun(state,bool),fun(com,fun(com,X0))),X5 : fun(com,fun(com,X0)),X6 : fun(loc,fun(fun(state,nat),fun(com,X0))),X7 : fun(vname,fun(fun(state,nat),X0)),X8 : X0] : com_case(X0,X8,X7,X6,X5,X4,X3,X2,X1,skip) = X8),
% 1.49/0.57 inference(rectify,[],[f50])).
% 1.49/0.57 tff(f50,axiom,(
% 1.49/0.57 ! [X1 : $tType,X48 : fun(vname,fun(pname,fun(fun(state,nat),X1))),X49 : fun(pname,X1),X50 : fun(fun(state,bool),fun(com,X1)),X51 : fun(fun(state,bool),fun(com,fun(com,X1))),X52 : fun(com,fun(com,X1)),X53 : fun(loc,fun(fun(state,nat),fun(com,X1))),X54 : fun(vname,fun(fun(state,nat),X1)),X22 : X1] : com_case(X1,X22,X54,X53,X52,X51,X50,X49,X48,skip) = X22),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_com_Osimps_I64_J)).
% 1.49/0.57 tff(f1028,plain,(
% 1.49/0.57 spl39_41),
% 1.49/0.57 inference(avatar_split_clause,[],[f572,f1026])).
% 1.49/0.57 tff(f572,plain,(
% 1.49/0.57 ( ! [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)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f314])).
% 1.49/0.57 tff(f314,plain,(
% 1.49/0.57 ! [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))),
% 1.49/0.57 inference(ennf_transformation,[],[f239])).
% 1.49/0.57 tff(f239,plain,(
% 1.49/0.57 ! [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)),
% 1.49/0.57 inference(rectify,[],[f71])).
% 1.49/0.57 tff(f71,axiom,(
% 1.49/0.57 ! [X1 : $tType,X2 : $tType,X15 : X2,X57 : X2,X47 : fun(X1,fun(X2,X2))] : (finite_fold_graph(X1,X2,X47,X57,bot_bot(fun(X1,bool)),X15) => X15 = X57)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_empty__fold__graphE)).
% 1.49/0.57 tff(f1024,plain,(
% 1.49/0.57 spl39_40),
% 1.49/0.57 inference(avatar_split_clause,[],[f458,f1022])).
% 1.49/0.57 tff(f458,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : X0] : (bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) | ~bot(X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f266])).
% 1.49/0.57 tff(f266,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0] : bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) | ~bot(X1))),
% 1.49/0.57 inference(ennf_transformation,[],[f162])).
% 1.49/0.57 tff(f162,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (bot(X1) => ! [X2 : X0] : bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2))),
% 1.49/0.57 inference(rectify,[],[f36])).
% 1.49/0.57 tff(f36,axiom,(
% 1.49/0.57 ! [X1 : $tType,X2 : $tType] : (bot(X2) => ! [X26 : X1] : aa(X1,X2,bot_bot(fun(X1,X2)),X26) = bot_bot(X2))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_bot__fun__def)).
% 1.49/0.57 tff(f1019,plain,(
% 1.49/0.57 spl39_39),
% 1.49/0.57 inference(avatar_split_clause,[],[f443,f1017])).
% 1.49/0.57 tff(f443,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (minus_minus(fun(X0,bool),X1,bot_bot(fun(X0,bool))) = X1) )),
% 1.49/0.57 inference(cnf_transformation,[],[f147])).
% 1.49/0.57 tff(f147,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : minus_minus(fun(X0,bool),X1,bot_bot(fun(X0,bool))) = X1),
% 1.49/0.57 inference(rectify,[],[f64])).
% 1.49/0.57 tff(f64,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool)] : minus_minus(fun(X1,bool),X14,bot_bot(fun(X1,bool))) = X14),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Diff__empty)).
% 1.49/0.57 tff(f1014,plain,(
% 1.49/0.57 spl39_38),
% 1.49/0.57 inference(avatar_split_clause,[],[f442,f1012])).
% 1.49/0.57 tff(f442,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f146])).
% 1.49/0.57 tff(f146,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool)] : bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,X1)),
% 1.49/0.57 inference(rectify,[],[f63])).
% 1.49/0.57 tff(f63,axiom,(
% 1.49/0.57 ! [X1 : $tType,X14 : fun(X1,bool)] : bot_bot(fun(X1,bool)) = minus_minus(fun(X1,bool),X14,X14)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Diff__cancel)).
% 1.49/0.57 tff(f1006,plain,(
% 1.49/0.57 spl39_37 | ~spl39_16 | ~spl39_36),
% 1.49/0.57 inference(avatar_split_clause,[],[f1002,f999,f901,f1004])).
% 1.49/0.57 tff(f999,plain,(
% 1.49/0.57 spl39_36 <=> ! [X0 : $tType] : bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_36])])).
% 1.49/0.57 tff(f1002,plain,(
% 1.49/0.57 ( ! [X0 : $tType] : (bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse)) ) | (~spl39_16 | ~spl39_36)),
% 1.49/0.57 inference(forward_demodulation,[],[f1000,f902])).
% 1.49/0.57 tff(f1000,plain,(
% 1.49/0.57 ( ! [X0 : $tType] : (bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse))) ) | ~spl39_36),
% 1.49/0.57 inference(avatar_component_clause,[],[f999])).
% 1.49/0.57 tff(f1001,plain,(
% 1.49/0.57 spl39_36),
% 1.49/0.57 inference(avatar_split_clause,[],[f431,f999])).
% 1.49/0.57 tff(f431,plain,(
% 1.49/0.57 ( ! [X0 : $tType] : (bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f135])).
% 1.49/0.57 tff(f135,plain,(
% 1.49/0.57 ! [X0 : $tType] : bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse))),
% 1.49/0.57 inference(rectify,[],[f19])).
% 1.49/0.57 tff(f19,axiom,(
% 1.49/0.57 ! [X1 : $tType] : bot_bot(fun(X1,bool)) = collect(X1,combk(bool,X1,fFalse))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_empty__def)).
% 1.49/0.57 tff(f987,plain,(
% 1.49/0.57 spl39_35),
% 1.49/0.57 inference(avatar_split_clause,[],[f589,f985])).
% 1.49/0.57 tff(f985,plain,(
% 1.49/0.57 spl39_35 <=> ! [X2 : $tType,X4 : X2,X0 : X2,X3 : X2,X1 : X2] : (X0 = X1 | X0 = X4 | ~sP1(X2,X0,X1,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_35])])).
% 1.49/0.57 tff(f589,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (X0 = X1 | X0 = X4 | ~sP1(X2,X0,X1,X3,X4)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f408])).
% 1.49/0.57 tff(f408,plain,(
% 1.49/0.57 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2,X4 : X2] : ((sP1(X2,X0,X1,X3,X4) | ((X0 != X1 | X3 != X4) & (X0 != X4 | X1 != X3))) & ((X0 = X1 & X3 = X4) | (X0 = X4 & X1 = X3) | ~sP1(X2,X0,X1,X3,X4)))),
% 1.49/0.57 inference(rectify,[],[f407])).
% 1.49/0.57 tff(f407,plain,(
% 1.49/0.57 ! [X3 : X0,X2 : X0,X0 : $tType,X4 : X0,X1 : X0] : ((sP1(X0,X3,X2,X4,X1) | ((X2 != X3 | X1 != X4) & (X1 != X3 | X2 != X4))) & ((X2 = X3 & X1 = X4) | (X1 = X3 & X2 = X4) | ~sP1(X0,X3,X2,X4,X1)))),
% 1.49/0.57 inference(flattening,[],[f406])).
% 1.49/0.57 tff(f406,plain,(
% 1.49/0.57 ! [X3 : X0,X2 : X0,X0 : $tType,X4 : X0,X1 : X0] : ((sP1(X0,X3,X2,X4,X1) | ((X2 != X3 | X1 != X4) & (X1 != X3 | X2 != X4))) & (((X2 = X3 & X1 = X4) | (X1 = X3 & X2 = X4)) | ~sP1(X0,X3,X2,X4,X1)))),
% 1.49/0.57 inference(nnf_transformation,[],[f324])).
% 1.49/0.57 tff(f983,plain,(
% 1.49/0.57 spl39_34),
% 1.49/0.57 inference(avatar_split_clause,[],[f588,f981])).
% 1.49/0.57 tff(f981,plain,(
% 1.49/0.57 spl39_34 <=> ! [X2 : $tType,X4 : X2,X0 : X2,X3 : X2,X1 : X2] : (X0 = X1 | X1 = X3 | ~sP1(X2,X0,X1,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_34])])).
% 1.49/0.57 tff(f588,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (X0 = X1 | X1 = X3 | ~sP1(X2,X0,X1,X3,X4)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f408])).
% 1.49/0.57 tff(f979,plain,(
% 1.49/0.57 spl39_33),
% 1.49/0.57 inference(avatar_split_clause,[],[f587,f977])).
% 1.49/0.57 tff(f977,plain,(
% 1.49/0.57 spl39_33 <=> ! [X2 : $tType,X4 : X2,X0 : X2,X3 : X2,X1 : X2] : (X3 = X4 | X0 = X4 | ~sP1(X2,X0,X1,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_33])])).
% 1.49/0.57 tff(f587,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (X3 = X4 | X0 = X4 | ~sP1(X2,X0,X1,X3,X4)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f408])).
% 1.49/0.57 tff(f975,plain,(
% 1.49/0.57 spl39_32),
% 1.49/0.57 inference(avatar_split_clause,[],[f586,f973])).
% 1.49/0.57 tff(f973,plain,(
% 1.49/0.57 spl39_32 <=> ! [X2 : $tType,X4 : X2,X0 : X2,X3 : X2,X1 : X2] : (X3 = X4 | X1 = X3 | ~sP1(X2,X0,X1,X3,X4))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_32])])).
% 1.49/0.57 tff(f586,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (X3 = X4 | X1 = X3 | ~sP1(X2,X0,X1,X3,X4)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f408])).
% 1.49/0.57 tff(f971,plain,(
% 1.49/0.57 spl39_30 | ~spl39_31 | ~spl39_10),
% 1.49/0.57 inference(avatar_split_clause,[],[f899,f874,f968,f965])).
% 1.49/0.57 tff(f965,plain,(
% 1.49/0.57 spl39_30 <=> ! [X0 : bool] : fTrue = X0),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_30])])).
% 1.49/0.57 tff(f968,plain,(
% 1.49/0.57 spl39_31 <=> fFalse = fTrue),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_31])])).
% 1.49/0.57 tff(f899,plain,(
% 1.49/0.57 ( ! [X0 : bool] : (fFalse != fTrue | fTrue = X0) ) | ~spl39_10),
% 1.49/0.57 inference(equality_factoring,[],[f875])).
% 1.49/0.57 tff(f963,plain,(
% 1.49/0.57 spl39_29),
% 1.49/0.57 inference(avatar_split_clause,[],[f548,f961])).
% 1.49/0.57 tff(f961,plain,(
% 1.49/0.57 spl39_29 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,X0)),X2 : fun(X0,bool),X1 : X0] : (sK29(X0,X1,X2,X3) = X1 | ~finite_fold1Set(X0,X3,X2,X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_29])])).
% 1.49/0.57 tff(f548,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : fun(X0,fun(X0,X0)),X1 : X0] : (sK29(X0,X1,X2,X3) = X1 | ~finite_fold1Set(X0,X3,X2,X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f383])).
% 1.49/0.57 tff(f959,plain,(
% 1.49/0.57 spl39_28),
% 1.49/0.57 inference(avatar_split_clause,[],[f531,f957])).
% 1.49/0.57 tff(f957,plain,(
% 1.49/0.57 spl39_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))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_28])])).
% 1.49/0.57 tff(f531,plain,(
% 1.49/0.57 ( ! [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)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f293])).
% 1.49/0.57 tff(f293,plain,(
% 1.49/0.57 ! [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))),
% 1.49/0.57 inference(flattening,[],[f292])).
% 1.49/0.57 tff(f292,plain,(
% 1.49/0.57 ! [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))),
% 1.49/0.57 inference(ennf_transformation,[],[f214])).
% 1.49/0.57 tff(f214,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(rectify,[],[f3])).
% 1.49/0.57 tff(f3,axiom,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cut)).
% 1.49/0.57 tff(f955,plain,(
% 1.49/0.57 spl39_27),
% 1.49/0.57 inference(avatar_split_clause,[],[f496,f953])).
% 1.49/0.57 tff(f953,plain,(
% 1.49/0.57 spl39_27 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X2,X1)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_27])])).
% 1.49/0.57 tff(f496,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X2,X1)) | ~finite_finite1(X0,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f275])).
% 1.49/0.57 tff(f275,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (finite_finite1(X0,minus_minus(fun(X0,bool),X2,X1)) | ~finite_finite1(X0,X2))),
% 1.49/0.57 inference(ennf_transformation,[],[f190])).
% 1.49/0.57 tff(f190,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool)] : (finite_finite1(X0,X2) => finite_finite1(X0,minus_minus(fun(X0,bool),X2,X1)))),
% 1.49/0.57 inference(rectify,[],[f90])).
% 1.49/0.57 tff(f90,axiom,(
% 1.49/0.57 ! [X1 : $tType,X18 : fun(X1,bool),X14 : fun(X1,bool)] : (finite_finite1(X1,X14) => finite_finite1(X1,minus_minus(fun(X1,bool),X14,X18)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_finite__Diff)).
% 1.49/0.57 tff(f948,plain,(
% 1.49/0.57 spl39_26),
% 1.49/0.57 inference(avatar_split_clause,[],[f553,f946])).
% 1.49/0.57 tff(f946,plain,(
% 1.49/0.57 spl39_26 <=> ! [X2 : com,X0 : com,X1 : com,X3 : com] : (X0 = X2 | semi(X1,X0) != semi(X3,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_26])])).
% 1.49/0.57 tff(f553,plain,(
% 1.49/0.57 ( ! [X2 : com,X3 : com,X0 : com,X1 : com] : (X0 = X2 | semi(X1,X0) != semi(X3,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f385])).
% 1.49/0.57 tff(f385,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(flattening,[],[f384])).
% 1.49/0.57 tff(f384,plain,(
% 1.49/0.57 ! [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)))),
% 1.49/0.57 inference(nnf_transformation,[],[f228])).
% 1.49/0.57 tff(f228,plain,(
% 1.49/0.57 ! [X0 : com,X1 : com,X2 : com,X3 : com] : (semi(X1,X0) = semi(X3,X2) <=> (X0 = X2 & X1 = X3))),
% 1.49/0.57 inference(rectify,[],[f42])).
% 1.49/0.57 tff(f42,axiom,(
% 1.49/0.57 ! [X33 : com,X34 : com,X35 : com,X36 : com] : (semi(X36,X35) = semi(X34,X33) <=> (X33 = X35 & X34 = X36))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_com_Osimps_I3_J)).
% 1.49/0.57 tff(f944,plain,(
% 1.49/0.57 spl39_25),
% 1.49/0.57 inference(avatar_split_clause,[],[f552,f942])).
% 1.49/0.57 tff(f942,plain,(
% 1.49/0.57 spl39_25 <=> ! [X0 : com,X3 : com,X2 : com,X1 : com] : (X1 = X3 | semi(X1,X0) != semi(X3,X2))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_25])])).
% 1.49/0.57 tff(f552,plain,(
% 1.49/0.57 ( ! [X2 : com,X3 : com,X0 : com,X1 : com] : (X1 = X3 | semi(X1,X0) != semi(X3,X2)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f385])).
% 1.49/0.57 tff(f938,plain,(
% 1.49/0.57 spl39_24),
% 1.49/0.57 inference(avatar_split_clause,[],[f525,f936])).
% 1.49/0.57 tff(f525,plain,(
% 1.49/0.57 ( ! [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)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f207])).
% 1.49/0.57 tff(f207,plain,(
% 1.49/0.57 ! [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)),
% 1.49/0.57 inference(rectify,[],[f70])).
% 1.49/0.57 tff(f70,axiom,(
% 1.49/0.57 ! [X1 : $tType,X2 : $tType,X57 : X2,X47 : fun(X1,fun(X2,X2))] : finite_fold_graph(X1,X2,X47,X57,bot_bot(fun(X1,bool)),X57)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fold__graph_OemptyI)).
% 1.49/0.57 tff(f934,plain,(
% 1.49/0.57 spl39_23),
% 1.49/0.57 inference(avatar_split_clause,[],[f524,f932])).
% 1.49/0.57 tff(f524,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (aa(X0,X1,combk(X1,X0,X3),X2) = X3) )),
% 1.49/0.57 inference(cnf_transformation,[],[f206])).
% 1.49/0.57 tff(f206,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : aa(X0,X1,combk(X1,X0,X3),X2) = X3),
% 1.49/0.57 inference(rectify,[],[f113])).
% 1.49/0.57 tff(f113,axiom,(
% 1.49/0.57 ! [X1 : $tType,X0 : $tType,X74 : X1,X72 : X0] : aa(X1,X0,combk(X0,X1,X72),X74) = X72),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U)).
% 1.49/0.57 tff(f927,plain,(
% 1.49/0.57 spl39_22),
% 1.49/0.57 inference(avatar_split_clause,[],[f482,f925])).
% 1.49/0.57 tff(f482,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,X0)),X1 : X0] : (~finite_fold1Set(X0,X2,bot_bot(fun(X0,bool)),X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f176])).
% 1.49/0.57 tff(f176,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(X0,fun(X0,X0))] : ~finite_fold1Set(X0,X2,bot_bot(fun(X0,bool)),X1)),
% 1.49/0.57 inference(rectify,[],[f52])).
% 1.49/0.57 tff(f52,axiom,(
% 1.49/0.57 ! [X1 : $tType,X15 : X1,X47 : fun(X1,fun(X1,X1))] : ~finite_fold1Set(X1,X47,bot_bot(fun(X1,bool)),X15)),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_empty__fold1SetE)).
% 1.49/0.57 tff(f923,plain,(
% 1.49/0.57 spl39_21),
% 1.49/0.57 inference(avatar_split_clause,[],[f462,f921])).
% 1.49/0.57 tff(f921,plain,(
% 1.49/0.57 spl39_21 <=> ! [X1 : $tType,X0 : $tType] : (finite_finite(fun(X0,X1)) | ~finite_finite(X0) | ~finite_finite(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_21])])).
% 1.49/0.57 tff(f462,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType] : (finite_finite(fun(X0,X1)) | ~finite_finite(X0) | ~finite_finite(X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f271])).
% 1.49/0.57 tff(f271,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (finite_finite(fun(X0,X1)) | ~finite_finite(X0) | ~finite_finite(X1))),
% 1.49/0.57 inference(flattening,[],[f270])).
% 1.49/0.57 tff(f270,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (finite_finite(fun(X0,X1)) | (~finite_finite(X0) | ~finite_finite(X1)))),
% 1.49/0.57 inference(ennf_transformation,[],[f166])).
% 1.49/0.57 tff(f166,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : ((finite_finite(X0) & finite_finite(X1)) => finite_finite(fun(X0,X1)))),
% 1.49/0.57 inference(rectify,[],[f101])).
% 1.49/0.57 tff(f101,axiom,(
% 1.49/0.57 ! [X70 : $tType,X71 : $tType] : ((finite_finite(X70) & finite_finite(X71)) => finite_finite(fun(X70,X71)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite)).
% 1.49/0.57 tff(f919,plain,(
% 1.49/0.57 spl39_20),
% 1.49/0.57 inference(avatar_split_clause,[],[f440,f917])).
% 1.49/0.57 tff(f440,plain,(
% 1.49/0.57 ( ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : (hoare_992312373derivs(X0,X1,bot_bot(fun(hoare_28830079triple(X0),bool)))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f144])).
% 1.49/0.57 tff(f144,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : fun(hoare_28830079triple(X0),bool)] : hoare_992312373derivs(X0,X1,bot_bot(fun(hoare_28830079triple(X0),bool)))),
% 1.49/0.57 inference(rectify,[],[f2])).
% 1.49/0.57 tff(f2,axiom,(
% 1.49/0.57 ! [X1 : $tType,X10 : fun(hoare_28830079triple(X1),bool)] : hoare_992312373derivs(X1,X10,bot_bot(fun(hoare_28830079triple(X1),bool)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_empty)).
% 1.49/0.57 tff(f915,plain,(
% 1.49/0.57 spl39_19 | spl39_2 | ~spl39_10),
% 1.49/0.57 inference(avatar_split_clause,[],[f898,f874,f837,f913])).
% 1.49/0.57 tff(f898,plain,(
% 1.49/0.57 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | (spl39_2 | ~spl39_10)),
% 1.49/0.57 inference(superposition,[],[f839,f875])).
% 1.49/0.57 tff(f911,plain,(
% 1.49/0.57 spl39_18),
% 1.49/0.57 inference(avatar_split_clause,[],[f434,f909])).
% 1.49/0.57 tff(f909,plain,(
% 1.49/0.57 spl39_18 <=> ! [X0 : bool] : (~pp(X0) | ~pp(aa(bool,bool,fNot,X0)))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_18])])).
% 1.49/0.57 tff(f434,plain,(
% 1.49/0.57 ( ! [X0 : bool] : (~pp(X0) | ~pp(aa(bool,bool,fNot,X0))) )),
% 1.49/0.57 inference(cnf_transformation,[],[f138])).
% 1.49/0.57 tff(f138,plain,(
% 1.49/0.57 ! [X0 : bool] : (~pp(X0) | ~pp(aa(bool,bool,fNot,X0)))),
% 1.49/0.57 inference(rectify,[],[f109])).
% 1.49/0.57 tff(f109,axiom,(
% 1.49/0.57 ! [X72 : bool] : (~pp(X72) | ~pp(aa(bool,bool,fNot,X72)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U)).
% 1.49/0.57 tff(f907,plain,(
% 1.49/0.57 spl39_17),
% 1.49/0.57 inference(avatar_split_clause,[],[f432,f905])).
% 1.49/0.57 tff(f432,plain,(
% 1.49/0.57 ( ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f136])).
% 1.49/0.57 tff(f136,plain,(
% 1.49/0.57 ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0))),
% 1.49/0.57 inference(rectify,[],[f110])).
% 1.49/0.57 tff(f110,axiom,(
% 1.49/0.57 ! [X72 : bool] : (pp(aa(bool,bool,fNot,X72)) | pp(X72))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U)).
% 1.49/0.57 tff(f903,plain,(
% 1.49/0.57 spl39_16),
% 1.49/0.57 inference(avatar_split_clause,[],[f439,f901])).
% 1.49/0.57 tff(f896,plain,(
% 1.49/0.57 spl39_15),
% 1.49/0.57 inference(avatar_split_clause,[],[f716,f894])).
% 1.49/0.57 tff(f894,plain,(
% 1.49/0.57 spl39_15 <=> ! [X2 : $tType,X4 : X2,X3 : X2] : sP1(X2,X4,X3,X3,X4)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_15])])).
% 1.49/0.57 tff(f716,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X3 : X2,X4 : X2] : (sP1(X2,X4,X3,X3,X4)) )),
% 1.49/0.57 inference(equality_resolution,[],[f715])).
% 1.49/0.57 tff(f715,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X3 : X2,X1 : X2,X4 : X2] : (sP1(X2,X4,X1,X3,X4) | X1 != X3) )),
% 1.49/0.57 inference(equality_resolution,[],[f590])).
% 1.49/0.57 tff(f590,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (sP1(X2,X0,X1,X3,X4) | X0 != X4 | X1 != X3) )),
% 1.49/0.57 inference(cnf_transformation,[],[f408])).
% 1.49/0.57 tff(f892,plain,(
% 1.49/0.57 spl39_14),
% 1.49/0.57 inference(avatar_split_clause,[],[f714,f890])).
% 1.49/0.57 tff(f890,plain,(
% 1.49/0.57 spl39_14 <=> ! [X2 : $tType,X4 : X2,X1 : X2] : sP1(X2,X1,X1,X4,X4)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_14])])).
% 1.49/0.57 tff(f714,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X1 : X2,X4 : X2] : (sP1(X2,X1,X1,X4,X4)) )),
% 1.49/0.57 inference(equality_resolution,[],[f713])).
% 1.49/0.57 tff(f713,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X3 : X2,X1 : X2,X4 : X2] : (sP1(X2,X1,X1,X3,X4) | X3 != X4) )),
% 1.49/0.57 inference(equality_resolution,[],[f591])).
% 1.49/0.57 tff(f591,plain,(
% 1.49/0.57 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2,X4 : X2] : (sP1(X2,X0,X1,X3,X4) | X0 != X1 | X3 != X4) )),
% 1.49/0.57 inference(cnf_transformation,[],[f408])).
% 1.49/0.57 tff(f888,plain,(
% 1.49/0.57 spl39_13),
% 1.49/0.57 inference(avatar_split_clause,[],[f710,f886])).
% 1.49/0.57 tff(f886,plain,(
% 1.49/0.57 spl39_13 <=> ! [X1 : $tType,X4 : fun(X1,bool),X2 : fun(X1,bool),X3 : X1] : sP0(X1,X3,X2,X3,X4)),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_13])])).
% 1.49/0.57 tff(f710,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X4 : fun(X1,bool)] : (sP0(X1,X3,X2,X3,X4)) )),
% 1.49/0.57 inference(equality_resolution,[],[f577])).
% 1.49/0.57 tff(f577,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X2 : fun(X1,bool),X3 : X1,X0 : X1,X4 : fun(X1,bool)] : (sP0(X1,X0,X2,X3,X4) | X0 != X3) )),
% 1.49/0.57 inference(cnf_transformation,[],[f400])).
% 1.49/0.57 tff(f884,plain,(
% 1.49/0.57 spl39_12),
% 1.49/0.57 inference(avatar_split_clause,[],[f457,f882])).
% 1.49/0.57 tff(f882,plain,(
% 1.49/0.57 spl39_12 <=> ! [X1 : $tType,X0 : $tType] : (cl_Groups_Ominus(fun(X0,X1)) | ~cl_Groups_Ominus(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_12])])).
% 1.49/0.57 tff(f457,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType] : (cl_Groups_Ominus(fun(X0,X1)) | ~cl_Groups_Ominus(X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f265])).
% 1.49/0.57 tff(f265,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (cl_Groups_Ominus(fun(X0,X1)) | ~cl_Groups_Ominus(X1))),
% 1.49/0.57 inference(ennf_transformation,[],[f161])).
% 1.49/0.57 tff(f161,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (cl_Groups_Ominus(X1) => cl_Groups_Ominus(fun(X0,X1)))),
% 1.49/0.57 inference(rectify,[],[f103])).
% 1.49/0.57 tff(f103,axiom,(
% 1.49/0.57 ! [X70 : $tType,X71 : $tType] : (cl_Groups_Ominus(X71) => cl_Groups_Ominus(fun(X70,X71)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus)).
% 1.49/0.57 tff(f880,plain,(
% 1.49/0.57 spl39_11),
% 1.49/0.57 inference(avatar_split_clause,[],[f456,f878])).
% 1.49/0.57 tff(f878,plain,(
% 1.49/0.57 spl39_11 <=> ! [X1 : $tType,X0 : $tType] : (bot(fun(X0,X1)) | ~bot(X1))),
% 1.49/0.57 introduced(avatar_definition,[new_symbols(naming,[spl39_11])])).
% 1.49/0.57 tff(f456,plain,(
% 1.49/0.57 ( ! [X1 : $tType,X0 : $tType] : (bot(fun(X0,X1)) | ~bot(X1)) )),
% 1.49/0.57 inference(cnf_transformation,[],[f264])).
% 1.49/0.57 tff(f264,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (bot(fun(X0,X1)) | ~bot(X1))),
% 1.49/0.57 inference(ennf_transformation,[],[f160])).
% 1.49/0.57 tff(f160,plain,(
% 1.49/0.57 ! [X0 : $tType,X1 : $tType] : (bot(X1) => bot(fun(X0,X1)))),
% 1.49/0.57 inference(rectify,[],[f102])).
% 1.49/0.57 tff(f102,axiom,(
% 1.49/0.57 ! [X70 : $tType,X71 : $tType] : (bot(X71) => bot(fun(X70,X71)))),
% 1.49/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot)).
% 1.49/0.58 tff(f876,plain,(
% 1.49/0.58 spl39_10),
% 1.49/0.58 inference(avatar_split_clause,[],[f433,f874])).
% 1.49/0.58 tff(f433,plain,(
% 1.49/0.58 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) )),
% 1.49/0.58 inference(cnf_transformation,[],[f137])).
% 1.49/0.58 tff(f137,plain,(
% 1.49/0.58 ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 1.49/0.58 inference(rectify,[],[f122])).
% 1.49/0.58 tff(f122,axiom,(
% 1.49/0.58 ! [X72 : bool] : (fFalse = X72 | fTrue = X72)),
% 1.49/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T)).
% 1.49/0.58 tff(f872,plain,(
% 1.49/0.58 spl39_9),
% 1.49/0.58 inference(avatar_split_clause,[],[f430,f870])).
% 1.49/0.58 tff(f430,plain,(
% 1.49/0.58 ( ! [X0 : $tType] : (finite_finite1(X0,bot_bot(fun(X0,bool)))) )),
% 1.49/0.58 inference(cnf_transformation,[],[f134])).
% 1.49/0.58 tff(f134,plain,(
% 1.49/0.58 ! [X0 : $tType] : finite_finite1(X0,bot_bot(fun(X0,bool)))),
% 1.49/0.58 inference(rectify,[],[f87])).
% 1.49/0.58 tff(f87,axiom,(
% 1.49/0.58 ! [X1 : $tType] : finite_finite1(X1,bot_bot(fun(X1,bool)))),
% 1.49/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite_OemptyI)).
% 1.49/0.58 tff(f868,plain,(
% 1.49/0.58 spl39_8),
% 1.49/0.58 inference(avatar_split_clause,[],[f437,f866])).
% 1.49/0.58 tff(f866,plain,(
% 1.49/0.58 spl39_8 <=> ! [X0 : com,X1 : com] : skip != semi(X1,X0)),
% 1.49/0.58 introduced(avatar_definition,[new_symbols(naming,[spl39_8])])).
% 1.49/0.58 tff(f437,plain,(
% 1.49/0.58 ( ! [X0 : com,X1 : com] : (skip != semi(X1,X0)) )),
% 1.49/0.58 inference(cnf_transformation,[],[f141])).
% 1.49/0.58 tff(f141,plain,(
% 1.49/0.58 ! [X0 : com,X1 : com] : skip != semi(X1,X0)),
% 1.49/0.58 inference(rectify,[],[f44])).
% 1.49/0.58 tff(f44,axiom,(
% 1.49/0.58 ! [X37 : com,X38 : com] : skip != semi(X38,X37)),
% 1.49/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_com_Osimps_I12_J)).
% 1.49/0.58 tff(f864,plain,(
% 1.49/0.58 spl39_7),
% 1.49/0.58 inference(avatar_split_clause,[],[f435,f862])).
% 1.49/0.58 tff(f862,plain,(
% 1.49/0.58 spl39_7 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite(X0))),
% 1.49/0.58 introduced(avatar_definition,[new_symbols(naming,[spl39_7])])).
% 1.49/0.58 tff(f435,plain,(
% 1.49/0.58 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (finite_finite1(X0,X1) | ~finite_finite(X0)) )),
% 1.49/0.58 inference(cnf_transformation,[],[f262])).
% 1.49/0.58 tff(f262,plain,(
% 1.49/0.58 ! [X0 : $tType] : (! [X1 : fun(X0,bool)] : finite_finite1(X0,X1) | ~finite_finite(X0))),
% 1.49/0.58 inference(ennf_transformation,[],[f139])).
% 1.49/0.58 tff(f139,plain,(
% 1.49/0.58 ! [X0 : $tType] : (finite_finite(X0) => ! [X1 : fun(X0,bool)] : finite_finite1(X0,X1))),
% 1.49/0.58 inference(rectify,[],[f86])).
% 1.49/0.58 tff(f86,axiom,(
% 1.49/0.58 ! [X1 : $tType] : (finite_finite(X1) => ! [X14 : fun(X1,bool)] : finite_finite1(X1,X14))),
% 1.49/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__code)).
% 1.49/0.58 tff(f860,plain,(
% 1.49/0.58 spl39_6),
% 1.49/0.58 inference(avatar_split_clause,[],[f429,f857])).
% 1.49/0.58 tff(f429,plain,(
% 1.49/0.58 pp(fTrue)),
% 1.49/0.58 inference(cnf_transformation,[],[f108])).
% 1.49/0.58 tff(f108,axiom,(
% 1.49/0.58 pp(fTrue)),
% 1.49/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U)).
% 1.49/0.58 tff(f855,plain,(
% 1.49/0.58 spl39_5),
% 1.49/0.58 inference(avatar_split_clause,[],[f428,f852])).
% 1.49/0.58 tff(f852,plain,(
% 1.49/0.58 spl39_5 <=> finite_finite(bool)),
% 1.49/0.58 introduced(avatar_definition,[new_symbols(naming,[spl39_5])])).
% 1.49/0.58 tff(f428,plain,(
% 1.49/0.58 finite_finite(bool)),
% 1.49/0.58 inference(cnf_transformation,[],[f104])).
% 1.49/0.58 tff(f104,axiom,(
% 1.49/0.58 finite_finite(bool)),
% 1.49/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite)).
% 1.49/0.58 tff(f850,plain,(
% 1.49/0.58 spl39_4),
% 1.49/0.58 inference(avatar_split_clause,[],[f427,f847])).
% 1.49/0.58 tff(f847,plain,(
% 1.49/0.58 spl39_4 <=> cl_Groups_Ominus(bool)),
% 1.49/0.58 introduced(avatar_definition,[new_symbols(naming,[spl39_4])])).
% 1.49/0.58 tff(f427,plain,(
% 1.49/0.58 cl_Groups_Ominus(bool)),
% 1.49/0.58 inference(cnf_transformation,[],[f106])).
% 1.49/0.58 tff(f106,axiom,(
% 1.49/0.58 cl_Groups_Ominus(bool)),
% 1.49/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus)).
% 1.49/0.58 tff(f845,plain,(
% 1.49/0.58 spl39_3),
% 1.49/0.58 inference(avatar_split_clause,[],[f426,f842])).
% 1.49/0.58 tff(f426,plain,(
% 1.49/0.58 bot(bool)),
% 1.49/0.58 inference(cnf_transformation,[],[f105])).
% 1.49/0.58 tff(f105,axiom,(
% 1.49/0.58 bot(bool)),
% 1.49/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot)).
% 1.49/0.58 tff(f840,plain,(
% 1.49/0.58 ~spl39_2),
% 1.49/0.58 inference(avatar_split_clause,[],[f424,f837])).
% 1.49/0.58 tff(f424,plain,(
% 1.49/0.58 ~pp(fFalse)),
% 1.49/0.58 inference(cnf_transformation,[],[f107])).
% 1.49/0.58 tff(f107,axiom,(
% 1.49/0.58 ~pp(fFalse)),
% 1.49/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U)).
% 1.49/0.58 tff(f835,plain,(
% 1.49/0.58 spl39_1),
% 1.49/0.58 inference(avatar_split_clause,[],[f418,f832])).
% 1.49/0.58 tff(f418,plain,(
% 1.49/0.58 p(sK3,sK4)),
% 1.49/0.58 inference(cnf_transformation,[],[f330])).
% 1.49/0.58 % SZS output end Proof for theBenchmark
% 1.49/0.58 % (5597)------------------------------
% 1.49/0.58 % (5597)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.49/0.58 % (5597)Termination reason: Refutation
% 1.49/0.58
% 1.49/0.58 % (5597)Memory used [KB]: 2951
% 1.49/0.58 % (5597)Time elapsed: 0.180 s
% 1.49/0.58 % (5597)Instructions burned: 438 (million)
% 1.49/0.58 % (5597)------------------------------
% 1.49/0.58 % (5597)------------------------------
% 1.49/0.58 % (5592)Success in time 0.213 s
%------------------------------------------------------------------------------