TSTP Solution File: ITP131^2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP131^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:52:48 EDT 2024
% Result : Theorem 1.77s 0.61s
% Output : Refutation 1.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP131^2 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat May 18 17:04:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (10520)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (10523)WARNING: value z3 for option sas not known
% 0.13/0.38 % (10522)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (10521)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 % (10524)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (10525)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)
% 0.13/0.38 % (10526)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)
% 0.13/0.38 % (10527)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)
% 0.13/0.38 % (10523)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)
% 0.20/0.41 % (10527)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.41 % Exception at run slice level
% 0.20/0.41 User error: % Exception at run slice levelFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.41
% 0.20/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.41 % Exception at run slice level
% 0.20/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.43 % (10528)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.43 % (10529)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)
% 0.20/0.43 % (10530)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)
% 0.20/0.45 % (10528)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.45 % (10529)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.45 % Exception at run slice level
% 0.20/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.47 % (10531)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)
% 0.20/0.58 % (10525)First to succeed.
% 1.77/0.61 % (10525)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10520"
% 1.77/0.61 % (10525)Refutation found. Thanks to Tanya!
% 1.77/0.61 % SZS status Theorem for theBenchmark
% 1.77/0.61 % SZS output start Proof for theBenchmark
% 1.77/0.61 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.77/0.61 thf(type_def_6, type, nat: $tType).
% 1.77/0.61 thf(func_def_0, type, nat: $tType).
% 1.77/0.61 thf(func_def_1, type, zero: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_2, type, group_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_3, type, monoid_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_4, type, ab_group_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_5, type, wellorder: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_6, type, semigroup_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_7, type, semigroup_mult: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_8, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_9, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_10, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_11, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_12, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_13, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_14, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_15, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_16, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_17, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_19, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_20, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_21, type, ordere623563068d_diff: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_22, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_23, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 1.77/0.61 thf(func_def_24, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 1.77/0.61 thf(func_def_25, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 1.77/0.61 thf(func_def_26, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 1.77/0.61 thf(func_def_27, type, zero_zero: !>[X0: $tType]:(X0)).
% 1.77/0.61 thf(func_def_28, type, number2016821345itions: (nat > nat) > nat > $o).
% 1.77/0.61 thf(func_def_29, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 1.77/0.61 thf(func_def_30, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 1.77/0.61 thf(func_def_31, type, i: nat).
% 1.77/0.61 thf(func_def_32, type, k: nat).
% 1.77/0.61 thf(func_def_33, type, n: nat).
% 1.77/0.61 thf(func_def_34, type, p: nat > nat).
% 1.77/0.61 thf(func_def_38, type, vAND: $o > $o > $o).
% 1.77/0.61 thf(func_def_39, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 1.77/0.61 thf(func_def_40, type, vNOT: $o > $o).
% 1.77/0.61 thf(func_def_41, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 1.77/0.61 thf(func_def_42, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 1.77/0.61 thf(func_def_43, type, vOR: $o > $o > $o).
% 1.77/0.61 thf(func_def_44, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
% 1.77/0.61 thf(func_def_45, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 1.77/0.61 thf(func_def_46, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 1.77/0.61 thf(func_def_47, type, vIMP: $o > $o > $o).
% 1.77/0.61 thf(func_def_48, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
% 1.77/0.61 thf(func_def_49, type, sP0: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > $o)).
% 1.77/0.61 thf(func_def_50, type, sK1: !>[X0: $tType]:(X0 > X0 > X0)).
% 1.77/0.61 thf(func_def_51, type, sK2: (nat > $o) > nat).
% 1.77/0.61 thf(func_def_52, type, sK3: (nat > $o) > nat).
% 1.77/0.61 thf(func_def_53, type, sK4: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 1.77/0.61 thf(func_def_54, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 1.77/0.61 thf(func_def_55, type, sK6: (nat > $o) > nat).
% 1.77/0.61 thf(func_def_56, type, sK7: (nat > nat) > nat).
% 1.77/0.61 thf(func_def_57, type, sK8: (nat > nat) > nat).
% 1.77/0.61 thf(func_def_58, type, sK9: (nat > $o) > nat).
% 1.77/0.61 thf(func_def_59, type, sK10: nat > (nat > $o) > nat).
% 1.77/0.61 thf(func_def_60, type, sK11: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 1.77/0.61 thf(func_def_61, type, sK12: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 1.77/0.61 thf(func_def_62, type, sK13: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 1.77/0.61 thf(func_def_64, type, sK15: nat > (nat > $o) > nat > nat).
% 1.77/0.61 thf(func_def_65, type, sK16: nat > (nat > $o) > nat > nat).
% 1.77/0.61 thf(f5030,plain,(
% 1.77/0.61 $false),
% 1.77/0.61 inference(avatar_sat_refutation,[],[f1746,f1751,f1756,f1761,f1766,f1771,f1776,f1781,f1786,f1791,f1796,f1801,f1806,f1811,f1816,f1821,f1826,f1831,f1836,f1841,f1846,f1850,f1883,f1887,f1891,f1896,f1901,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1936,f1946,f1950,f1954,f1958,f1964,f1968,f1972,f1976,f1980,f1984,f1988,f1992,f1996,f2000,f2004,f2012,f2016,f2021,f2054,f2072,f2076,f2080,f2109,f2113,f2117,f2121,f2125,f2130,f2142,f2163,f2170,f2174,f2178,f2182,f2186,f2190,f2235,f2239,f2243,f2247,f2251,f2255,f2259,f2295,f2304,f2308,f2312,f2316,f2378,f2382,f2399,f2403,f2407,f2417,f2421,f2425,f2515,f2519,f2523,f2527,f2531,f2535,f2539,f2543,f2651,f2687,f2691,f2700,f2727,f2731,f2735,f2818,f2849,f2853,f2857,f2861,f2972,f2984,f2988,f2992,f2996,f3000,f3072,f3076,f3080,f3084,f3088,f3092,f3096,f3100,f3104,f3108,f3112,f3116,f3121,f3134,f3138,f3142,f3146,f3150,f3154,f3259,f3413,f3417,f3476,f3480,f3484,f3488,f3492,f3496,f3500,f3504,f3508,f3512,f3517,f3521,f3525,f3529,f3860,f3864,f3869,f3874,f4008,f4016,f4020,f4024,f4028,f4033,f4309,f4313,f4317,f4410,f4414,f4451,f4455,f4459,f4463,f4513,f4561,f4565,f4569,f4654,f4703,f4707,f4711,f4715,f4719,f4836,f4878,f4882,f4914,f4918,f4982,f4986,f4990,f4999,f5008,f5016,f5029])).
% 1.77/0.61 thf(f5029,plain,(
% 1.77/0.61 ~spl14_157 | ~spl14_189),
% 1.77/0.61 inference(avatar_contradiction_clause,[],[f5028])).
% 1.77/0.61 thf(f5028,plain,(
% 1.77/0.61 $false | (~spl14_157 | ~spl14_189)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f5021])).
% 1.77/0.61 thf(f5021,plain,(
% 1.77/0.61 ($true != $true) | (~spl14_157 | ~spl14_189)),
% 1.77/0.61 inference(superposition,[],[f4981,f3868])).
% 1.77/0.61 thf(f3868,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))) = $true) | ~spl14_157),
% 1.77/0.61 inference(avatar_component_clause,[],[f3866])).
% 1.77/0.61 thf(f3866,plain,(
% 1.77/0.61 spl14_157 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))) = $true)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_157])])).
% 1.77/0.61 thf(f4981,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),X0))) ) | ~spl14_189),
% 1.77/0.61 inference(avatar_component_clause,[],[f4980])).
% 1.77/0.61 thf(f4980,plain,(
% 1.77/0.61 spl14_189 <=> ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_189])])).
% 1.77/0.61 thf(f5016,plain,(
% 1.77/0.61 spl14_194),
% 1.77/0.61 inference(avatar_split_clause,[],[f1159,f5014])).
% 1.77/0.61 thf(f5014,plain,(
% 1.77/0.61 spl14_194 <=> ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vSIGMA(X0))),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,vEQ(X0))),plus_plus(X0))))) | (canoni770627133id_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_194])])).
% 1.77/0.61 thf(f1159,plain,(
% 1.77/0.61 ( ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vSIGMA(X0))),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,vEQ(X0))),plus_plus(X0))))) | (canoni770627133id_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f905])).
% 1.77/0.61 thf(f905,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vSIGMA(X0))),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,vEQ(X0))),plus_plus(X0))))) | (canoni770627133id_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f461])).
% 1.77/0.61 thf(f461,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => (ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vSIGMA(X0))),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,vEQ(X0))),plus_plus(X0))))))),
% 1.77/0.61 inference(fool_elimination,[],[f460])).
% 1.77/0.61 thf(f460,plain,(
% 1.77/0.61 ! [X0 : $tType] : (canoni770627133id_add(X0) => (ord_less_eq(X0) = (^[X1 : X0, X2 : X0] : (? [X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) = X2)))))),
% 1.77/0.61 inference(rectify,[],[f201])).
% 1.77/0.61 thf(f201,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (canoni770627133id_add(X0) => (ord_less_eq(X0) = (^[X16 : X0, X17 : X0] : (? [X34 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X16),X34) = X17)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_le__iff__add)).
% 1.77/0.61 thf(f5008,plain,(
% 1.77/0.61 spl14_193),
% 1.77/0.61 inference(avatar_split_clause,[],[f1063,f5005])).
% 1.77/0.61 thf(f5005,plain,(
% 1.77/0.61 spl14_193 <=> (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat))),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),plus_plus(nat)))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_193])])).
% 1.77/0.61 thf(f1063,plain,(
% 1.77/0.61 (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat))),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),plus_plus(nat)))))),
% 1.77/0.61 inference(cnf_transformation,[],[f283])).
% 1.77/0.61 thf(f283,plain,(
% 1.77/0.61 (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat))),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),plus_plus(nat)))))),
% 1.77/0.61 inference(fool_elimination,[],[f282])).
% 1.77/0.61 thf(f282,plain,(
% 1.77/0.61 (ord_less_eq(nat) = (^[X0 : nat, X1 : nat] : (? [X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) = X1))))),
% 1.77/0.61 inference(rectify,[],[f250])).
% 1.77/0.61 thf(f250,axiom,(
% 1.77/0.61 (ord_less_eq(nat) = (^[X38 : nat, X39 : nat] : (? [X40 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X38),X40) = X39))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_nat__le__iff__add)).
% 1.77/0.61 thf(f4999,plain,(
% 1.77/0.61 spl14_192),
% 1.77/0.61 inference(avatar_split_clause,[],[f1062,f4996])).
% 1.77/0.61 thf(f4996,plain,(
% 1.77/0.61 spl14_192 <=> (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vOR)),ord_less(nat)))),vEQ(nat)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_192])])).
% 1.77/0.61 thf(f1062,plain,(
% 1.77/0.61 (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vOR)),ord_less(nat)))),vEQ(nat)))),
% 1.77/0.61 inference(cnf_transformation,[],[f281])).
% 1.77/0.61 thf(f281,plain,(
% 1.77/0.61 (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vOR)),ord_less(nat)))),vEQ(nat)))),
% 1.77/0.61 inference(fool_elimination,[],[f280])).
% 1.77/0.61 thf(f280,plain,(
% 1.77/0.61 (ord_less_eq(nat) = (^[X0 : nat, X1 : nat] : ((X0 = X1) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))))),
% 1.77/0.61 inference(rectify,[],[f237])).
% 1.77/0.61 thf(f237,axiom,(
% 1.77/0.61 (ord_less_eq(nat) = (^[X38 : nat, X39 : nat] : ((X38 = X39) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X38),X39))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_le__eq__less__or__eq)).
% 1.77/0.61 thf(f4990,plain,(
% 1.77/0.61 spl14_191),
% 1.77/0.61 inference(avatar_split_clause,[],[f1185,f4988])).
% 1.77/0.61 thf(f4988,plain,(
% 1.77/0.61 spl14_191 <=> ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(X0,sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,ord_less_eq(X0))),minus_minus(X0)))),zero_zero(X0))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_191])])).
% 1.77/0.61 thf(f1185,plain,(
% 1.77/0.61 ( ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(X0,sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,ord_less_eq(X0))),minus_minus(X0)))),zero_zero(X0))) | (ordered_ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f931])).
% 1.77/0.61 thf(f931,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(X0,sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,ord_less_eq(X0))),minus_minus(X0)))),zero_zero(X0))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f513])).
% 1.77/0.61 thf(f513,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordered_ab_group_add(X0) = $true) => (ord_less_eq(X0) = vAPP(X0,sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,ord_less_eq(X0))),minus_minus(X0)))),zero_zero(X0))))),
% 1.77/0.61 inference(fool_elimination,[],[f512])).
% 1.77/0.61 thf(f512,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => (ord_less_eq(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),zero_zero(X0))))))),
% 1.77/0.61 inference(rectify,[],[f123])).
% 1.77/0.61 thf(f123,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => (ord_less_eq(X0) = (^[X16 : X0, X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X16),X17)),zero_zero(X0))))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_le__iff__diff__le__0)).
% 1.77/0.61 thf(f4986,plain,(
% 1.77/0.61 spl14_190),
% 1.77/0.61 inference(avatar_split_clause,[],[f1184,f4984])).
% 1.77/0.61 thf(f4984,plain,(
% 1.77/0.61 spl14_190 <=> ! [X0 : $tType] : ((ord_less(X0) = vAPP(X0,sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,ord_less(X0))),minus_minus(X0)))),zero_zero(X0))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_190])])).
% 1.77/0.61 thf(f1184,plain,(
% 1.77/0.61 ( ! [X0 : $tType] : ((ord_less(X0) = vAPP(X0,sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,ord_less(X0))),minus_minus(X0)))),zero_zero(X0))) | (ordered_ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f930])).
% 1.77/0.61 thf(f930,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ord_less(X0) = vAPP(X0,sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,ord_less(X0))),minus_minus(X0)))),zero_zero(X0))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f511])).
% 1.77/0.61 thf(f511,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordered_ab_group_add(X0) = $true) => (ord_less(X0) = vAPP(X0,sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,ord_less(X0))),minus_minus(X0)))),zero_zero(X0))))),
% 1.77/0.61 inference(fool_elimination,[],[f510])).
% 1.77/0.61 thf(f510,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => (ord_less(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),zero_zero(X0))))))),
% 1.77/0.61 inference(rectify,[],[f124])).
% 1.77/0.61 thf(f124,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => (ord_less(X0) = (^[X16 : X0, X17 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X16),X17)),zero_zero(X0))))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_less__iff__diff__less__0)).
% 1.77/0.61 thf(f4982,plain,(
% 1.77/0.61 spl14_189 | ~spl14_40 | ~spl14_77 | ~spl14_157 | ~spl14_158 | ~spl14_170),
% 1.77/0.61 inference(avatar_split_clause,[],[f4484,f4449,f3871,f3866,f2253,f1962,f4980])).
% 1.77/0.61 thf(f1962,plain,(
% 1.77/0.61 spl14_40 <=> ! [X0 : nat] : ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_40])])).
% 1.77/0.61 thf(f2253,plain,(
% 1.77/0.61 spl14_77 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_77])])).
% 1.77/0.61 thf(f3871,plain,(
% 1.77/0.61 spl14_158 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n) = $true)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_158])])).
% 1.77/0.61 thf(f4449,plain,(
% 1.77/0.61 spl14_170 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_170])])).
% 1.77/0.61 thf(f4484,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),X0))) ) | (~spl14_40 | ~spl14_77 | ~spl14_157 | ~spl14_158 | ~spl14_170)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f4483])).
% 1.77/0.61 thf(f4483,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true = $false) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),X0))) ) | (~spl14_40 | ~spl14_77 | ~spl14_157 | ~spl14_158 | ~spl14_170)),
% 1.77/0.61 inference(forward_demodulation,[],[f4482,f1963])).
% 1.77/0.61 thf(f1963,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | ~spl14_40),
% 1.77/0.61 inference(avatar_component_clause,[],[f1962])).
% 1.77/0.61 thf(f4482,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),X0)),zero_zero(nat))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),X0))) ) | (~spl14_77 | ~spl14_157 | ~spl14_158 | ~spl14_170)),
% 1.77/0.61 inference(forward_demodulation,[],[f4476,f3992])).
% 1.77/0.61 thf(f3992,plain,(
% 1.77/0.61 (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n)) | (~spl14_77 | ~spl14_158)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f3953])).
% 1.77/0.61 thf(f3953,plain,(
% 1.77/0.61 ($true != $true) | (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n)) | (~spl14_77 | ~spl14_158)),
% 1.77/0.61 inference(superposition,[],[f2254,f3873])).
% 1.77/0.61 thf(f3873,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n) = $true) | ~spl14_158),
% 1.77/0.61 inference(avatar_component_clause,[],[f3871])).
% 1.77/0.61 thf(f2254,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))) ) | ~spl14_77),
% 1.77/0.61 inference(avatar_component_clause,[],[f2253])).
% 1.77/0.61 thf(f4476,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),X0))) ) | (~spl14_157 | ~spl14_170)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f4469])).
% 1.77/0.61 thf(f4469,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),X0))) ) | (~spl14_157 | ~spl14_170)),
% 1.77/0.61 inference(superposition,[],[f4450,f3868])).
% 1.77/0.61 thf(f4450,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl14_170),
% 1.77/0.61 inference(avatar_component_clause,[],[f4449])).
% 1.77/0.61 thf(f4918,plain,(
% 1.77/0.61 spl14_188),
% 1.77/0.61 inference(avatar_split_clause,[],[f1319,f4916])).
% 1.77/0.61 thf(f4916,plain,(
% 1.77/0.61 spl14_188 <=> ! [X4 : nat,X0 : nat,X3 : nat,X2 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_188])])).
% 1.77/0.61 thf(f1319,plain,(
% 1.77/0.61 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1028])).
% 1.77/0.61 thf(f1028,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f717])).
% 1.77/0.61 thf(f717,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X3)),X4)))),
% 1.77/0.61 inference(fool_elimination,[],[f716])).
% 1.77/0.61 thf(f716,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X3)),X4)))),
% 1.77/0.61 inference(rectify,[],[f154])).
% 1.77/0.61 thf(f154,axiom,(
% 1.77/0.61 ! [X12 : nat,X4 : nat,X22 : nat,X5 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X12),X4) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X22)),X5)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X12),X22)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X4),X12)),X22)),X5)),X3)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_nat__diff__add__eq1)).
% 1.77/0.61 thf(f4914,plain,(
% 1.77/0.61 spl14_187),
% 1.77/0.61 inference(avatar_split_clause,[],[f1318,f4912])).
% 1.77/0.61 thf(f4912,plain,(
% 1.77/0.61 spl14_187 <=> ! [X4 : nat,X0 : nat,X3 : nat,X2 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_187])])).
% 1.77/0.61 thf(f1318,plain,(
% 1.77/0.61 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1027])).
% 1.77/0.61 thf(f1027,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f715])).
% 1.77/0.61 thf(f715,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X4))))),
% 1.77/0.61 inference(fool_elimination,[],[f714])).
% 1.77/0.61 thf(f714,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2)),X4))))),
% 1.77/0.61 inference(rectify,[],[f153])).
% 1.77/0.61 thf(f153,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X22 : nat,X5 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X12) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X4),X22)),X5)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X12),X22)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X12),X4)),X22)),X3))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_nat__diff__add__eq2)).
% 1.77/0.61 thf(f4882,plain,(
% 1.77/0.61 spl14_186),
% 1.77/0.61 inference(avatar_split_clause,[],[f1293,f4880])).
% 1.77/0.61 thf(f4880,plain,(
% 1.77/0.61 spl14_186 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_186])])).
% 1.77/0.61 thf(f1293,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1000])).
% 1.77/0.61 thf(f1000,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f999])).
% 1.77/0.61 thf(f999,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f675])).
% 1.77/0.61 thf(f675,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0)))))),
% 1.77/0.61 inference(fool_elimination,[],[f674])).
% 1.77/0.61 thf(f674,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0)))))),
% 1.77/0.61 inference(rectify,[],[f114])).
% 1.77/0.61 thf(f114,axiom,(
% 1.77/0.61 ! [X6 : nat,X5 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X6),X5) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X6),X3) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X6)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),X6)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Nat_Odiff__diff__eq)).
% 1.77/0.61 thf(f4878,plain,(
% 1.77/0.61 spl14_185),
% 1.77/0.61 inference(avatar_split_clause,[],[f1170,f4876])).
% 1.77/0.61 thf(f4876,plain,(
% 1.77/0.61 spl14_185 <=> ! [X0 : $tType] : ((vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X0),sTfun(X0,$o)),bCOMB,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)))),minus_minus(X0))) | (group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_185])])).
% 1.77/0.61 thf(f1170,plain,(
% 1.77/0.61 ( ! [X0 : $tType] : ((vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X0),sTfun(X0,$o)),bCOMB,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)))),minus_minus(X0))) | (group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f916])).
% 1.77/0.61 thf(f916,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X0),sTfun(X0,$o)),bCOMB,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)))),minus_minus(X0))) | (group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f483])).
% 1.77/0.61 thf(f483,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((group_add(X0) = $true) => (vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X0),sTfun(X0,$o)),bCOMB,vAPP(X0,sTfun(X0,$o),vEQ(X0),zero_zero(X0)))),minus_minus(X0))))),
% 1.77/0.61 inference(fool_elimination,[],[f482])).
% 1.77/0.61 thf(f482,plain,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ((^[X1 : X0, X2 : X0] : ((X1 = X2))) = (^[X3 : X0, X4 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4))))))),
% 1.77/0.61 inference(rectify,[],[f92])).
% 1.77/0.61 thf(f92,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ((^[X14 : X0, X15 : X0] : ((X14 = X15))) = (^[X16 : X0, X17 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X16),X17))))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_eq__iff__diff__eq__0)).
% 1.77/0.61 thf(f4836,plain,(
% 1.77/0.61 spl14_184),
% 1.77/0.61 inference(avatar_split_clause,[],[f1272,f4834])).
% 1.77/0.61 thf(f4834,plain,(
% 1.77/0.61 spl14_184 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK7,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK8,X0)))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_184])])).
% 1.77/0.61 thf(f1272,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK7,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK8,X0))))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1046])).
% 1.77/0.61 thf(f1046,plain,(
% 1.77/0.61 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK7,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK8,X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK7,X0)),vAPP(sTfun(nat,nat),nat,sK8,X0)))))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f976,f1045])).
% 1.77/0.61 thf(f1045,plain,(
% 1.77/0.61 ! [X0 : nat > nat] : (? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4))) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK7,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK8,X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK7,X0)),vAPP(sTfun(nat,nat),nat,sK8,X0)))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f976,plain,(
% 1.77/0.61 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4))))),
% 1.77/0.61 inference(flattening,[],[f975])).
% 1.77/0.61 thf(f975,plain,(
% 1.77/0.61 ! [X0 : nat > nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))) | ? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4))))),
% 1.77/0.61 inference(ennf_transformation,[],[f639])).
% 1.77/0.61 thf(f639,plain,(
% 1.77/0.61 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (! [X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)))) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)))))),
% 1.77/0.61 inference(fool_elimination,[],[f638])).
% 1.77/0.61 thf(f638,plain,(
% 1.77/0.61 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (! [X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))))),
% 1.77/0.61 inference(rectify,[],[f234])).
% 1.77/0.61 thf(f234,axiom,(
% 1.77/0.61 ! [X24 : nat > nat,X4 : nat,X12 : nat] : (! [X36 : nat,X37 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X36),X37) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X24,X36)),vAPP(nat,nat,X24,X37))) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X24,X4)),vAPP(nat,nat,X24,X12))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_less__mono__imp__le__mono)).
% 1.77/0.61 thf(f4719,plain,(
% 1.77/0.61 spl14_183),
% 1.77/0.61 inference(avatar_split_clause,[],[f1199,f4717])).
% 1.77/0.61 thf(f4717,plain,(
% 1.77/0.61 spl14_183 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_183])])).
% 1.77/0.61 thf(f1199,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f947])).
% 1.77/0.61 thf(f947,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(flattening,[],[f946])).
% 1.77/0.61 thf(f946,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f541])).
% 1.77/0.61 thf(f541,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordered_ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))))))),
% 1.77/0.61 inference(fool_elimination,[],[f540])).
% 1.77/0.61 thf(f540,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)))))),
% 1.77/0.61 inference(rectify,[],[f91])).
% 1.77/0.61 thf(f91,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X8 : X0,X7 : X0,X13 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X13),X9) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X13)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_diff__mono)).
% 1.77/0.61 thf(f4715,plain,(
% 1.77/0.61 spl14_182),
% 1.77/0.61 inference(avatar_split_clause,[],[f1198,f4713])).
% 1.77/0.61 thf(f4713,plain,(
% 1.77/0.61 spl14_182 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_182])])).
% 1.77/0.61 thf(f1198,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f945])).
% 1.77/0.61 thf(f945,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(flattening,[],[f944])).
% 1.77/0.61 thf(f944,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f539])).
% 1.77/0.61 thf(f539,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordered_ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))))))),
% 1.77/0.61 inference(fool_elimination,[],[f538])).
% 1.77/0.61 thf(f538,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)))))),
% 1.77/0.61 inference(rectify,[],[f96])).
% 1.77/0.61 thf(f96,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X8 : X0,X7 : X0,X13 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X8),X7) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X13),X9) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X13)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_diff__strict__mono)).
% 1.77/0.61 thf(f4711,plain,(
% 1.77/0.61 spl14_181),
% 1.77/0.61 inference(avatar_split_clause,[],[f1131,f4709])).
% 1.77/0.61 thf(f4709,plain,(
% 1.77/0.61 spl14_181 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_181])])).
% 1.77/0.61 thf(f1131,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f875])).
% 1.77/0.61 thf(f875,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere779506340up_add(X0) != $true))),
% 1.77/0.61 inference(flattening,[],[f874])).
% 1.77/0.61 thf(f874,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))) | (ordere779506340up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f405])).
% 1.77/0.61 thf(f405,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4)))))),
% 1.77/0.61 inference(fool_elimination,[],[f404])).
% 1.77/0.61 thf(f404,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))))),
% 1.77/0.61 inference(rectify,[],[f206])).
% 1.77/0.61 thf(f206,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X4 : X0,X12 : X0,X6 : X0,X19 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X19) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X12)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X12),X19))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_add__mono__thms__linordered__semiring_I1_J)).
% 1.77/0.61 thf(f4707,plain,(
% 1.77/0.61 spl14_180),
% 1.77/0.61 inference(avatar_split_clause,[],[f1112,f4705])).
% 1.77/0.61 thf(f4705,plain,(
% 1.77/0.61 spl14_180 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_180])])).
% 1.77/0.61 thf(f1112,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f852])).
% 1.77/0.61 thf(f852,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordere223160158up_add(X0) != $true))),
% 1.77/0.61 inference(flattening,[],[f851])).
% 1.77/0.61 thf(f851,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))) | (ordere223160158up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f367])).
% 1.77/0.61 thf(f367,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4)))))),
% 1.77/0.61 inference(fool_elimination,[],[f366])).
% 1.77/0.61 thf(f366,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))))),
% 1.77/0.61 inference(rectify,[],[f219])).
% 1.77/0.61 thf(f219,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X4 : X0,X12 : X0,X6 : X0,X19 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X19) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X12)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X12),X19))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add__mono__thms__linordered__field_I5_J)).
% 1.77/0.61 thf(f4703,plain,(
% 1.77/0.61 spl14_179),
% 1.77/0.61 inference(avatar_split_clause,[],[f1083,f4701])).
% 1.77/0.61 thf(f4701,plain,(
% 1.77/0.61 spl14_179 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (strict2144017051up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_179])])).
% 1.77/0.61 thf(f1083,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (strict2144017051up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f820])).
% 1.77/0.61 thf(f820,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (strict2144017051up_add(X0) != $true))),
% 1.77/0.61 inference(flattening,[],[f819])).
% 1.77/0.61 thf(f819,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (strict2144017051up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f309])).
% 1.77/0.61 thf(f309,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((strict2144017051up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))))))),
% 1.77/0.61 inference(fool_elimination,[],[f308])).
% 1.77/0.61 thf(f308,plain,(
% 1.77/0.61 ! [X0 : $tType] : (strict2144017051up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4)))))),
% 1.77/0.61 inference(rectify,[],[f216])).
% 1.77/0.61 thf(f216,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (strict2144017051up_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0,X13 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X8),X7) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X9),X13) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X13)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_add__strict__mono)).
% 1.77/0.61 thf(f4654,plain,(
% 1.77/0.61 spl14_178),
% 1.77/0.61 inference(avatar_split_clause,[],[f1306,f4652])).
% 1.77/0.61 thf(f4652,plain,(
% 1.77/0.61 spl14_178 <=> ! [X1 : $tType,X2 : X1 > nat,X4 : X1,X0 : X1 > $o] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP0(X1),X2),X0)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_178])])).
% 1.77/0.61 thf(f1306,plain,(
% 1.77/0.61 ( ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP0(X1),X2),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1054])).
% 1.77/0.61 thf(f1054,plain,(
% 1.77/0.61 ! [X0 : X1 > $o,X1 : $tType,X2 : X1 > nat] : ((! [X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0))))) & ($true != vAPP(X1,$o,X0,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0))))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP0(X1),X2),X0)))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f1052,f1053])).
% 1.77/0.61 thf(f1053,plain,(
% 1.77/0.61 ! [X1 : $tType,X0 : X1 > $o,X2 : X1 > nat] : (? [X3 : X1] : (! [X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,X3)))) & ($true != vAPP(X1,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,X3)))) => (! [X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0))))) & ($true != vAPP(X1,$o,X0,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0))))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f1052,plain,(
% 1.77/0.61 ! [X0 : X1 > $o,X1 : $tType,X2 : X1 > nat] : (? [X3 : X1] : (! [X4 : X1] : (($true = vAPP(X1,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X1,nat,X2,X4)),vAPP(X1,nat,X2,X3)))) & ($true != vAPP(X1,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,X3)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP0(X1),X2),X0)))),
% 1.77/0.61 inference(rectify,[],[f1051])).
% 1.77/0.61 thf(f1051,plain,(
% 1.77/0.61 ! [X2 : X0 > $o,X0 : $tType,X1 : X0 > nat] : (? [X5 : X0] : (! [X6 : X0] : (($true = vAPP(X0,$o,X2,X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))) & ($true != vAPP(X0,$o,X2,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5)))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP0(X0),X1),X2)))),
% 1.77/0.61 inference(nnf_transformation,[],[f1031])).
% 1.77/0.61 thf(f1031,plain,(
% 1.77/0.61 ! [X2 : X0 > $o,X0 : $tType,X1 : X0 > nat] : (? [X5 : X0] : (! [X6 : X0] : (($true = vAPP(X0,$o,X2,X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))) & ($true != vAPP(X0,$o,X2,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5)))) | ~($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP0(X0),X1),X2)))),
% 1.77/0.61 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 1.77/0.61 thf(f4569,plain,(
% 1.77/0.61 spl14_177),
% 1.77/0.61 inference(avatar_split_clause,[],[f1155,f4567])).
% 1.77/0.61 thf(f4567,plain,(
% 1.77/0.61 spl14_177 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_177])])).
% 1.77/0.61 thf(f1155,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f900])).
% 1.77/0.61 thf(f900,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f453])).
% 1.77/0.61 thf(f453,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere623563068d_diff(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f452])).
% 1.77/0.61 thf(f452,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X3))))),
% 1.77/0.61 inference(rectify,[],[f129])).
% 1.77/0.61 thf(f129,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9)),X8) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X8)),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2)).
% 1.77/0.61 thf(f4565,plain,(
% 1.77/0.61 spl14_176),
% 1.77/0.61 inference(avatar_split_clause,[],[f1153,f4563])).
% 1.77/0.61 thf(f4563,plain,(
% 1.77/0.61 spl14_176 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_176])])).
% 1.77/0.61 thf(f1153,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f898])).
% 1.77/0.61 thf(f898,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f449])).
% 1.77/0.61 thf(f449,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere623563068d_diff(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)))))),
% 1.77/0.61 inference(fool_elimination,[],[f448])).
% 1.77/0.61 thf(f448,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)))))),
% 1.77/0.61 inference(rectify,[],[f131])).
% 1.77/0.61 thf(f131,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X7)),X8) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X8)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc)).
% 1.77/0.61 thf(f4561,plain,(
% 1.77/0.61 spl14_175),
% 1.77/0.61 inference(avatar_split_clause,[],[f1152,f4559])).
% 1.77/0.61 thf(f4559,plain,(
% 1.77/0.61 spl14_175 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_175])])).
% 1.77/0.61 thf(f1152,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f897])).
% 1.77/0.61 thf(f897,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f447])).
% 1.77/0.61 thf(f447,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere623563068d_diff(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),X2))))),
% 1.77/0.61 inference(fool_elimination,[],[f446])).
% 1.77/0.61 thf(f446,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),X2))))),
% 1.77/0.61 inference(rectify,[],[f127])).
% 1.77/0.61 thf(f127,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X8)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X8)),X7))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right)).
% 1.77/0.61 thf(f4513,plain,(
% 1.77/0.61 ~spl14_174 | spl14_23 | ~spl14_114),
% 1.77/0.61 inference(avatar_split_clause,[],[f4399,f2981,f1880,f4510])).
% 1.77/0.61 thf(f4510,plain,(
% 1.77/0.61 spl14_174 <=> (zero_zero(nat) = vAPP(nat,nat,p,n))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_174])])).
% 1.77/0.61 thf(f1880,plain,(
% 1.77/0.61 spl14_23 <=> (vAPP(nat,nat,p,i) = zero_zero(nat))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_23])])).
% 1.77/0.61 thf(f2981,plain,(
% 1.77/0.61 spl14_114 <=> (i = n)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_114])])).
% 1.77/0.61 thf(f4399,plain,(
% 1.77/0.61 (zero_zero(nat) != vAPP(nat,nat,p,n)) | (spl14_23 | ~spl14_114)),
% 1.77/0.61 inference(superposition,[],[f1882,f2982])).
% 1.77/0.61 thf(f2982,plain,(
% 1.77/0.61 (i = n) | ~spl14_114),
% 1.77/0.61 inference(avatar_component_clause,[],[f2981])).
% 1.77/0.61 thf(f1882,plain,(
% 1.77/0.61 (vAPP(nat,nat,p,i) != zero_zero(nat)) | spl14_23),
% 1.77/0.61 inference(avatar_component_clause,[],[f1880])).
% 1.77/0.61 thf(f4463,plain,(
% 1.77/0.61 spl14_173),
% 1.77/0.61 inference(avatar_split_clause,[],[f1313,f4461])).
% 1.77/0.61 thf(f4461,plain,(
% 1.77/0.61 spl14_173 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_173])])).
% 1.77/0.61 thf(f1313,plain,(
% 1.77/0.61 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1022])).
% 1.77/0.61 thf(f1022,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f1021])).
% 1.77/0.61 thf(f1021,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f705])).
% 1.77/0.61 thf(f705,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)))))),
% 1.77/0.61 inference(fool_elimination,[],[f704])).
% 1.77/0.61 thf(f704,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))))),
% 1.77/0.61 inference(rectify,[],[f254])).
% 1.77/0.61 thf(f254,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X6 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X12) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X6),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),X6)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X12),X19))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_add__le__mono)).
% 1.77/0.61 thf(f4459,plain,(
% 1.77/0.61 spl14_172),
% 1.77/0.61 inference(avatar_split_clause,[],[f1312,f4457])).
% 1.77/0.61 thf(f4457,plain,(
% 1.77/0.61 spl14_172 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_172])])).
% 1.77/0.61 thf(f1312,plain,(
% 1.77/0.61 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1020])).
% 1.77/0.61 thf(f1020,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f1019])).
% 1.77/0.61 thf(f1019,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f703])).
% 1.77/0.61 thf(f703,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)))))),
% 1.77/0.61 inference(fool_elimination,[],[f702])).
% 1.77/0.61 thf(f702,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))))),
% 1.77/0.61 inference(rectify,[],[f246])).
% 1.77/0.61 thf(f246,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X6 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X12) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X6),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),X6)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X12),X19))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_add__less__mono)).
% 1.77/0.61 thf(f4455,plain,(
% 1.77/0.61 spl14_171),
% 1.77/0.61 inference(avatar_split_clause,[],[f1278,f4453])).
% 1.77/0.61 thf(f4453,plain,(
% 1.77/0.61 spl14_171 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_171])])).
% 1.77/0.61 thf(f1278,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f982])).
% 1.77/0.61 thf(f982,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f981])).
% 1.77/0.61 thf(f981,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f645])).
% 1.77/0.61 thf(f645,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)))))),
% 1.77/0.61 inference(fool_elimination,[],[f644])).
% 1.77/0.61 thf(f644,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))))),
% 1.77/0.61 inference(rectify,[],[f141])).
% 1.77/0.61 thf(f141,axiom,(
% 1.77/0.61 ! [X8 : nat,X7 : nat,X9 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X8),X7) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X9),X8) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X8),X9)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_diff__less__mono)).
% 1.77/0.61 thf(f4451,plain,(
% 1.77/0.61 spl14_170),
% 1.77/0.61 inference(avatar_split_clause,[],[f1277,f4449])).
% 1.77/0.61 thf(f1277,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f980])).
% 1.77/0.61 thf(f980,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f979])).
% 1.77/0.61 thf(f979,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f643])).
% 1.77/0.61 thf(f643,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0)))))),
% 1.77/0.61 inference(fool_elimination,[],[f642])).
% 1.77/0.61 thf(f642,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))))),
% 1.77/0.61 inference(rectify,[],[f109])).
% 1.77/0.61 thf(f109,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X3) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X19),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X19),X5))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_diff__less__mono2)).
% 1.77/0.61 thf(f4414,plain,(
% 1.77/0.61 spl14_169),
% 1.77/0.61 inference(avatar_split_clause,[],[f1276,f4412])).
% 1.77/0.61 thf(f4412,plain,(
% 1.77/0.61 spl14_169 <=> ! [X4 : nat,X0 : nat > $o,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true != vAPP(nat,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0)),X2)) | ($true != vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_169])])).
% 1.77/0.61 thf(f1276,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat > $o,X1 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true != vAPP(nat,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0)),X2)) | ($true != vAPP(nat,$o,X0,X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1050])).
% 1.77/0.61 thf(f1050,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat,X2 : nat] : ((! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true != vAPP(nat,$o,X0,X4))) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)))) | (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0)),X2)) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0)))) | ($true != vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f1047,f1049,f1048])).
% 1.77/0.61 thf(f1048,plain,(
% 1.77/0.61 ! [X0 : nat > $o] : (? [X3 : nat] : (! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X3) = $true) | ($true != vAPP(nat,$o,X0,X4))) & ($true = vAPP(nat,$o,X0,X3))) => (! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true != vAPP(nat,$o,X0,X4))) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f1049,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X2 : nat] : (? [X5 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X2)) & ($true = vAPP(nat,$o,X0,X5))) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0)),X2)) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0)))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f1047,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (? [X3 : nat] : (! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X3) = $true) | ($true != vAPP(nat,$o,X0,X4))) & ($true = vAPP(nat,$o,X0,X3))) | ? [X5 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X2)) & ($true = vAPP(nat,$o,X0,X5))) | ($true != vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 inference(rectify,[],[f978])).
% 1.77/0.61 thf(f978,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (? [X4 : nat] : (! [X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X4)) | ($true != vAPP(nat,$o,X0,X5))) & ($true = vAPP(nat,$o,X0,X4))) | ? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X2)) & ($true = vAPP(nat,$o,X0,X3))) | ($true != vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 inference(flattening,[],[f977])).
% 1.77/0.61 thf(f977,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat,X2 : nat] : ((? [X4 : nat] : (! [X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X4)) | ($true != vAPP(nat,$o,X0,X5))) & ($true = vAPP(nat,$o,X0,X4))) | ? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X2)) & ($true = vAPP(nat,$o,X0,X3)))) | ($true != vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f641])).
% 1.77/0.61 thf(f641,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,X0,X1)) => (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X2))) => ? [X4 : nat] : (! [X5 : nat] : (($true = vAPP(nat,$o,X0,X5)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X4))) & ($true = vAPP(nat,$o,X0,X4)))))),
% 1.77/0.61 inference(fool_elimination,[],[f640])).
% 1.77/0.61 thf(f640,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (vAPP(nat,$o,X0,X1) => (! [X3 : nat] : (vAPP(nat,$o,X0,X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X2)) => ? [X4 : nat] : (! [X5 : nat] : (vAPP(nat,$o,X0,X5) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X4)) & vAPP(nat,$o,X0,X4))))),
% 1.77/0.61 inference(rectify,[],[f188])).
% 1.77/0.61 thf(f188,axiom,(
% 1.77/0.61 ! [X20 : nat > $o,X6 : nat,X7 : nat] : (vAPP(nat,$o,X20,X6) => (! [X33 : nat] : (vAPP(nat,$o,X20,X33) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X33),X7)) => ? [X25 : nat] : (! [X26 : nat] : (vAPP(nat,$o,X20,X26) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X26),X25)) & vAPP(nat,$o,X20,X25))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Nat_Oex__has__greatest__nat)).
% 1.77/0.61 thf(f4410,plain,(
% 1.77/0.61 spl14_168),
% 1.77/0.61 inference(avatar_split_clause,[],[f1271,f4408])).
% 1.77/0.61 thf(f4408,plain,(
% 1.77/0.61 spl14_168 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK7,X0)),vAPP(sTfun(nat,nat),nat,sK8,X0))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_168])])).
% 1.77/0.61 thf(f1271,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK7,X0)),vAPP(sTfun(nat,nat),nat,sK8,X0)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1046])).
% 1.77/0.61 thf(f4317,plain,(
% 1.77/0.61 spl14_167),
% 1.77/0.61 inference(avatar_split_clause,[],[f1288,f4315])).
% 1.77/0.61 thf(f4315,plain,(
% 1.77/0.61 spl14_167 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_167])])).
% 1.77/0.61 thf(f1288,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f992])).
% 1.77/0.61 thf(f992,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f665])).
% 1.77/0.61 thf(f665,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)))),
% 1.77/0.61 inference(fool_elimination,[],[f664])).
% 1.77/0.61 thf(f664,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)))),
% 1.77/0.61 inference(rectify,[],[f83])).
% 1.77/0.61 thf(f83,axiom,(
% 1.77/0.61 ! [X6 : nat,X12 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X6),X12) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X12),X6)),X4) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X12),X4)),X6)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Nat_Oadd__diff__assoc2)).
% 1.77/0.61 thf(f4313,plain,(
% 1.77/0.61 spl14_166),
% 1.77/0.61 inference(avatar_split_clause,[],[f1286,f4311])).
% 1.77/0.61 thf(f4311,plain,(
% 1.77/0.61 spl14_166 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_166])])).
% 1.77/0.61 thf(f1286,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f990])).
% 1.77/0.61 thf(f990,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f661])).
% 1.77/0.61 thf(f661,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X0)))),
% 1.77/0.61 inference(fool_elimination,[],[f660])).
% 1.77/0.61 thf(f660,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X0)))),
% 1.77/0.61 inference(rectify,[],[f84])).
% 1.77/0.61 thf(f84,axiom,(
% 1.77/0.61 ! [X6 : nat,X12 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X6),X12) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X12),X6)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),X12)),X6)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Nat_Oadd__diff__assoc)).
% 1.77/0.61 thf(f4309,plain,(
% 1.77/0.61 spl14_165),
% 1.77/0.61 inference(avatar_split_clause,[],[f1285,f4307])).
% 1.77/0.61 thf(f4307,plain,(
% 1.77/0.61 spl14_165 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_165])])).
% 1.77/0.61 thf(f1285,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f989])).
% 1.77/0.61 thf(f989,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f659])).
% 1.77/0.61 thf(f659,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f658])).
% 1.77/0.61 thf(f658,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),X1)))),
% 1.77/0.61 inference(rectify,[],[f82])).
% 1.77/0.61 thf(f82,axiom,(
% 1.77/0.61 ! [X6 : nat,X12 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X6),X12) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X12),X6)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),X6)),X12)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Nat_Odiff__diff__right)).
% 1.77/0.61 thf(f4033,plain,(
% 1.77/0.61 spl14_164 | spl14_114 | ~spl14_26 | ~spl14_81),
% 1.77/0.61 inference(avatar_split_clause,[],[f2328,f2306,f1893,f2981,f4030])).
% 1.77/0.61 thf(f4030,plain,(
% 1.77/0.61 spl14_164 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),i),n))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_164])])).
% 1.77/0.61 thf(f1893,plain,(
% 1.77/0.61 spl14_26 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),i),n) = $true)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_26])])).
% 1.77/0.61 thf(f2306,plain,(
% 1.77/0.61 spl14_81 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_81])])).
% 1.77/0.61 thf(f2328,plain,(
% 1.77/0.61 (i = n) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),i),n)) | (~spl14_26 | ~spl14_81)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f2321])).
% 1.77/0.61 thf(f2321,plain,(
% 1.77/0.61 ($true != $true) | (i = n) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),i),n)) | (~spl14_26 | ~spl14_81)),
% 1.77/0.61 inference(superposition,[],[f2307,f1895])).
% 1.77/0.61 thf(f1895,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),i),n) = $true) | ~spl14_26),
% 1.77/0.61 inference(avatar_component_clause,[],[f1893])).
% 1.77/0.61 thf(f2307,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | (X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl14_81),
% 1.77/0.61 inference(avatar_component_clause,[],[f2306])).
% 1.77/0.61 thf(f4028,plain,(
% 1.77/0.61 spl14_163),
% 1.77/0.61 inference(avatar_split_clause,[],[f1261,f4026])).
% 1.77/0.61 thf(f4026,plain,(
% 1.77/0.61 spl14_163 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_163])])).
% 1.77/0.61 thf(f1261,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f810])).
% 1.77/0.61 thf(f810,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X1),X2)))),
% 1.77/0.61 inference(rectify,[],[f122])).
% 1.77/0.61 thf(f122,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat,X6 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3)),X6) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X5),X6)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X3),X6)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_diff__mult__distrib)).
% 1.77/0.61 thf(f4024,plain,(
% 1.77/0.61 spl14_162),
% 1.77/0.61 inference(avatar_split_clause,[],[f1260,f4022])).
% 1.77/0.61 thf(f4022,plain,(
% 1.77/0.61 spl14_162 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_162])])).
% 1.77/0.61 thf(f1260,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f809])).
% 1.77/0.61 thf(f809,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),X2)))),
% 1.77/0.61 inference(rectify,[],[f121])).
% 1.77/0.61 thf(f121,axiom,(
% 1.77/0.61 ! [X6 : nat,X5 : nat,X3 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X6),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X6),X5)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X6),X3)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_diff__mult__distrib2)).
% 1.77/0.61 thf(f4020,plain,(
% 1.77/0.61 spl14_161),
% 1.77/0.61 inference(avatar_split_clause,[],[f1235,f4018])).
% 1.77/0.61 thf(f4018,plain,(
% 1.77/0.61 spl14_161 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1,X6 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK5(X0,X1),X3),X2)))) | ($true != wellorder(X0)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_161])])).
% 1.77/0.61 thf(f1235,plain,(
% 1.77/0.61 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK5(X0,X1),X3),X2)))) | ($true != wellorder(X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1042])).
% 1.77/0.61 thf(f1042,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK5(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK5(X0,X1),X3),X2))))))) | ($true != wellorder(X0)))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f960,f1041])).
% 1.77/0.61 thf(f1041,plain,(
% 1.77/0.61 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o] : (? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))))) => (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK5(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK5(X0,X1),X3),X2)))))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f960,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)))))) | ($true != wellorder(X0)))),
% 1.77/0.61 inference(ennf_transformation,[],[f593])).
% 1.77/0.61 thf(f593,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : $tType] : (($true = wellorder(X0)) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))) => ($true = vAPP(X1,$o,X3,X6))) => ($true = vAPP(X1,$o,X3,X5))) => ($true = vAPP(X1,$o,X3,X4))))),
% 1.77/0.61 inference(fool_elimination,[],[f592])).
% 1.77/0.61 thf(f592,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : $tType] : (wellorder(X0) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)) => vAPP(X1,$o,X3,X6)) => vAPP(X1,$o,X3,X5)) => vAPP(X1,$o,X3,X4)))),
% 1.77/0.61 inference(rectify,[],[f163])).
% 1.77/0.61 thf(f163,axiom,(
% 1.77/0.61 ! [X23 : $tType,X0 : $tType] : (wellorder(X23) => ! [X24 : X0 > X23,X20 : X0 > $o,X8 : X0] : (! [X25 : X0] : (! [X26 : X0] : (vAPP(X23,$o,vAPP(X23,sTfun(X23,$o),ord_less(X23),vAPP(X0,X23,X24,X26)),vAPP(X0,X23,X24,X25)) => vAPP(X0,$o,X20,X26)) => vAPP(X0,$o,X20,X25)) => vAPP(X0,$o,X20,X8)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_measure__induct)).
% 1.77/0.61 thf(f4016,plain,(
% 1.77/0.61 spl14_160),
% 1.77/0.61 inference(avatar_split_clause,[],[f1233,f4014])).
% 1.77/0.61 thf(f4014,plain,(
% 1.77/0.61 spl14_160 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1,X6 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK4(X0,X1),X3),X2)))) | ($true != wellorder(X0)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_160])])).
% 1.77/0.61 thf(f1233,plain,(
% 1.77/0.61 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK4(X0,X1),X3),X2)))) | ($true != wellorder(X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1040])).
% 1.77/0.61 thf(f1040,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK4(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK4(X0,X1),X3),X2))))))) | ($true != wellorder(X0)))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f959,f1039])).
% 1.77/0.61 thf(f1039,plain,(
% 1.77/0.61 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o] : (? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))))) => (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK4(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK4(X0,X1),X3),X2)))))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f959,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)))))) | ($true != wellorder(X0)))),
% 1.77/0.61 inference(ennf_transformation,[],[f591])).
% 1.77/0.61 thf(f591,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : $tType] : (($true = wellorder(X0)) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))) => ($true = vAPP(X1,$o,X3,X6))) => ($true = vAPP(X1,$o,X3,X5))) => ($true = vAPP(X1,$o,X3,X4))))),
% 1.77/0.61 inference(fool_elimination,[],[f590])).
% 1.77/0.61 thf(f590,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : $tType] : (wellorder(X0) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)) => vAPP(X1,$o,X3,X6)) => vAPP(X1,$o,X3,X5)) => vAPP(X1,$o,X3,X4)))),
% 1.77/0.61 inference(rectify,[],[f162])).
% 1.77/0.61 thf(f162,axiom,(
% 1.77/0.61 ! [X23 : $tType,X0 : $tType] : (wellorder(X23) => ! [X24 : X0 > X23,X20 : X0 > $o,X8 : X0] : (! [X25 : X0] : (! [X26 : X0] : (vAPP(X23,$o,vAPP(X23,sTfun(X23,$o),ord_less(X23),vAPP(X0,X23,X24,X26)),vAPP(X0,X23,X24,X25)) => vAPP(X0,$o,X20,X26)) => vAPP(X0,$o,X20,X25)) => vAPP(X0,$o,X20,X8)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_measure__induct__rule)).
% 1.77/0.61 thf(f4008,plain,(
% 1.77/0.61 spl14_159),
% 1.77/0.61 inference(avatar_split_clause,[],[f1304,f4006])).
% 1.77/0.61 thf(f4006,plain,(
% 1.77/0.61 spl14_159 <=> ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP0(X1),X2),X0)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_159])])).
% 1.77/0.61 thf(f1304,plain,(
% 1.77/0.61 ( ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X1,nat,X2,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0)))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP0(X1),X2),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1054])).
% 1.77/0.61 thf(f3874,plain,(
% 1.77/0.61 spl14_158),
% 1.77/0.61 inference(avatar_split_clause,[],[f1347,f3871])).
% 1.77/0.61 thf(f1347,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n) = $true)),
% 1.77/0.61 inference(cnf_transformation,[],[f773])).
% 1.77/0.61 thf(f773,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n) = $true)),
% 1.77/0.61 inference(fool_elimination,[],[f772])).
% 1.77/0.61 thf(f772,plain,(
% 1.77/0.61 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n)),
% 1.77/0.61 inference(rectify,[],[f3])).
% 1.77/0.61 thf(f3,axiom,(
% 1.77/0.61 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))),n)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_upper__bound)).
% 1.77/0.61 thf(f3869,plain,(
% 1.77/0.61 spl14_157),
% 1.77/0.61 inference(avatar_split_clause,[],[f1346,f3866])).
% 1.77/0.61 thf(f1346,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))) = $true)),
% 1.77/0.61 inference(cnf_transformation,[],[f771])).
% 1.77/0.61 thf(f771,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k))) = $true)),
% 1.77/0.61 inference(fool_elimination,[],[f770])).
% 1.77/0.61 thf(f770,plain,(
% 1.77/0.61 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k)))),
% 1.77/0.61 inference(rectify,[],[f4])).
% 1.77/0.61 thf(f4,axiom,(
% 1.77/0.61 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),n),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,i)),i)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),vAPP(nat,nat,p,k)),k)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_lower__bound)).
% 1.77/0.61 thf(f3864,plain,(
% 1.77/0.61 spl14_156),
% 1.77/0.61 inference(avatar_split_clause,[],[f1275,f3862])).
% 1.77/0.61 thf(f3862,plain,(
% 1.77/0.61 spl14_156 <=> ! [X4 : nat,X0 : nat > $o,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true != vAPP(nat,$o,X0,X4)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0))) | ($true != vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_156])])).
% 1.77/0.61 thf(f1275,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat > $o,X1 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true != vAPP(nat,$o,X0,X4)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0))) | ($true != vAPP(nat,$o,X0,X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1050])).
% 1.77/0.61 thf(f3860,plain,(
% 1.77/0.61 spl14_155),
% 1.77/0.61 inference(avatar_split_clause,[],[f1248,f3858])).
% 1.77/0.61 thf(f3858,plain,(
% 1.77/0.61 spl14_155 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_155])])).
% 1.77/0.61 thf(f1248,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f974])).
% 1.77/0.61 thf(f974,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 1.77/0.61 inference(flattening,[],[f973])).
% 1.77/0.61 thf(f973,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)))),
% 1.77/0.61 inference(ennf_transformation,[],[f613])).
% 1.77/0.61 thf(f613,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X1))))),
% 1.77/0.61 inference(fool_elimination,[],[f612])).
% 1.77/0.61 thf(f612,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)),X1)))),
% 1.77/0.61 inference(rectify,[],[f139])).
% 1.77/0.61 thf(f139,axiom,(
% 1.77/0.61 ! [X3 : nat,X5 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X3) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X5) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3)),X5)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_diff__less)).
% 1.77/0.61 thf(f3529,plain,(
% 1.77/0.61 spl14_154),
% 1.77/0.61 inference(avatar_split_clause,[],[f1195,f3527])).
% 1.77/0.61 thf(f3527,plain,(
% 1.77/0.61 spl14_154 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_154])])).
% 1.77/0.61 thf(f1195,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f941])).
% 1.77/0.61 thf(f941,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f533])).
% 1.77/0.61 thf(f533,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordered_ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)))))),
% 1.77/0.61 inference(fool_elimination,[],[f532])).
% 1.77/0.61 thf(f532,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))))),
% 1.77/0.61 inference(rectify,[],[f89])).
% 1.77/0.61 thf(f89,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_diff__right__mono)).
% 1.77/0.61 thf(f3525,plain,(
% 1.77/0.61 spl14_153),
% 1.77/0.61 inference(avatar_split_clause,[],[f1194,f3523])).
% 1.77/0.61 thf(f3523,plain,(
% 1.77/0.61 spl14_153 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_153])])).
% 1.77/0.61 thf(f1194,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f940])).
% 1.77/0.61 thf(f940,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f531])).
% 1.77/0.61 thf(f531,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordered_ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1)))))),
% 1.77/0.61 inference(fool_elimination,[],[f530])).
% 1.77/0.61 thf(f530,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1))))),
% 1.77/0.61 inference(rectify,[],[f90])).
% 1.77/0.61 thf(f90,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X7 : X0,X8 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X7),X8) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X9),X8)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X9),X7))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_diff__left__mono)).
% 1.77/0.61 thf(f3521,plain,(
% 1.77/0.61 spl14_152),
% 1.77/0.61 inference(avatar_split_clause,[],[f1193,f3519])).
% 1.77/0.61 thf(f3519,plain,(
% 1.77/0.61 spl14_152 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_152])])).
% 1.77/0.61 thf(f1193,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f939])).
% 1.77/0.61 thf(f939,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f529])).
% 1.77/0.61 thf(f529,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordered_ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)))))),
% 1.77/0.61 inference(fool_elimination,[],[f528])).
% 1.77/0.61 thf(f528,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))))),
% 1.77/0.61 inference(rectify,[],[f93])).
% 1.77/0.61 thf(f93,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X8),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_diff__strict__right__mono)).
% 1.77/0.61 thf(f3517,plain,(
% 1.77/0.61 spl14_151 | ~spl14_22 | spl14_131),
% 1.77/0.61 inference(avatar_split_clause,[],[f3472,f3118,f1848,f3514])).
% 1.77/0.61 thf(f3514,plain,(
% 1.77/0.61 spl14_151 <=> ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),i))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_151])])).
% 1.77/0.61 thf(f1848,plain,(
% 1.77/0.61 spl14_22 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_22])])).
% 1.77/0.61 thf(f3118,plain,(
% 1.77/0.61 spl14_131 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),i))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_131])])).
% 1.77/0.61 thf(f3472,plain,(
% 1.77/0.61 ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),i)) | (~spl14_22 | spl14_131)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f3471])).
% 1.77/0.61 thf(f3471,plain,(
% 1.77/0.61 ($true != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),i)) | (~spl14_22 | spl14_131)),
% 1.77/0.61 inference(superposition,[],[f3119,f1849])).
% 1.77/0.61 thf(f1849,plain,(
% 1.77/0.61 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl14_22),
% 1.77/0.61 inference(avatar_component_clause,[],[f1848])).
% 1.77/0.61 thf(f3119,plain,(
% 1.77/0.61 ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),i)) | spl14_131),
% 1.77/0.61 inference(avatar_component_clause,[],[f3118])).
% 1.77/0.61 thf(f3512,plain,(
% 1.77/0.61 spl14_150),
% 1.77/0.61 inference(avatar_split_clause,[],[f1192,f3510])).
% 1.77/0.61 thf(f3510,plain,(
% 1.77/0.61 spl14_150 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_150])])).
% 1.77/0.61 thf(f1192,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordered_ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f938])).
% 1.77/0.61 thf(f938,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordered_ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f527])).
% 1.77/0.61 thf(f527,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordered_ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1)))))),
% 1.77/0.61 inference(fool_elimination,[],[f526])).
% 1.77/0.61 thf(f526,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X1))))),
% 1.77/0.61 inference(rectify,[],[f94])).
% 1.77/0.61 thf(f94,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordered_ab_group_add(X0) => ! [X7 : X0,X8 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X7),X8) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X9),X8)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X9),X7))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_diff__strict__left__mono)).
% 1.77/0.61 thf(f3508,plain,(
% 1.77/0.61 spl14_149),
% 1.77/0.61 inference(avatar_split_clause,[],[f1158,f3506])).
% 1.77/0.61 thf(f3506,plain,(
% 1.77/0.61 spl14_149 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_149])])).
% 1.77/0.61 thf(f1158,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f904])).
% 1.77/0.61 thf(f904,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f459])).
% 1.77/0.61 thf(f459,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere623563068d_diff(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1)))))),
% 1.77/0.61 inference(fool_elimination,[],[f458])).
% 1.77/0.61 thf(f458,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X1))))),
% 1.77/0.61 inference(rectify,[],[f133])).
% 1.77/0.61 thf(f133,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9)),X8))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_le__add__diff)).
% 1.77/0.61 thf(f3504,plain,(
% 1.77/0.61 spl14_148),
% 1.77/0.61 inference(avatar_split_clause,[],[f1148,f3502])).
% 1.77/0.61 thf(f3502,plain,(
% 1.77/0.61 spl14_148 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ordere236663937imp_le(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_148])])).
% 1.77/0.61 thf(f1148,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ordere236663937imp_le(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f893])).
% 1.77/0.61 thf(f893,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)))) | (ordere236663937imp_le(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f439])).
% 1.77/0.61 thf(f439,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f438])).
% 1.77/0.61 thf(f438,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)))),
% 1.77/0.61 inference(rectify,[],[f200])).
% 1.77/0.61 thf(f200,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X9 : X0,X8 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X8)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X7)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_add__le__imp__le__left)).
% 1.77/0.61 thf(f3500,plain,(
% 1.77/0.61 spl14_147),
% 1.77/0.61 inference(avatar_split_clause,[],[f1147,f3498])).
% 1.77/0.61 thf(f3498,plain,(
% 1.77/0.61 spl14_147 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (ordere236663937imp_le(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_147])])).
% 1.77/0.61 thf(f1147,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (ordere236663937imp_le(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f892])).
% 1.77/0.61 thf(f892,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)))) | (ordere236663937imp_le(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f437])).
% 1.77/0.61 thf(f437,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f436])).
% 1.77/0.61 thf(f436,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))),
% 1.77/0.61 inference(rectify,[],[f199])).
% 1.77/0.61 thf(f199,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X8 : X0,X9 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_add__le__imp__le__right)).
% 1.77/0.61 thf(f3496,plain,(
% 1.77/0.61 spl14_146),
% 1.77/0.61 inference(avatar_split_clause,[],[f1146,f3494])).
% 1.77/0.61 thf(f3494,plain,(
% 1.77/0.61 spl14_146 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ordere236663937imp_le(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_146])])).
% 1.77/0.61 thf(f1146,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ordere236663937imp_le(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f891])).
% 1.77/0.61 thf(f891,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)))) | (ordere236663937imp_le(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f435])).
% 1.77/0.61 thf(f435,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f434])).
% 1.77/0.61 thf(f434,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)))),
% 1.77/0.61 inference(rectify,[],[f213])).
% 1.77/0.61 thf(f213,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X9 : X0,X8 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X8)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X7)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X8),X7)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_add__less__imp__less__left)).
% 1.77/0.61 thf(f3492,plain,(
% 1.77/0.61 spl14_145),
% 1.77/0.61 inference(avatar_split_clause,[],[f1145,f3490])).
% 1.77/0.61 thf(f3490,plain,(
% 1.77/0.61 spl14_145 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (ordere236663937imp_le(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_145])])).
% 1.77/0.61 thf(f1145,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (ordere236663937imp_le(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f890])).
% 1.77/0.61 thf(f890,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)))) | (ordere236663937imp_le(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f433])).
% 1.77/0.61 thf(f433,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f432])).
% 1.77/0.61 thf(f432,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)))),
% 1.77/0.61 inference(rectify,[],[f212])).
% 1.77/0.61 thf(f212,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X8 : X0,X9 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X8),X7)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__less__imp__less__right)).
% 1.77/0.61 thf(f3488,plain,(
% 1.77/0.61 spl14_144),
% 1.77/0.61 inference(avatar_split_clause,[],[f1127,f3486])).
% 1.77/0.61 thf(f3486,plain,(
% 1.77/0.61 spl14_144 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_144])])).
% 1.77/0.61 thf(f1127,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f867])).
% 1.77/0.61 thf(f867,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere779506340up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f397])).
% 1.77/0.61 thf(f397,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)))))),
% 1.77/0.61 inference(fool_elimination,[],[f396])).
% 1.77/0.61 thf(f396,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))))),
% 1.77/0.61 inference(rectify,[],[f202])).
% 1.77/0.61 thf(f202,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_add__right__mono)).
% 1.77/0.61 thf(f3484,plain,(
% 1.77/0.61 spl14_143),
% 1.77/0.61 inference(avatar_split_clause,[],[f1126,f3482])).
% 1.77/0.61 thf(f3482,plain,(
% 1.77/0.61 spl14_143 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_143])])).
% 1.77/0.61 thf(f1126,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f866])).
% 1.77/0.61 thf(f866,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere779506340up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f395])).
% 1.77/0.61 thf(f395,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)))))),
% 1.77/0.61 inference(fool_elimination,[],[f394])).
% 1.77/0.61 thf(f394,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))))),
% 1.77/0.61 inference(rectify,[],[f204])).
% 1.77/0.61 thf(f204,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X8)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X7))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_add__left__mono)).
% 1.77/0.61 thf(f3480,plain,(
% 1.77/0.61 spl14_142),
% 1.77/0.61 inference(avatar_split_clause,[],[f1109,f3478])).
% 1.77/0.61 thf(f3478,plain,(
% 1.77/0.61 spl14_142 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_142])])).
% 1.77/0.61 thf(f1109,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f846])).
% 1.77/0.61 thf(f846,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordere223160158up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f361])).
% 1.77/0.61 thf(f361,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)))))),
% 1.77/0.61 inference(fool_elimination,[],[f360])).
% 1.77/0.61 thf(f360,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))))),
% 1.77/0.61 inference(rectify,[],[f215])).
% 1.77/0.61 thf(f215,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X8),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X8)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X7))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_add__strict__left__mono)).
% 1.77/0.61 thf(f3476,plain,(
% 1.77/0.61 spl14_141),
% 1.77/0.61 inference(avatar_split_clause,[],[f1108,f3474])).
% 1.77/0.61 thf(f3474,plain,(
% 1.77/0.61 spl14_141 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_141])])).
% 1.77/0.61 thf(f1108,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f845])).
% 1.77/0.61 thf(f845,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordere223160158up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f359])).
% 1.77/0.61 thf(f359,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)))))),
% 1.77/0.61 inference(fool_elimination,[],[f358])).
% 1.77/0.61 thf(f358,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))))),
% 1.77/0.61 inference(rectify,[],[f214])).
% 1.77/0.61 thf(f214,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X8),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_add__strict__right__mono)).
% 1.77/0.61 thf(f3417,plain,(
% 1.77/0.61 spl14_140),
% 1.77/0.61 inference(avatar_split_clause,[],[f1311,f3415])).
% 1.77/0.61 thf(f3415,plain,(
% 1.77/0.61 spl14_140 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_140])])).
% 1.77/0.61 thf(f1311,plain,(
% 1.77/0.61 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1018])).
% 1.77/0.61 thf(f1018,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f1017])).
% 1.77/0.61 thf(f1017,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f701])).
% 1.77/0.61 thf(f701,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f700])).
% 1.77/0.61 thf(f700,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)))),
% 1.77/0.61 inference(rectify,[],[f240])).
% 1.77/0.61 thf(f240,axiom,(
% 1.77/0.61 ! [X6 : nat,X19 : nat,X5 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X6),X19) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X6),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X5),X19)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X3)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_less__add__eq__less)).
% 1.77/0.61 thf(f3413,plain,(
% 1.77/0.61 spl14_139),
% 1.77/0.61 inference(avatar_split_clause,[],[f1310,f3411])).
% 1.77/0.61 thf(f3411,plain,(
% 1.77/0.61 spl14_139 <=> ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X5 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_139])])).
% 1.77/0.61 thf(f1310,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1058])).
% 1.77/0.61 thf(f1058,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))))) & ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)))))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f1016,f1057])).
% 1.77/0.61 thf(f1057,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat] : (? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4)))) & ($true != vAPP(X0,$o,X1,X4))) => (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))))) & ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f1016,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | ? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4)))) & ($true != vAPP(X0,$o,X1,X4))))),
% 1.77/0.61 inference(ennf_transformation,[],[f812])).
% 1.77/0.61 thf(f812,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) => ? [X5 : X0] : (($true != vAPP(X0,$o,X1,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4))))) => ($true = vAPP(X0,$o,X1,X3)))),
% 1.77/0.61 inference(flattening,[],[f699])).
% 1.77/0.61 thf(f699,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (! [X4 : X0] : (~($true = vAPP(X0,$o,X1,X4)) => ? [X5 : X0] : (~($true = vAPP(X0,$o,X1,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4))))) => ($true = vAPP(X0,$o,X1,X3)))),
% 1.77/0.61 inference(fool_elimination,[],[f698])).
% 1.77/0.61 thf(f698,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (! [X4 : X0] : (~vAPP(X0,$o,X1,X4) => ? [X5 : X0] : (~vAPP(X0,$o,X1,X5) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4)))) => vAPP(X0,$o,X1,X3))),
% 1.77/0.61 inference(rectify,[],[f179])).
% 1.77/0.61 thf(f179,axiom,(
% 1.77/0.61 ! [X0 : $tType,X20 : X0 > $o,X28 : X0 > nat,X10 : X0] : (! [X25 : X0] : (~vAPP(X0,$o,X20,X25) => ? [X26 : X0] : (~vAPP(X0,$o,X20,X26) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X28,X26)),vAPP(X0,nat,X28,X25)))) => vAPP(X0,$o,X20,X10))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_infinite__descent__measure)).
% 1.77/0.61 thf(f3259,plain,(
% 1.77/0.61 spl14_138),
% 1.77/0.61 inference(avatar_split_clause,[],[f1307,f3257])).
% 1.77/0.61 thf(f3257,plain,(
% 1.77/0.61 spl14_138 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0 > nat] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP0(X0),X1),X2)) | (zero_zero(nat) = vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK12(X0),X2),X1))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_138])])).
% 1.77/0.61 thf(f1307,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP0(X0),X1),X2)) | (zero_zero(nat) = vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK12(X0),X2),X1)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1056])).
% 1.77/0.61 thf(f1056,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP0(X0),X1),X2)) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK12(X0),X2),X1))) & (zero_zero(nat) = vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK12(X0),X2),X1)))))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f1032,f1055])).
% 1.77/0.61 thf(f1055,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o] : (? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & (zero_zero(nat) = vAPP(X0,nat,X1,X4))) => (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK12(X0),X2),X1))) & (zero_zero(nat) = vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK12(X0),X2),X1)))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f1032,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP0(X0),X1),X2)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & (zero_zero(nat) = vAPP(X0,nat,X1,X4))))),
% 1.77/0.61 inference(definition_folding,[],[f1015,f1031])).
% 1.77/0.61 thf(f1015,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ? [X5 : X0] : (! [X6 : X0] : (($true = vAPP(X0,$o,X2,X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))) & ($true != vAPP(X0,$o,X2,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5)))) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & (zero_zero(nat) = vAPP(X0,nat,X1,X4))))),
% 1.77/0.61 inference(flattening,[],[f1014])).
% 1.77/0.61 thf(f1014,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : ((($true = vAPP(X0,$o,X2,X3)) | ? [X5 : X0] : ((! [X6 : X0] : (($true = vAPP(X0,$o,X2,X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))) & ($true != vAPP(X0,$o,X2,X5))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5))))) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & (zero_zero(nat) = vAPP(X0,nat,X1,X4))))),
% 1.77/0.61 inference(ennf_transformation,[],[f811])).
% 1.77/0.61 thf(f811,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (! [X4 : X0] : ((zero_zero(nat) = vAPP(X0,nat,X1,X4)) => ($true = vAPP(X0,$o,X2,X4))) => (! [X5 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5))) => (($true != vAPP(X0,$o,X2,X5)) => ? [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))))) => ($true = vAPP(X0,$o,X2,X3))))),
% 1.77/0.61 inference(flattening,[],[f697])).
% 1.77/0.61 thf(f697,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (! [X4 : X0] : ((zero_zero(nat) = vAPP(X0,nat,X1,X4)) => ($true = vAPP(X0,$o,X2,X4))) => (! [X5 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5))) => (~($true = vAPP(X0,$o,X2,X5)) => ? [X6 : X0] : (~($true = vAPP(X0,$o,X2,X6)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5)))))) => ($true = vAPP(X0,$o,X2,X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f696])).
% 1.77/0.61 thf(f696,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0 > nat,X2 : X0 > $o,X3 : X0] : (! [X4 : X0] : ((zero_zero(nat) = vAPP(X0,nat,X1,X4)) => vAPP(X0,$o,X2,X4)) => (! [X5 : X0] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X1,X5)) => (~vAPP(X0,$o,X2,X5) => ? [X6 : X0] : (~vAPP(X0,$o,X2,X6) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X6)),vAPP(X0,nat,X1,X5))))) => vAPP(X0,$o,X2,X3)))),
% 1.77/0.61 inference(rectify,[],[f220])).
% 1.77/0.61 thf(f220,axiom,(
% 1.77/0.61 ! [X0 : $tType,X28 : X0 > nat,X20 : X0 > $o,X10 : X0] : (! [X25 : X0] : ((zero_zero(nat) = vAPP(X0,nat,X28,X25)) => vAPP(X0,$o,X20,X25)) => (! [X25 : X0] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(X0,nat,X28,X25)) => (~vAPP(X0,$o,X20,X25) => ? [X26 : X0] : (~vAPP(X0,$o,X20,X26) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X28,X26)),vAPP(X0,nat,X28,X25))))) => vAPP(X0,$o,X20,X10)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_infinite__descent0__measure)).
% 1.77/0.61 thf(f3154,plain,(
% 1.77/0.61 spl14_137),
% 1.77/0.61 inference(avatar_split_clause,[],[f1350,f3152])).
% 1.77/0.61 thf(f3152,plain,(
% 1.77/0.61 spl14_137 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4)) | (comm_monoid_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_137])])).
% 1.77/0.61 thf(f1350,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4)) | (comm_monoid_add(X0) != $true)) )),
% 1.77/0.61 inference(equality_resolution,[],[f1101])).
% 1.77/0.61 thf(f1101,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4)) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1) | (comm_monoid_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f838])).
% 1.77/0.61 thf(f838,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4)) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1)) | (comm_monoid_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f345])).
% 1.77/0.61 thf(f345,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4))))),
% 1.77/0.61 inference(fool_elimination,[],[f344])).
% 1.77/0.61 thf(f344,plain,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4))))),
% 1.77/0.61 inference(rectify,[],[f172])).
% 1.77/0.61 thf(f172,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X18 : X0,X6 : X0,X8 : X0,X7 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X8) = X18) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X18),X7))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_group__cancel_Oadd1)).
% 1.77/0.61 thf(f3150,plain,(
% 1.77/0.61 spl14_136),
% 1.77/0.61 inference(avatar_split_clause,[],[f1349,f3148])).
% 1.77/0.61 thf(f3148,plain,(
% 1.77/0.61 spl14_136 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (comm_monoid_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_136])])).
% 1.77/0.61 thf(f1349,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (comm_monoid_add(X0) != $true)) )),
% 1.77/0.61 inference(equality_resolution,[],[f1100])).
% 1.77/0.61 thf(f1100,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1) | (comm_monoid_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f837])).
% 1.77/0.61 thf(f837,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1)) | (comm_monoid_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f343])).
% 1.77/0.61 thf(f343,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)))))),
% 1.77/0.61 inference(fool_elimination,[],[f342])).
% 1.77/0.61 thf(f342,plain,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)))))),
% 1.77/0.61 inference(rectify,[],[f171])).
% 1.77/0.61 thf(f171,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X27 : X0,X6 : X0,X7 : X0,X8 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7) = X27) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X27) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_group__cancel_Oadd2)).
% 1.77/0.61 thf(f3146,plain,(
% 1.77/0.61 spl14_135),
% 1.77/0.61 inference(avatar_split_clause,[],[f1348,f3144])).
% 1.77/0.61 thf(f3144,plain,(
% 1.77/0.61 spl14_135 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4)) | (ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_135])])).
% 1.77/0.61 thf(f1348,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4)) | (ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(equality_resolution,[],[f1082])).
% 1.77/0.61 thf(f1082,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1) | (ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f818])).
% 1.77/0.61 thf(f818,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1)) | (ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f307])).
% 1.77/0.61 thf(f307,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)))))),
% 1.77/0.61 inference(fool_elimination,[],[f306])).
% 1.77/0.61 thf(f306,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)))))),
% 1.77/0.61 inference(rectify,[],[f105])).
% 1.77/0.61 thf(f105,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ab_group_add(X0) => ! [X18 : X0,X6 : X0,X8 : X0,X7 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X8) = X18) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X18),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X7)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_group__cancel_Osub1)).
% 1.77/0.61 thf(f3142,plain,(
% 1.77/0.61 spl14_134),
% 1.77/0.61 inference(avatar_split_clause,[],[f1308,f3140])).
% 1.77/0.61 thf(f3140,plain,(
% 1.77/0.61 spl14_134 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0 > nat] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP0(X0),X1),X2)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK12(X0),X2),X1))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_134])])).
% 1.77/0.61 thf(f1308,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),$o),sP0(X0),X1),X2)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,nat),X0),sK12(X0),X2),X1)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1056])).
% 1.77/0.61 thf(f3138,plain,(
% 1.77/0.61 spl14_133),
% 1.77/0.61 inference(avatar_split_clause,[],[f1178,f3136])).
% 1.77/0.61 thf(f3136,plain,(
% 1.77/0.61 spl14_133 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | (group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_133])])).
% 1.77/0.61 thf(f1178,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | (group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f924])).
% 1.77/0.61 thf(f924,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | (group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f499])).
% 1.77/0.61 thf(f499,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f498])).
% 1.77/0.61 thf(f498,plain,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))))),
% 1.77/0.61 inference(rectify,[],[f101])).
% 1.77/0.61 thf(f101,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X9)),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_diff__diff__eq2)).
% 1.77/0.61 thf(f3134,plain,(
% 1.77/0.61 spl14_132),
% 1.77/0.61 inference(avatar_split_clause,[],[f1177,f3132])).
% 1.77/0.61 thf(f3132,plain,(
% 1.77/0.61 spl14_132 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_132])])).
% 1.77/0.61 thf(f1177,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f923])).
% 1.77/0.61 thf(f923,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f497])).
% 1.77/0.61 thf(f497,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)))),
% 1.77/0.61 inference(fool_elimination,[],[f496])).
% 1.77/0.61 thf(f496,plain,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)))),
% 1.77/0.61 inference(rectify,[],[f99])).
% 1.77/0.61 thf(f99,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X9)),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_diff__add__eq__diff__diff__swap)).
% 1.77/0.61 thf(f3121,plain,(
% 1.77/0.61 spl14_131 | ~spl14_28 | ~spl14_63 | ~spl14_104),
% 1.77/0.61 inference(avatar_split_clause,[],[f2845,f2697,f2127,f1905,f3118])).
% 1.77/0.61 thf(f1905,plain,(
% 1.77/0.61 spl14_28 <=> ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_28])])).
% 1.77/0.61 thf(f2127,plain,(
% 1.77/0.61 spl14_63 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),n),k)),i) = $true)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_63])])).
% 1.77/0.61 thf(f2697,plain,(
% 1.77/0.61 spl14_104 <=> (n = k)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_104])])).
% 1.77/0.61 thf(f2845,plain,(
% 1.77/0.61 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),i)) | (~spl14_28 | ~spl14_63 | ~spl14_104)),
% 1.77/0.61 inference(forward_demodulation,[],[f2841,f1906])).
% 1.77/0.61 thf(f1906,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0))) ) | ~spl14_28),
% 1.77/0.61 inference(avatar_component_clause,[],[f1905])).
% 1.77/0.61 thf(f2841,plain,(
% 1.77/0.61 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),n),n)),i)) | (~spl14_63 | ~spl14_104)),
% 1.77/0.61 inference(superposition,[],[f2129,f2699])).
% 1.77/0.61 thf(f2699,plain,(
% 1.77/0.61 (n = k) | ~spl14_104),
% 1.77/0.61 inference(avatar_component_clause,[],[f2697])).
% 1.77/0.61 thf(f2129,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),n),k)),i) = $true) | ~spl14_63),
% 1.77/0.61 inference(avatar_component_clause,[],[f2127])).
% 1.77/0.61 thf(f3116,plain,(
% 1.77/0.61 spl14_130),
% 1.77/0.61 inference(avatar_split_clause,[],[f1176,f3114])).
% 1.77/0.61 thf(f3114,plain,(
% 1.77/0.61 spl14_130 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_130])])).
% 1.77/0.61 thf(f1176,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f922])).
% 1.77/0.61 thf(f922,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f495])).
% 1.77/0.61 thf(f495,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(fool_elimination,[],[f494])).
% 1.77/0.61 thf(f494,plain,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(rectify,[],[f102])).
% 1.77/0.61 thf(f102,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X9)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7)),X9)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add__diff__eq)).
% 1.77/0.61 thf(f3112,plain,(
% 1.77/0.61 spl14_129),
% 1.77/0.61 inference(avatar_split_clause,[],[f1118,f3110])).
% 1.77/0.61 thf(f3110,plain,(
% 1.77/0.61 spl14_129 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_129])])).
% 1.77/0.61 thf(f1118,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel146912293up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f858])).
% 1.77/0.61 thf(f858,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f379])).
% 1.77/0.61 thf(f379,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))))),
% 1.77/0.61 inference(fool_elimination,[],[f378])).
% 1.77/0.61 thf(f378,plain,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))))),
% 1.77/0.61 inference(rectify,[],[f47])).
% 1.77/0.61 thf(f47,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X8 : X0,X9 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X9)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X7)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__diff__cancel__right)).
% 1.77/0.61 thf(f3108,plain,(
% 1.77/0.61 spl14_128),
% 1.77/0.61 inference(avatar_split_clause,[],[f1117,f3106])).
% 1.77/0.61 thf(f3106,plain,(
% 1.77/0.61 spl14_128 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_128])])).
% 1.77/0.61 thf(f1117,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (cancel146912293up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f857])).
% 1.77/0.61 thf(f857,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f377])).
% 1.77/0.61 thf(f377,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)))),
% 1.77/0.61 inference(fool_elimination,[],[f376])).
% 1.77/0.61 thf(f376,plain,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)))),
% 1.77/0.61 inference(rectify,[],[f85])).
% 1.77/0.61 thf(f85,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X8 : X0,X9 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X9)),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X7)),X9)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_cancel__ab__semigroup__add__class_Odiff__right__commute)).
% 1.77/0.61 thf(f3104,plain,(
% 1.77/0.61 spl14_127),
% 1.77/0.61 inference(avatar_split_clause,[],[f1116,f3102])).
% 1.77/0.61 thf(f3102,plain,(
% 1.77/0.61 spl14_127 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_127])])).
% 1.77/0.61 thf(f1116,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f856])).
% 1.77/0.61 thf(f856,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f375])).
% 1.77/0.61 thf(f375,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f374])).
% 1.77/0.61 thf(f374,plain,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))))),
% 1.77/0.61 inference(rectify,[],[f98])).
% 1.77/0.61 thf(f98,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X7)),X9) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_diff__diff__add)).
% 1.77/0.61 thf(f3100,plain,(
% 1.77/0.61 spl14_126),
% 1.77/0.61 inference(avatar_split_clause,[],[f1115,f3098])).
% 1.77/0.61 thf(f3098,plain,(
% 1.77/0.61 spl14_126 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_126])])).
% 1.77/0.61 thf(f1115,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (cancel146912293up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f855])).
% 1.77/0.61 thf(f855,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f373])).
% 1.77/0.61 thf(f373,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f372])).
% 1.77/0.61 thf(f372,plain,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))))),
% 1.77/0.61 inference(rectify,[],[f49])).
% 1.77/0.61 thf(f49,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X9 : X0,X8 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X8)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X7))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_add__diff__cancel__left)).
% 1.77/0.61 thf(f3096,plain,(
% 1.77/0.61 spl14_125),
% 1.77/0.61 inference(avatar_split_clause,[],[f1093,f3094])).
% 1.77/0.61 thf(f3094,plain,(
% 1.77/0.61 spl14_125 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_semigroup_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_125])])).
% 1.77/0.61 thf(f1093,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_semigroup_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f830])).
% 1.77/0.61 thf(f830,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_semigroup_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f329])).
% 1.77/0.61 thf(f329,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(fool_elimination,[],[f328])).
% 1.77/0.61 thf(f328,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(rectify,[],[f174])).
% 1.77/0.61 thf(f174,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7)),X9)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_ab__semigroup__add__class_Oadd__ac_I1_J)).
% 1.77/0.61 thf(f3092,plain,(
% 1.77/0.61 spl14_124),
% 1.77/0.61 inference(avatar_split_clause,[],[f1092,f3090])).
% 1.77/0.61 thf(f3090,plain,(
% 1.77/0.61 spl14_124 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_semigroup_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_124])])).
% 1.77/0.61 thf(f1092,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_semigroup_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f829])).
% 1.77/0.61 thf(f829,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_semigroup_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f327])).
% 1.77/0.61 thf(f327,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f326])).
% 1.77/0.61 thf(f326,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))))),
% 1.77/0.61 inference(rectify,[],[f166])).
% 1.77/0.61 thf(f166,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X7 : X0,X8 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X9)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_add_Oleft__commute)).
% 1.77/0.61 thf(f3088,plain,(
% 1.77/0.61 spl14_123),
% 1.77/0.61 inference(avatar_split_clause,[],[f1091,f3086])).
% 1.77/0.61 thf(f3086,plain,(
% 1.77/0.61 spl14_123 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (ab_semigroup_mult(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_123])])).
% 1.77/0.61 thf(f1091,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (ab_semigroup_mult(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f828])).
% 1.77/0.61 thf(f828,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (ab_semigroup_mult(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f325])).
% 1.77/0.61 thf(f325,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ab_semigroup_mult(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(fool_elimination,[],[f324])).
% 1.77/0.61 thf(f324,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_mult(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(rectify,[],[f178])).
% 1.77/0.61 thf(f178,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_mult(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X7),X9)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X8),X7)),X9)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_ab__semigroup__mult__class_Omult__ac_I1_J)).
% 1.77/0.61 thf(f3084,plain,(
% 1.77/0.61 spl14_122),
% 1.77/0.61 inference(avatar_split_clause,[],[f1090,f3082])).
% 1.77/0.61 thf(f3082,plain,(
% 1.77/0.61 spl14_122 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (ab_semigroup_mult(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_122])])).
% 1.77/0.61 thf(f1090,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (ab_semigroup_mult(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f827])).
% 1.77/0.61 thf(f827,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))) | (ab_semigroup_mult(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f323])).
% 1.77/0.61 thf(f323,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ab_semigroup_mult(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))),
% 1.77/0.61 inference(fool_elimination,[],[f322])).
% 1.77/0.61 thf(f322,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_mult(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X3))))),
% 1.77/0.61 inference(rectify,[],[f175])).
% 1.77/0.61 thf(f175,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_mult(X0) => ! [X7 : X0,X8 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X7),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X8),X9)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X7),X9))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_mult_Oleft__commute)).
% 1.77/0.61 thf(f3080,plain,(
% 1.77/0.61 spl14_121),
% 1.77/0.61 inference(avatar_split_clause,[],[f1081,f3078])).
% 1.77/0.61 thf(f3078,plain,(
% 1.77/0.61 spl14_121 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2)) | (ab_group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_121])])).
% 1.77/0.61 thf(f1081,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2)) | (ab_group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f817])).
% 1.77/0.61 thf(f817,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2)) | (ab_group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f305])).
% 1.77/0.61 thf(f305,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2)))),
% 1.77/0.61 inference(fool_elimination,[],[f304])).
% 1.77/0.61 thf(f304,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2)))),
% 1.77/0.61 inference(rectify,[],[f100])).
% 1.77/0.61 thf(f100,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ab_group_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X7)),X9) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X9)),X7)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_diff__add__eq)).
% 1.77/0.61 thf(f3076,plain,(
% 1.77/0.61 spl14_120),
% 1.77/0.61 inference(avatar_split_clause,[],[f1080,f3074])).
% 1.77/0.61 thf(f3074,plain,(
% 1.77/0.61 spl14_120 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (semigroup_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_120])])).
% 1.77/0.61 thf(f1080,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (semigroup_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f816])).
% 1.77/0.61 thf(f816,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (semigroup_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f303])).
% 1.77/0.61 thf(f303,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((semigroup_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(fool_elimination,[],[f302])).
% 1.77/0.61 thf(f302,plain,(
% 1.77/0.61 ! [X0 : $tType] : (semigroup_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(rectify,[],[f170])).
% 1.77/0.61 thf(f170,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (semigroup_add(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X9)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7)),X9)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_add_Oassoc)).
% 1.77/0.61 thf(f3072,plain,(
% 1.77/0.61 spl14_119),
% 1.77/0.61 inference(avatar_split_clause,[],[f1079,f3070])).
% 1.77/0.61 thf(f3070,plain,(
% 1.77/0.61 spl14_119 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (semigroup_mult(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_119])])).
% 1.77/0.61 thf(f1079,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (semigroup_mult(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f815])).
% 1.77/0.61 thf(f815,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)) | (semigroup_mult(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f301])).
% 1.77/0.61 thf(f301,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((semigroup_mult(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(fool_elimination,[],[f300])).
% 1.77/0.61 thf(f300,plain,(
% 1.77/0.61 ! [X0 : $tType] : (semigroup_mult(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X1),X2)),X3)))),
% 1.77/0.61 inference(rectify,[],[f177])).
% 1.77/0.61 thf(f177,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (semigroup_mult(X0) => ! [X8 : X0,X7 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X7),X9)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X8),X7)),X9)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_mult_Oassoc)).
% 1.77/0.61 thf(f3000,plain,(
% 1.77/0.61 spl14_118),
% 1.77/0.61 inference(avatar_split_clause,[],[f1301,f2998])).
% 1.77/0.61 thf(f2998,plain,(
% 1.77/0.61 spl14_118 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_118])])).
% 1.77/0.61 thf(f1301,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1011])).
% 1.77/0.61 thf(f1011,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f691])).
% 1.77/0.61 thf(f691,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 1.77/0.61 inference(fool_elimination,[],[f690])).
% 1.77/0.61 thf(f690,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 1.77/0.61 inference(rectify,[],[f253])).
% 1.77/0.61 thf(f253,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),X6)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X12),X6)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__le__mono1)).
% 1.77/0.61 thf(f2996,plain,(
% 1.77/0.61 spl14_117),
% 1.77/0.61 inference(avatar_split_clause,[],[f1300,f2994])).
% 1.77/0.61 thf(f2994,plain,(
% 1.77/0.61 spl14_117 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_117])])).
% 1.77/0.61 thf(f1300,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1010])).
% 1.77/0.61 thf(f1010,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f689])).
% 1.77/0.61 thf(f689,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))))),
% 1.77/0.61 inference(fool_elimination,[],[f688])).
% 1.77/0.61 thf(f688,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)))),
% 1.77/0.61 inference(rectify,[],[f113])).
% 1.77/0.61 thf(f113,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X19)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),X19)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_diff__le__mono)).
% 1.77/0.61 thf(f2992,plain,(
% 1.77/0.61 spl14_116),
% 1.77/0.61 inference(avatar_split_clause,[],[f1299,f2990])).
% 1.77/0.61 thf(f2990,plain,(
% 1.77/0.61 spl14_116 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_116])])).
% 1.77/0.61 thf(f1299,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1009])).
% 1.77/0.61 thf(f1009,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f687])).
% 1.77/0.61 thf(f687,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0))))),
% 1.77/0.61 inference(fool_elimination,[],[f686])).
% 1.77/0.61 thf(f686,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),X0)))),
% 1.77/0.61 inference(rectify,[],[f110])).
% 1.77/0.61 thf(f110,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X19),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X19),X5)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_diff__le__mono2)).
% 1.77/0.61 thf(f2988,plain,(
% 1.77/0.61 spl14_115),
% 1.77/0.61 inference(avatar_split_clause,[],[f1282,f2986])).
% 1.77/0.61 thf(f2986,plain,(
% 1.77/0.61 spl14_115 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_115])])).
% 1.77/0.61 thf(f1282,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f986])).
% 1.77/0.61 thf(f986,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f653])).
% 1.77/0.61 thf(f653,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 1.77/0.61 inference(fool_elimination,[],[f652])).
% 1.77/0.61 thf(f652,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 1.77/0.61 inference(rectify,[],[f243])).
% 1.77/0.61 thf(f243,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),X6)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X12),X6)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_add__less__mono1)).
% 1.77/0.61 thf(f2984,plain,(
% 1.77/0.61 ~spl14_114 | spl14_2 | ~spl14_104),
% 1.77/0.61 inference(avatar_split_clause,[],[f2844,f2697,f1748,f2981])).
% 1.77/0.61 thf(f1748,plain,(
% 1.77/0.61 spl14_2 <=> (i = k)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_2])])).
% 1.77/0.61 thf(f2844,plain,(
% 1.77/0.61 (i != n) | (spl14_2 | ~spl14_104)),
% 1.77/0.61 inference(superposition,[],[f1750,f2699])).
% 1.77/0.61 thf(f1750,plain,(
% 1.77/0.61 (i != k) | spl14_2),
% 1.77/0.61 inference(avatar_component_clause,[],[f1748])).
% 1.77/0.61 thf(f2972,plain,(
% 1.77/0.61 spl14_113),
% 1.77/0.61 inference(avatar_split_clause,[],[f1274,f2970])).
% 1.77/0.61 thf(f2970,plain,(
% 1.77/0.61 spl14_113 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0)),X2)) | ($true != vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_113])])).
% 1.77/0.61 thf(f1274,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0)),X2)) | ($true != vAPP(nat,$o,X0,X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1050])).
% 1.77/0.61 thf(f2861,plain,(
% 1.77/0.61 spl14_112),
% 1.77/0.61 inference(avatar_split_clause,[],[f1741,f2859])).
% 1.77/0.61 thf(f2859,plain,(
% 1.77/0.61 spl14_112 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_112])])).
% 1.77/0.61 thf(f1741,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) )),
% 1.77/0.61 inference(forward_demodulation,[],[f1259,f1258])).
% 1.77/0.61 thf(f1258,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f807])).
% 1.77/0.61 thf(f807,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 1.77/0.61 inference(rectify,[],[f68])).
% 1.77/0.61 thf(f68,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X6 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X4),X12)),X6) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X12),X6)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_diff__diff__left)).
% 1.77/0.61 thf(f1259,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f808])).
% 1.77/0.61 thf(f808,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X1))),
% 1.77/0.61 inference(rectify,[],[f87])).
% 1.77/0.61 thf(f87,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X6 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X4),X12)),X6) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X4),X6)),X12))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_diff__commute)).
% 1.77/0.61 thf(f2857,plain,(
% 1.77/0.61 spl14_111),
% 1.77/0.61 inference(avatar_split_clause,[],[f1258,f2855])).
% 1.77/0.61 thf(f2855,plain,(
% 1.77/0.61 spl14_111 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_111])])).
% 1.77/0.61 thf(f2853,plain,(
% 1.77/0.61 spl14_110),
% 1.77/0.61 inference(avatar_split_clause,[],[f1255,f2851])).
% 1.77/0.61 thf(f2851,plain,(
% 1.77/0.61 spl14_110 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_110])])).
% 1.77/0.61 thf(f1255,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f804])).
% 1.77/0.61 thf(f804,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 1.77/0.61 inference(rectify,[],[f119])).
% 1.77/0.61 thf(f119,axiom,(
% 1.77/0.61 ! [X5 : nat,X6 : nat,X3 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X5),X6)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X6)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_diff__cancel2)).
% 1.77/0.61 thf(f2849,plain,(
% 1.77/0.61 spl14_109),
% 1.77/0.61 inference(avatar_split_clause,[],[f1254,f2847])).
% 1.77/0.61 thf(f2847,plain,(
% 1.77/0.61 spl14_109 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_109])])).
% 1.77/0.61 thf(f1254,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f803])).
% 1.77/0.61 thf(f803,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))),
% 1.77/0.61 inference(rectify,[],[f120])).
% 1.77/0.61 thf(f120,axiom,(
% 1.77/0.61 ! [X6 : nat,X5 : nat,X3 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X6),X5)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X6),X3)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Nat_Odiff__cancel)).
% 1.77/0.61 thf(f2818,plain,(
% 1.77/0.61 spl14_108),
% 1.77/0.61 inference(avatar_split_clause,[],[f1305,f2816])).
% 1.77/0.61 thf(f2816,plain,(
% 1.77/0.61 spl14_108 <=> ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true != vAPP(X1,$o,X0,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP0(X1),X2),X0)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_108])])).
% 1.77/0.61 thf(f1305,plain,(
% 1.77/0.61 ( ! [X1 : $tType,X2 : X1 > nat,X0 : X1 > $o] : (($true != vAPP(X1,$o,X0,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),X1),sK11(X1),X2),X0))) | ($true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X1,nat),sTfun(sTfun(X1,$o),$o),sP0(X1),X2),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1054])).
% 1.77/0.61 thf(f2735,plain,(
% 1.77/0.61 spl14_107),
% 1.77/0.61 inference(avatar_split_clause,[],[f1169,f2733])).
% 1.77/0.61 thf(f2733,plain,(
% 1.77/0.61 spl14_107 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK1(X0),X2),X1)) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (canoni770627133id_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_107])])).
% 1.77/0.61 thf(f1169,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK1(X0),X2),X1)) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (canoni770627133id_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1034])).
% 1.77/0.61 thf(f1034,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK1(X0),X2),X1)) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (canoni770627133id_add(X0) != $true))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f915,f1033])).
% 1.77/0.61 thf(f1033,plain,(
% 1.77/0.61 ! [X0 : $tType,X1 : X0,X2 : X0] : (? [X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) = X2) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK1(X0),X2),X1)) = X2))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f915,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (? [X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (canoni770627133id_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f481])).
% 1.77/0.61 thf(f481,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ~! [X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) != X2)))),
% 1.77/0.61 inference(fool_elimination,[],[f480])).
% 1.77/0.61 thf(f480,plain,(
% 1.77/0.61 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => ~! [X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) != X2)))),
% 1.77/0.61 inference(rectify,[],[f203])).
% 1.77/0.61 thf(f203,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X8 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => ~! [X35 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X35) != X7)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_less__eqE)).
% 1.77/0.61 thf(f2731,plain,(
% 1.77/0.61 spl14_106),
% 1.77/0.61 inference(avatar_split_clause,[],[f1150,f2729])).
% 1.77/0.61 thf(f2729,plain,(
% 1.77/0.61 spl14_106 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_106])])).
% 1.77/0.61 thf(f1150,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f895])).
% 1.77/0.61 thf(f895,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f443])).
% 1.77/0.61 thf(f443,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere623563068d_diff(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2)))),
% 1.77/0.61 inference(fool_elimination,[],[f442])).
% 1.77/0.61 thf(f442,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2)))),
% 1.77/0.61 inference(rectify,[],[f134])).
% 1.77/0.61 thf(f134,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X8 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X8)),X8) = X7)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_ordered__cancel__comm__monoid__diff__class_Odiff__add)).
% 1.77/0.61 thf(f2727,plain,(
% 1.77/0.61 spl14_105),
% 1.77/0.61 inference(avatar_split_clause,[],[f1149,f2725])).
% 1.77/0.61 thf(f2725,plain,(
% 1.77/0.61 spl14_105 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_105])])).
% 1.77/0.61 thf(f1149,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere623563068d_diff(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f894])).
% 1.77/0.61 thf(f894,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere623563068d_diff(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f441])).
% 1.77/0.61 thf(f441,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ordere623563068d_diff(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = X2)))),
% 1.77/0.61 inference(fool_elimination,[],[f440])).
% 1.77/0.61 thf(f440,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) = X2)))),
% 1.77/0.61 inference(rectify,[],[f126])).
% 1.77/0.61 thf(f126,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ordere623563068d_diff(X0) => ! [X8 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X7) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X8)) = X7)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse)).
% 1.77/0.61 thf(f2700,plain,(
% 1.77/0.61 spl14_103 | spl14_104 | ~spl14_27 | ~spl14_81),
% 1.77/0.61 inference(avatar_split_clause,[],[f2327,f2306,f1898,f2697,f2693])).
% 1.77/0.61 thf(f2693,plain,(
% 1.77/0.61 spl14_103 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),k),n))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_103])])).
% 1.77/0.61 thf(f1898,plain,(
% 1.77/0.61 spl14_27 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),k),n) = $true)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_27])])).
% 1.77/0.61 thf(f2327,plain,(
% 1.77/0.61 (n = k) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),k),n)) | (~spl14_27 | ~spl14_81)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f2322])).
% 1.77/0.61 thf(f2322,plain,(
% 1.77/0.61 ($true != $true) | (n = k) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),k),n)) | (~spl14_27 | ~spl14_81)),
% 1.77/0.61 inference(superposition,[],[f2307,f1900])).
% 1.77/0.61 thf(f1900,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),k),n) = $true) | ~spl14_27),
% 1.77/0.61 inference(avatar_component_clause,[],[f1898])).
% 1.77/0.61 thf(f2691,plain,(
% 1.77/0.61 spl14_102),
% 1.77/0.61 inference(avatar_split_clause,[],[f1296,f2689])).
% 1.77/0.61 thf(f2689,plain,(
% 1.77/0.61 spl14_102 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_102])])).
% 1.77/0.61 thf(f1296,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1006])).
% 1.77/0.61 thf(f1006,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f1005])).
% 1.77/0.61 thf(f1005,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f681])).
% 1.77/0.61 thf(f681,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2))))),
% 1.77/0.61 inference(fool_elimination,[],[f680])).
% 1.77/0.61 thf(f680,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)))),
% 1.77/0.61 inference(rectify,[],[f192])).
% 1.77/0.61 thf(f192,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X12) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X12),X6) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X6)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_le__trans)).
% 1.77/0.61 thf(f2687,plain,(
% 1.77/0.61 spl14_101),
% 1.77/0.61 inference(avatar_split_clause,[],[f1239,f2685])).
% 1.77/0.61 thf(f2685,plain,(
% 1.77/0.61 spl14_101 <=> ! [X0 : nat > $o,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK6,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_101])])).
% 1.77/0.61 thf(f1239,plain,(
% 1.77/0.61 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK6,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1044])).
% 1.77/0.61 thf(f1044,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK6,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK6,X0)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f962,f1043])).
% 1.77/0.61 thf(f1043,plain,(
% 1.77/0.61 ! [X0 : nat > $o] : (? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) & ($true != vAPP(nat,$o,X0,X2)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2))) => (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK6,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK6,X0)))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f962,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) & ($true != vAPP(nat,$o,X0,X2)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 1.77/0.61 inference(flattening,[],[f961])).
% 1.77/0.61 thf(f961,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : ((($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : ((! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) & ($true != vAPP(nat,$o,X0,X2))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2)))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 1.77/0.61 inference(ennf_transformation,[],[f798])).
% 1.77/0.61 thf(f798,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) => (! [X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2)) => (($true != vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (($true != vAPP(nat,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))))) => ($true = vAPP(nat,$o,X0,X1))))),
% 1.77/0.61 inference(flattening,[],[f595])).
% 1.77/0.61 thf(f595,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,zero_zero(nat))) => (! [X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2)) => (~($true = vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (~($true = vAPP(nat,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))))) => ($true = vAPP(nat,$o,X0,X1))))),
% 1.77/0.61 inference(fool_elimination,[],[f594])).
% 1.77/0.61 thf(f594,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (vAPP(nat,$o,X0,zero_zero(nat)) => (! [X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) => (~vAPP(nat,$o,X0,X2) => ? [X3 : nat] : (~vAPP(nat,$o,X0,X3) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))) => vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 inference(rectify,[],[f222])).
% 1.77/0.61 thf(f222,axiom,(
% 1.77/0.61 ! [X20 : nat > $o,X3 : nat] : (vAPP(nat,$o,X20,zero_zero(nat)) => (! [X29 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X29) => (~vAPP(nat,$o,X20,X29) => ? [X30 : nat] : (~vAPP(nat,$o,X20,X30) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X30),X29)))) => vAPP(nat,$o,X20,X3)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_infinite__descent0)).
% 1.77/0.61 thf(f2651,plain,(
% 1.77/0.61 spl14_100),
% 1.77/0.61 inference(avatar_split_clause,[],[f1273,f2649])).
% 1.77/0.61 thf(f2649,plain,(
% 1.77/0.61 spl14_100 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0))) | ($true != vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_100])])).
% 1.77/0.61 thf(f1273,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK10,X2),X0))) | ($true != vAPP(nat,$o,X0,X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1050])).
% 1.77/0.61 thf(f2543,plain,(
% 1.77/0.61 spl14_99),
% 1.77/0.61 inference(avatar_split_clause,[],[f1303,f2541])).
% 1.77/0.61 thf(f2541,plain,(
% 1.77/0.61 spl14_99 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_99])])).
% 1.77/0.61 thf(f1303,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1013])).
% 1.77/0.61 thf(f1013,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 1.77/0.61 inference(ennf_transformation,[],[f695])).
% 1.77/0.61 thf(f695,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)))),
% 1.77/0.61 inference(fool_elimination,[],[f694])).
% 1.77/0.61 thf(f694,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2))),
% 1.77/0.61 inference(rectify,[],[f247])).
% 1.77/0.61 thf(f247,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),X12)),X6) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X6))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__lessD1)).
% 1.77/0.61 thf(f2539,plain,(
% 1.77/0.61 spl14_98),
% 1.77/0.61 inference(avatar_split_clause,[],[f1298,f2537])).
% 1.77/0.61 thf(f2537,plain,(
% 1.77/0.61 spl14_98 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_98])])).
% 1.77/0.61 thf(f1298,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1008])).
% 1.77/0.61 thf(f1008,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f685])).
% 1.77/0.61 thf(f685,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 1.77/0.61 inference(fool_elimination,[],[f684])).
% 1.77/0.61 thf(f684,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 1.77/0.61 inference(rectify,[],[f252])).
% 1.77/0.61 thf(f252,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X5 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X12),X5)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_trans__le__add1)).
% 1.77/0.61 thf(f2535,plain,(
% 1.77/0.61 spl14_97),
% 1.77/0.61 inference(avatar_split_clause,[],[f1297,f2533])).
% 1.77/0.61 thf(f2533,plain,(
% 1.77/0.61 spl14_97 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_97])])).
% 1.77/0.61 thf(f1297,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1007])).
% 1.77/0.61 thf(f1007,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f683])).
% 1.77/0.61 thf(f683,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))),
% 1.77/0.61 inference(fool_elimination,[],[f682])).
% 1.77/0.61 thf(f682,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 1.77/0.61 inference(rectify,[],[f251])).
% 1.77/0.61 thf(f251,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X5 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X5),X12)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_trans__le__add2)).
% 1.77/0.61 thf(f2531,plain,(
% 1.77/0.61 spl14_96),
% 1.77/0.61 inference(avatar_split_clause,[],[f1281,f2529])).
% 1.77/0.61 thf(f2529,plain,(
% 1.77/0.61 spl14_96 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_96])])).
% 1.77/0.61 thf(f1281,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f985])).
% 1.77/0.61 thf(f985,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f651])).
% 1.77/0.61 thf(f651,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f650])).
% 1.77/0.61 thf(f650,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X1))),
% 1.77/0.61 inference(rectify,[],[f108])).
% 1.77/0.61 thf(f108,axiom,(
% 1.77/0.61 ! [X12 : nat,X6 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X12),X6) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X12),X3)),X6))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_less__imp__diff__less)).
% 1.77/0.61 thf(f2527,plain,(
% 1.77/0.61 spl14_95),
% 1.77/0.61 inference(avatar_split_clause,[],[f1280,f2525])).
% 1.77/0.61 thf(f2525,plain,(
% 1.77/0.61 spl14_95 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_95])])).
% 1.77/0.61 thf(f1280,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f984])).
% 1.77/0.61 thf(f984,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f649])).
% 1.77/0.61 thf(f649,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))),
% 1.77/0.61 inference(fool_elimination,[],[f648])).
% 1.77/0.61 thf(f648,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 1.77/0.61 inference(rectify,[],[f241])).
% 1.77/0.61 thf(f241,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X5 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X5),X12)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_trans__less__add2)).
% 1.77/0.61 thf(f2523,plain,(
% 1.77/0.61 spl14_94),
% 1.77/0.61 inference(avatar_split_clause,[],[f1279,f2521])).
% 1.77/0.61 thf(f2521,plain,(
% 1.77/0.61 spl14_94 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_94])])).
% 1.77/0.61 thf(f1279,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f983])).
% 1.77/0.61 thf(f983,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f647])).
% 1.77/0.61 thf(f647,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 1.77/0.61 inference(fool_elimination,[],[f646])).
% 1.77/0.61 thf(f646,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 1.77/0.61 inference(rectify,[],[f242])).
% 1.77/0.61 thf(f242,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat,X5 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X12),X5)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_trans__less__add1)).
% 1.77/0.61 thf(f2519,plain,(
% 1.77/0.61 spl14_93),
% 1.77/0.61 inference(avatar_split_clause,[],[f1245,f2517])).
% 1.77/0.61 thf(f2517,plain,(
% 1.77/0.61 spl14_93 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_93])])).
% 1.77/0.61 thf(f1245,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f968])).
% 1.77/0.61 thf(f968,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f607])).
% 1.77/0.61 thf(f607,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = X0))),
% 1.77/0.61 inference(fool_elimination,[],[f606])).
% 1.77/0.61 thf(f606,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) = X0))),
% 1.77/0.61 inference(rectify,[],[f67])).
% 1.77/0.61 thf(f67,axiom,(
% 1.77/0.61 ! [X4 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X3) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),X4)) = X4))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_diff__diff__cancel)).
% 1.77/0.61 thf(f2515,plain,(
% 1.77/0.61 spl14_92),
% 1.77/0.61 inference(avatar_split_clause,[],[f1228,f2513])).
% 1.77/0.61 thf(f2513,plain,(
% 1.77/0.61 spl14_92 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_92])])).
% 1.77/0.61 thf(f1228,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f956])).
% 1.77/0.61 thf(f956,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f796])).
% 1.77/0.61 thf(f796,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X0))),
% 1.77/0.61 inference(flattening,[],[f585])).
% 1.77/0.61 thf(f585,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X0))),
% 1.77/0.61 inference(fool_elimination,[],[f584])).
% 1.77/0.61 thf(f584,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X0))),
% 1.77/0.61 inference(rectify,[],[f143])).
% 1.77/0.61 thf(f143,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X3) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3)) = X5))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_add__diff__inverse__nat)).
% 1.77/0.61 thf(f2425,plain,(
% 1.77/0.61 spl14_91),
% 1.77/0.61 inference(avatar_split_clause,[],[f1237,f2423])).
% 1.77/0.61 thf(f2423,plain,(
% 1.77/0.61 spl14_91 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK6,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_91])])).
% 1.77/0.61 thf(f1237,plain,(
% 1.77/0.61 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(sTfun(nat,$o),nat,sK6,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1044])).
% 1.77/0.61 thf(f2421,plain,(
% 1.77/0.61 spl14_90),
% 1.77/0.61 inference(avatar_split_clause,[],[f1236,f2419])).
% 1.77/0.61 thf(f2419,plain,(
% 1.77/0.61 spl14_90 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1 > $o,X2 : X1 > X0] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK5(X0,X1),X3),X2))) | ($true != wellorder(X0)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_90])])).
% 1.77/0.61 thf(f1236,plain,(
% 1.77/0.61 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK5(X0,X1),X3),X2))) | ($true != wellorder(X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1042])).
% 1.77/0.61 thf(f2417,plain,(
% 1.77/0.61 spl14_89),
% 1.77/0.61 inference(avatar_split_clause,[],[f1234,f2415])).
% 1.77/0.61 thf(f2415,plain,(
% 1.77/0.61 spl14_89 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1 > $o,X2 : X1 > X0] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK4(X0,X1),X3),X2))) | ($true != wellorder(X0)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_89])])).
% 1.77/0.61 thf(f1234,plain,(
% 1.77/0.61 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK4(X0,X1),X3),X2))) | ($true != wellorder(X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1040])).
% 1.77/0.61 thf(f2407,plain,(
% 1.77/0.61 spl14_88),
% 1.77/0.61 inference(avatar_split_clause,[],[f1231,f2405])).
% 1.77/0.61 thf(f2405,plain,(
% 1.77/0.61 spl14_88 <=> ! [X0 : nat > $o,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK3,X0))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_88])])).
% 1.77/0.61 thf(f1231,plain,(
% 1.77/0.61 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK3,X0)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1038])).
% 1.77/0.61 thf(f1038,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK3,X0))) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK3,X0))))))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f958,f1037])).
% 1.77/0.61 thf(f1037,plain,(
% 1.77/0.61 ! [X0 : nat > $o] : (? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))) => (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK3,X0))) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK3,X0))))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f958,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))))),
% 1.77/0.61 inference(ennf_transformation,[],[f589])).
% 1.77/0.61 thf(f589,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) => ($true = vAPP(nat,$o,X0,X3))) => ($true = vAPP(nat,$o,X0,X2))) => ($true = vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f588])).
% 1.77/0.61 thf(f588,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (! [X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => vAPP(nat,$o,X0,X3)) => vAPP(nat,$o,X0,X2)) => vAPP(nat,$o,X0,X1))),
% 1.77/0.61 inference(rectify,[],[f182])).
% 1.77/0.61 thf(f182,axiom,(
% 1.77/0.61 ! [X20 : nat > $o,X3 : nat] : (! [X29 : nat] : (! [X30 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X30),X29) => vAPP(nat,$o,X20,X30)) => vAPP(nat,$o,X20,X29)) => vAPP(nat,$o,X20,X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_nat__less__induct)).
% 1.77/0.61 thf(f2403,plain,(
% 1.77/0.61 spl14_87),
% 1.77/0.61 inference(avatar_split_clause,[],[f1230,f2401])).
% 1.77/0.61 thf(f2401,plain,(
% 1.77/0.61 spl14_87 <=> ! [X0 : nat > $o,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK2,X0))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_87])])).
% 1.77/0.61 thf(f1230,plain,(
% 1.77/0.61 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK2,X0)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1036])).
% 1.77/0.61 thf(f1036,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK2,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK2,X0)))))),
% 1.77/0.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f957,f1035])).
% 1.77/0.61 thf(f1035,plain,(
% 1.77/0.61 ! [X0 : nat > $o] : (? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) & ($true != vAPP(nat,$o,X0,X2))) => (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK2,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK2,X0)))))),
% 1.77/0.61 introduced(choice_axiom,[])).
% 1.77/0.61 thf(f957,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) & ($true != vAPP(nat,$o,X0,X2))))),
% 1.77/0.61 inference(ennf_transformation,[],[f797])).
% 1.77/0.61 thf(f797,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (($true != vAPP(nat,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))) => ($true = vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 inference(flattening,[],[f587])).
% 1.77/0.61 thf(f587,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (~($true = vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (~($true = vAPP(nat,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))) => ($true = vAPP(nat,$o,X0,X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f586])).
% 1.77/0.61 thf(f586,plain,(
% 1.77/0.61 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (~vAPP(nat,$o,X0,X2) => ? [X3 : nat] : (~vAPP(nat,$o,X0,X3) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) => vAPP(nat,$o,X0,X1))),
% 1.77/0.61 inference(rectify,[],[f181])).
% 1.77/0.61 thf(f181,axiom,(
% 1.77/0.61 ! [X20 : nat > $o,X3 : nat] : (! [X29 : nat] : (~vAPP(nat,$o,X20,X29) => ? [X30 : nat] : (~vAPP(nat,$o,X20,X30) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X30),X29))) => vAPP(nat,$o,X20,X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_infinite__descent)).
% 1.77/0.61 thf(f2399,plain,(
% 1.77/0.61 spl14_86 | ~spl14_26 | ~spl14_77),
% 1.77/0.61 inference(avatar_split_clause,[],[f2283,f2253,f1893,f2396])).
% 1.77/0.61 thf(f2396,plain,(
% 1.77/0.61 spl14_86 <=> (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),i),n))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_86])])).
% 1.77/0.61 thf(f2283,plain,(
% 1.77/0.61 (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),i),n)) | (~spl14_26 | ~spl14_77)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f2276])).
% 1.77/0.61 thf(f2276,plain,(
% 1.77/0.61 ($true != $true) | (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),i),n)) | (~spl14_26 | ~spl14_77)),
% 1.77/0.61 inference(superposition,[],[f2254,f1895])).
% 1.77/0.61 thf(f2382,plain,(
% 1.77/0.61 spl14_85),
% 1.77/0.61 inference(avatar_split_clause,[],[f1302,f2380])).
% 1.77/0.61 thf(f2380,plain,(
% 1.77/0.61 spl14_85 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X2)),X1)) | ($true != vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_85])])).
% 1.77/0.61 thf(f1302,plain,(
% 1.77/0.61 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X2)),X1)) | ($true != vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1012])).
% 1.77/0.61 thf(f1012,plain,(
% 1.77/0.61 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X2)),X1)) | ($true != vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f693])).
% 1.77/0.61 thf(f693,plain,(
% 1.77/0.61 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X2)),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f692])).
% 1.77/0.61 thf(f692,plain,(
% 1.77/0.61 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X2)),X1))),
% 1.77/0.61 inference(rectify,[],[f11])).
% 1.77/0.61 thf(f11,axiom,(
% 1.77/0.61 ! [X1 : nat > nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,X1),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X1,X4)),X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_partitions__bounds)).
% 1.77/0.61 thf(f2378,plain,(
% 1.77/0.61 spl14_84),
% 1.77/0.61 inference(avatar_split_clause,[],[f1225,f2376])).
% 1.77/0.61 thf(f2376,plain,(
% 1.77/0.61 spl14_84 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_84])])).
% 1.77/0.61 thf(f1225,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f954])).
% 1.77/0.61 thf(f954,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((X0 = X1) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f953])).
% 1.77/0.61 thf(f953,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (((X0 = X1) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0))) | (zero_zero(nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f795])).
% 1.77/0.61 thf(f795,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) => ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X0)) => (X0 = X1)))),
% 1.77/0.61 inference(rectify,[],[f107])).
% 1.77/0.61 thf(f107,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3)) => ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),X5)) => (X3 = X5)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_diffs0__imp__equal)).
% 1.77/0.61 thf(f2316,plain,(
% 1.77/0.61 spl14_83),
% 1.77/0.61 inference(avatar_split_clause,[],[f1309,f2314])).
% 1.77/0.61 thf(f2314,plain,(
% 1.77/0.61 spl14_83 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > nat,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_83])])).
% 1.77/0.61 thf(f1309,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1058])).
% 1.77/0.61 thf(f2312,plain,(
% 1.77/0.61 spl14_82),
% 1.77/0.61 inference(avatar_split_clause,[],[f1247,f2310])).
% 1.77/0.61 thf(f2310,plain,(
% 1.77/0.61 spl14_82 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_82])])).
% 1.77/0.61 thf(f1247,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f972])).
% 1.77/0.61 thf(f972,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f971])).
% 1.77/0.61 thf(f971,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f611])).
% 1.77/0.61 thf(f611,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) => (X0 = X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f610])).
% 1.77/0.61 thf(f610,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) => (X0 = X1)))),
% 1.77/0.61 inference(rectify,[],[f190])).
% 1.77/0.61 thf(f190,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X3) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X5) => (X3 = X5)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_le__antisym)).
% 1.77/0.61 thf(f2308,plain,(
% 1.77/0.61 spl14_81),
% 1.77/0.61 inference(avatar_split_clause,[],[f1246,f2306])).
% 1.77/0.61 thf(f1246,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f970])).
% 1.77/0.61 thf(f970,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(flattening,[],[f969])).
% 1.77/0.61 thf(f969,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (X0 = X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f609])).
% 1.77/0.61 thf(f609,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ((X0 != X1) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))))),
% 1.77/0.61 inference(fool_elimination,[],[f608])).
% 1.77/0.61 thf(f608,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => ((X0 != X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 inference(rectify,[],[f235])).
% 1.77/0.61 thf(f235,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X3) => ((X3 != X5) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X3)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_le__neq__implies__less)).
% 1.77/0.61 thf(f2304,plain,(
% 1.77/0.61 spl14_80 | ~spl14_27 | ~spl14_77),
% 1.77/0.61 inference(avatar_split_clause,[],[f2282,f2253,f1898,f2301])).
% 1.77/0.61 thf(f2301,plain,(
% 1.77/0.61 spl14_80 <=> (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),k),n))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_80])])).
% 1.77/0.61 thf(f2282,plain,(
% 1.77/0.61 (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),k),n)) | (~spl14_27 | ~spl14_77)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f2277])).
% 1.77/0.61 thf(f2277,plain,(
% 1.77/0.61 ($true != $true) | (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),k),n)) | (~spl14_27 | ~spl14_77)),
% 1.77/0.61 inference(superposition,[],[f2254,f1900])).
% 1.77/0.61 thf(f2295,plain,(
% 1.77/0.61 spl14_79),
% 1.77/0.61 inference(avatar_split_clause,[],[f1087,f2293])).
% 1.77/0.61 thf(f2293,plain,(
% 1.77/0.61 spl14_79 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2))) | (comm_monoid_diff(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_79])])).
% 1.77/0.61 thf(f1087,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2))) | (comm_monoid_diff(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f824])).
% 1.77/0.61 thf(f824,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2))) | (comm_monoid_diff(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f317])).
% 1.77/0.61 thf(f317,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((comm_monoid_diff(X0) = $true) => ! [X1 : X0,X2 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2))))),
% 1.77/0.61 inference(fool_elimination,[],[f316])).
% 1.77/0.61 thf(f316,plain,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_diff(X0) => ! [X1 : X0,X2 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2))))),
% 1.77/0.61 inference(rectify,[],[f78])).
% 1.77/0.61 thf(f78,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_diff(X0) => ! [X8 : X0,X7 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_diff__add__zero)).
% 1.77/0.61 thf(f2259,plain,(
% 1.77/0.61 spl14_78),
% 1.77/0.61 inference(avatar_split_clause,[],[f1353,f2257])).
% 1.77/0.61 thf(f2257,plain,(
% 1.77/0.61 spl14_78 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel1352612707id_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_78])])).
% 1.77/0.61 thf(f1353,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel1352612707id_add(X0) != $true)) )),
% 1.77/0.61 inference(equality_resolution,[],[f1125])).
% 1.77/0.61 thf(f1125,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != X3) | (cancel1352612707id_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f865])).
% 1.77/0.61 thf(f865,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != X3)) | (cancel1352612707id_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f393])).
% 1.77/0.61 thf(f393,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((cancel1352612707id_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = X3) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2) = X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f392])).
% 1.77/0.61 thf(f392,plain,(
% 1.77/0.61 ! [X0 : $tType] : (cancel1352612707id_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = X3) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2) = X1)))),
% 1.77/0.61 inference(rectify,[],[f97])).
% 1.77/0.61 thf(f97,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (cancel1352612707id_add(X0) => ! [X9 : X0,X7 : X0,X8 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X7) = X8) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X7) = X9)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add__implies__diff)).
% 1.77/0.61 thf(f2255,plain,(
% 1.77/0.61 spl14_77),
% 1.77/0.61 inference(avatar_split_clause,[],[f1244,f2253])).
% 1.77/0.61 thf(f1244,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f967])).
% 1.77/0.61 thf(f967,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(ennf_transformation,[],[f605])).
% 1.77/0.61 thf(f605,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f604])).
% 1.77/0.61 thf(f604,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))),
% 1.77/0.61 inference(rectify,[],[f80])).
% 1.77/0.61 thf(f80,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X3) => (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_diff__is__0__eq_H)).
% 1.77/0.61 thf(f2251,plain,(
% 1.77/0.61 spl14_76),
% 1.77/0.61 inference(avatar_split_clause,[],[f1740,f2249])).
% 1.77/0.61 thf(f2249,plain,(
% 1.77/0.61 spl14_76 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (zero_zero(nat) = X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_76])])).
% 1.77/0.61 thf(f1740,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | (zero_zero(nat) = X0)) )),
% 1.77/0.61 inference(equality_proxy_clausification,[],[f1739])).
% 1.77/0.61 thf(f1739,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0))) )),
% 1.77/0.61 inference(not_proxy_clausification,[],[f1735])).
% 1.77/0.61 thf(f1735,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)) | ($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 1.77/0.61 inference(binary_proxy_clausification,[],[f1071])).
% 1.77/0.61 thf(f1071,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f285])).
% 1.77/0.61 thf(f285,plain,(
% 1.77/0.61 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)))),
% 1.77/0.61 inference(fool_elimination,[],[f284])).
% 1.77/0.61 thf(f284,plain,(
% 1.77/0.61 ! [X0 : nat] : ((zero_zero(nat) != X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0))),
% 1.77/0.61 inference(rectify,[],[f52])).
% 1.77/0.61 thf(f52,axiom,(
% 1.77/0.61 ! [X8 : nat] : ((zero_zero(nat) != X8) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_bot__nat__0_Onot__eq__extremum)).
% 1.77/0.61 thf(f2247,plain,(
% 1.77/0.61 spl14_75),
% 1.77/0.61 inference(avatar_split_clause,[],[f1175,f2245])).
% 1.77/0.61 thf(f2245,plain,(
% 1.77/0.61 spl14_75 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_75])])).
% 1.77/0.61 thf(f1175,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f921])).
% 1.77/0.61 thf(f921,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f493])).
% 1.77/0.61 thf(f493,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f492])).
% 1.77/0.61 thf(f492,plain,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1))),
% 1.77/0.61 inference(rectify,[],[f50])).
% 1.77/0.61 thf(f50,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X8 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X7)),X7) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_diff__add__cancel)).
% 1.77/0.61 thf(f2243,plain,(
% 1.77/0.61 spl14_74),
% 1.77/0.61 inference(avatar_split_clause,[],[f1174,f2241])).
% 1.77/0.61 thf(f2241,plain,(
% 1.77/0.61 spl14_74 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_74])])).
% 1.77/0.61 thf(f1174,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f920])).
% 1.77/0.61 thf(f920,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f491])).
% 1.77/0.61 thf(f491,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f490])).
% 1.77/0.61 thf(f490,plain,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1))),
% 1.77/0.61 inference(rectify,[],[f51])).
% 1.77/0.61 thf(f51,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X8 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7)),X7) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_add__diff__cancel)).
% 1.77/0.61 thf(f2239,plain,(
% 1.77/0.61 spl14_73),
% 1.77/0.61 inference(avatar_split_clause,[],[f1114,f2237])).
% 1.77/0.61 thf(f2237,plain,(
% 1.77/0.61 spl14_73 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_73])])).
% 1.77/0.61 thf(f1114,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel146912293up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f854])).
% 1.77/0.61 thf(f854,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f371])).
% 1.77/0.61 thf(f371,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f370])).
% 1.77/0.61 thf(f370,plain,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1))),
% 1.77/0.61 inference(rectify,[],[f46])).
% 1.77/0.61 thf(f46,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X8 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7)),X7) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__diff__cancel__right_H)).
% 1.77/0.61 thf(f2235,plain,(
% 1.77/0.61 spl14_72),
% 1.77/0.61 inference(avatar_split_clause,[],[f1113,f2233])).
% 1.77/0.61 thf(f2233,plain,(
% 1.77/0.61 spl14_72 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_72])])).
% 1.77/0.61 thf(f1113,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2) | (cancel146912293up_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f853])).
% 1.77/0.61 thf(f853,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2) | (cancel146912293up_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f369])).
% 1.77/0.61 thf(f369,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2))),
% 1.77/0.61 inference(fool_elimination,[],[f368])).
% 1.77/0.61 thf(f368,plain,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2))),
% 1.77/0.61 inference(rectify,[],[f48])).
% 1.77/0.61 thf(f48,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X8 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7)),X8) = X7))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_add__diff__cancel__left_H)).
% 1.77/0.61 thf(f2190,plain,(
% 1.77/0.61 spl14_71),
% 1.77/0.61 inference(avatar_split_clause,[],[f1238,f2188])).
% 1.77/0.61 thf(f2188,plain,(
% 1.77/0.61 spl14_71 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_71])])).
% 1.77/0.61 thf(f1238,plain,(
% 1.77/0.61 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK6,X0))) | ($true != vAPP(nat,$o,X0,zero_zero(nat)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1044])).
% 1.77/0.61 thf(f2186,plain,(
% 1.77/0.61 spl14_70),
% 1.77/0.61 inference(avatar_split_clause,[],[f1722,f2184])).
% 1.77/0.61 thf(f2184,plain,(
% 1.77/0.61 spl14_70 <=> ! [X0 : nat] : ((zero_zero(nat) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_70])])).
% 1.77/0.61 thf(f1722,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((zero_zero(nat) = X0) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)))) )),
% 1.77/0.61 inference(equality_proxy_clausification,[],[f1719])).
% 1.77/0.61 thf(f1719,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)))) )),
% 1.77/0.61 inference(binary_proxy_clausification,[],[f1074])).
% 1.77/0.61 thf(f1074,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f291])).
% 1.77/0.61 thf(f291,plain,(
% 1.77/0.61 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)))),
% 1.77/0.61 inference(fool_elimination,[],[f290])).
% 1.77/0.61 thf(f290,plain,(
% 1.77/0.61 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) = (zero_zero(nat) = X0))),
% 1.77/0.61 inference(rectify,[],[f230])).
% 1.77/0.61 thf(f230,axiom,(
% 1.77/0.61 ! [X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),zero_zero(nat)) = (zero_zero(nat) = X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_le__0__eq)).
% 1.77/0.61 thf(f2182,plain,(
% 1.77/0.61 spl14_69),
% 1.77/0.61 inference(avatar_split_clause,[],[f1226,f2180])).
% 1.77/0.61 thf(f2180,plain,(
% 1.77/0.61 spl14_69 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_69])])).
% 1.77/0.61 thf(f1226,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f955])).
% 1.77/0.61 thf(f955,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ((X0 != X1) & ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))))),
% 1.77/0.61 inference(ennf_transformation,[],[f583])).
% 1.77/0.61 thf(f583,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f582])).
% 1.77/0.61 thf(f582,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (((X0 = X1) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))),
% 1.77/0.61 inference(rectify,[],[f236])).
% 1.77/0.61 thf(f236,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : (((X3 = X5) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X3)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_less__or__eq__imp__le)).
% 1.77/0.61 thf(f2178,plain,(
% 1.77/0.61 spl14_68),
% 1.77/0.61 inference(avatar_split_clause,[],[f1221,f2176])).
% 1.77/0.61 thf(f2176,plain,(
% 1.77/0.61 spl14_68 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_68])])).
% 1.77/0.61 thf(f1221,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f577])).
% 1.77/0.61 thf(f577,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f576])).
% 1.77/0.61 thf(f576,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))),
% 1.77/0.61 inference(rectify,[],[f189])).
% 1.77/0.61 thf(f189,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X5) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_nat__le__linear)).
% 1.77/0.61 thf(f2174,plain,(
% 1.77/0.61 spl14_67),
% 1.77/0.61 inference(avatar_split_clause,[],[f1089,f2172])).
% 1.77/0.61 thf(f2172,plain,(
% 1.77/0.61 spl14_67 <=> ! [X0 : $tType] : ((plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))) | (ab_semigroup_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_67])])).
% 1.77/0.61 thf(f1089,plain,(
% 1.77/0.61 ( ! [X0 : $tType] : ((plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))) | (ab_semigroup_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f826])).
% 1.77/0.61 thf(f826,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))) | (ab_semigroup_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f321])).
% 1.77/0.61 thf(f321,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) => (plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))))),
% 1.77/0.61 inference(fool_elimination,[],[f320])).
% 1.77/0.61 thf(f320,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_add(X0) => (plus_plus(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X1)))))),
% 1.77/0.61 inference(rectify,[],[f167])).
% 1.77/0.61 thf(f167,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_add(X0) => (plus_plus(X0) = (^[X16 : X0, X17 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X17),X16)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_add_Ocommute)).
% 1.77/0.61 thf(f2170,plain,(
% 1.77/0.61 spl14_66),
% 1.77/0.61 inference(avatar_split_clause,[],[f1088,f2168])).
% 1.77/0.61 thf(f2168,plain,(
% 1.77/0.61 spl14_66 <=> ! [X0 : $tType] : ((times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))) | (ab_semigroup_mult(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_66])])).
% 1.77/0.61 thf(f1088,plain,(
% 1.77/0.61 ( ! [X0 : $tType] : ((times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))) | (ab_semigroup_mult(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f825])).
% 1.77/0.61 thf(f825,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))) | (ab_semigroup_mult(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f319])).
% 1.77/0.61 thf(f319,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((ab_semigroup_mult(X0) = $true) => (times_times(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,times_times(X0))))),
% 1.77/0.61 inference(fool_elimination,[],[f318])).
% 1.77/0.61 thf(f318,plain,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_mult(X0) => (times_times(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X2),X1)))))),
% 1.77/0.61 inference(rectify,[],[f176])).
% 1.77/0.61 thf(f176,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (ab_semigroup_mult(X0) => (times_times(X0) = (^[X16 : X0, X17 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),times_times(X0),X17),X16)))))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_mult_Ocommute)).
% 1.77/0.61 thf(f2163,plain,(
% 1.77/0.61 spl14_65),
% 1.77/0.61 inference(avatar_split_clause,[],[f1213,f2161])).
% 1.77/0.61 thf(f2161,plain,(
% 1.77/0.61 spl14_65 <=> ! [X0 : nat,X1 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_65])])).
% 1.77/0.61 thf(f1213,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f791])).
% 1.77/0.61 thf(f791,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))),
% 1.77/0.61 inference(rectify,[],[f140])).
% 1.77/0.61 thf(f140,axiom,(
% 1.77/0.61 ! [X3 : nat,X5 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_diff__add__0)).
% 1.77/0.61 thf(f2142,plain,(
% 1.77/0.61 spl14_64),
% 1.77/0.61 inference(avatar_split_clause,[],[f1721,f2140])).
% 1.77/0.61 thf(f2140,plain,(
% 1.77/0.61 spl14_64 <=> ! [X0 : nat] : ((zero_zero(nat) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_64])])).
% 1.77/0.61 thf(f1721,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((zero_zero(nat) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)))) )),
% 1.77/0.61 inference(equality_proxy_clausification,[],[f1720])).
% 1.77/0.61 thf(f1720,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)))) )),
% 1.77/0.61 inference(binary_proxy_clausification,[],[f1074])).
% 1.77/0.61 thf(f2130,plain,(
% 1.77/0.61 spl14_63),
% 1.77/0.61 inference(avatar_split_clause,[],[f1345,f2127])).
% 1.77/0.61 thf(f1345,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),n),k)),i) = $true)),
% 1.77/0.61 inference(cnf_transformation,[],[f769])).
% 1.77/0.61 thf(f769,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),n),k)),i) = $true)),
% 1.77/0.61 inference(fool_elimination,[],[f768])).
% 1.77/0.61 thf(f768,plain,(
% 1.77/0.61 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),n),k)),i)),
% 1.77/0.61 inference(rectify,[],[f9])).
% 1.77/0.61 thf(f9,axiom,(
% 1.77/0.61 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),n),k)),i)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062n_A_N_Ak_A_060_Ai_092_060close_062)).
% 1.77/0.61 thf(f2125,plain,(
% 1.77/0.61 spl14_62),
% 1.77/0.61 inference(avatar_split_clause,[],[f1251,f2123])).
% 1.77/0.61 thf(f2123,plain,(
% 1.77/0.61 spl14_62 <=> ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_62])])).
% 1.77/0.61 thf(f1251,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f619])).
% 1.77/0.61 thf(f619,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0))),
% 1.77/0.61 inference(fool_elimination,[],[f618])).
% 1.77/0.61 thf(f618,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0)),
% 1.77/0.61 inference(rectify,[],[f112])).
% 1.77/0.61 thf(f112,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X3)),X5)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_diff__le__self)).
% 1.77/0.61 thf(f2121,plain,(
% 1.77/0.61 spl14_61),
% 1.77/0.61 inference(avatar_split_clause,[],[f1250,f2119])).
% 1.77/0.61 thf(f2119,plain,(
% 1.77/0.61 spl14_61 <=> ! [X0 : nat,X1 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_61])])).
% 1.77/0.61 thf(f1250,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f800])).
% 1.77/0.61 thf(f800,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))),
% 1.77/0.61 inference(flattening,[],[f617])).
% 1.77/0.61 thf(f617,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))),
% 1.77/0.61 inference(fool_elimination,[],[f616])).
% 1.77/0.61 thf(f616,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1)),
% 1.77/0.61 inference(rectify,[],[f244])).
% 1.77/0.61 thf(f244,axiom,(
% 1.77/0.61 ! [X12 : nat,X4 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X12),X4)),X4)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_not__add__less2)).
% 1.77/0.61 thf(f2117,plain,(
% 1.77/0.61 spl14_60),
% 1.77/0.61 inference(avatar_split_clause,[],[f1249,f2115])).
% 1.77/0.61 thf(f2115,plain,(
% 1.77/0.61 spl14_60 <=> ! [X0 : nat,X1 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_60])])).
% 1.77/0.61 thf(f1249,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f799])).
% 1.77/0.61 thf(f799,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))),
% 1.77/0.61 inference(flattening,[],[f615])).
% 1.77/0.61 thf(f615,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))),
% 1.77/0.61 inference(fool_elimination,[],[f614])).
% 1.77/0.61 thf(f614,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0)),
% 1.77/0.61 inference(rectify,[],[f245])).
% 1.77/0.61 thf(f245,axiom,(
% 1.77/0.61 ! [X4 : nat,X12 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),X12)),X4)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_not__add__less1)).
% 1.77/0.61 thf(f2113,plain,(
% 1.77/0.61 spl14_59),
% 1.77/0.61 inference(avatar_split_clause,[],[f1212,f2111])).
% 1.77/0.61 thf(f2111,plain,(
% 1.77/0.61 spl14_59 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_59])])).
% 1.77/0.61 thf(f1212,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f790])).
% 1.77/0.61 thf(f790,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1)),
% 1.77/0.61 inference(rectify,[],[f118])).
% 1.77/0.61 thf(f118,axiom,(
% 1.77/0.61 ! [X3 : nat,X5 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)),X3) = X5)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_diff__add__inverse)).
% 1.77/0.61 thf(f2109,plain,(
% 1.77/0.61 spl14_58),
% 1.77/0.61 inference(avatar_split_clause,[],[f1211,f2107])).
% 1.77/0.61 thf(f2107,plain,(
% 1.77/0.61 spl14_58 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_58])])).
% 1.77/0.61 thf(f1211,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f789])).
% 1.77/0.61 thf(f789,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0)),
% 1.77/0.61 inference(rectify,[],[f117])).
% 1.77/0.61 thf(f117,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X5),X3)),X3) = X5)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_diff__add__inverse2)).
% 1.77/0.61 thf(f2080,plain,(
% 1.77/0.61 spl14_57),
% 1.77/0.61 inference(avatar_split_clause,[],[f1232,f2078])).
% 1.77/0.61 thf(f2078,plain,(
% 1.77/0.61 spl14_57 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK3,X0))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_57])])).
% 1.77/0.61 thf(f1232,plain,(
% 1.77/0.61 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK3,X0)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1038])).
% 1.77/0.61 thf(f2076,plain,(
% 1.77/0.61 spl14_56),
% 1.77/0.61 inference(avatar_split_clause,[],[f1229,f2074])).
% 1.77/0.61 thf(f2074,plain,(
% 1.77/0.61 spl14_56 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK2,X0))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_56])])).
% 1.77/0.61 thf(f1229,plain,(
% 1.77/0.61 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK2,X0)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f1036])).
% 1.77/0.61 thf(f2072,plain,(
% 1.77/0.61 spl14_55),
% 1.77/0.61 inference(avatar_split_clause,[],[f1086,f2070])).
% 1.77/0.61 thf(f2070,plain,(
% 1.77/0.61 spl14_55 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),zero_zero(X0)),X1)) | (comm_monoid_diff(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_55])])).
% 1.77/0.61 thf(f1086,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),zero_zero(X0)),X1)) | (comm_monoid_diff(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f823])).
% 1.77/0.61 thf(f823,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),zero_zero(X0)),X1)) | (comm_monoid_diff(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f315])).
% 1.77/0.61 thf(f315,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((comm_monoid_diff(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),zero_zero(X0)),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f314])).
% 1.77/0.61 thf(f314,plain,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_diff(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),zero_zero(X0)),X1)))),
% 1.77/0.61 inference(rectify,[],[f41])).
% 1.77/0.61 thf(f41,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_diff(X0) => ! [X8 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),zero_zero(X0)),X8)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zero__diff)).
% 1.77/0.61 thf(f2054,plain,(
% 1.77/0.61 spl14_54),
% 1.77/0.61 inference(avatar_split_clause,[],[f1534,f2052])).
% 1.77/0.61 thf(f2052,plain,(
% 1.77/0.61 spl14_54 <=> ! [X0 : nat,X1 : nat] : ((X0 != X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_54])])).
% 1.77/0.61 thf(f1534,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0))) )),
% 1.77/0.61 inference(binary_proxy_clausification,[],[f1533])).
% 1.77/0.61 thf(f1533,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 1.77/0.61 inference(equality_proxy_clausification,[],[f1532])).
% 1.77/0.61 thf(f1532,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 1.77/0.61 inference(not_proxy_clausification,[],[f1527])).
% 1.77/0.61 thf(f1527,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : (($true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 1.77/0.61 inference(binary_proxy_clausification,[],[f1215])).
% 1.77/0.61 thf(f1215,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f565])).
% 1.77/0.61 thf(f565,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : (vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))),
% 1.77/0.61 inference(fool_elimination,[],[f564])).
% 1.77/0.61 thf(f564,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((X0 != X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))),
% 1.77/0.61 inference(rectify,[],[f187])).
% 1.77/0.61 thf(f187,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : ((X3 != X5) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X5) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_nat__neq__iff)).
% 1.77/0.61 thf(f2021,plain,(
% 1.77/0.61 spl14_53),
% 1.77/0.61 inference(avatar_split_clause,[],[f1344,f2018])).
% 1.77/0.61 thf(f2018,plain,(
% 1.77/0.61 spl14_53 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,p,k)) = $true)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_53])])).
% 1.77/0.61 thf(f1344,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,p,k)) = $true)),
% 1.77/0.61 inference(cnf_transformation,[],[f767])).
% 1.77/0.61 thf(f767,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,p,k)) = $true)),
% 1.77/0.61 inference(fool_elimination,[],[f766])).
% 1.77/0.61 thf(f766,plain,(
% 1.77/0.61 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,p,k))),
% 1.77/0.61 inference(rectify,[],[f7])).
% 1.77/0.61 thf(f7,axiom,(
% 1.77/0.61 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,p,k))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_assms_I2_J)).
% 1.77/0.61 thf(f2016,plain,(
% 1.77/0.61 spl14_52),
% 1.77/0.61 inference(avatar_split_clause,[],[f1200,f2014])).
% 1.77/0.61 thf(f2014,plain,(
% 1.77/0.61 spl14_52 <=> ! [X0 : nat] : ((zero_zero(nat) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat))))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_52])])).
% 1.77/0.61 thf(f1200,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((zero_zero(nat) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f948])).
% 1.77/0.61 thf(f948,plain,(
% 1.77/0.61 ! [X0 : nat] : ((zero_zero(nat) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat))))),
% 1.77/0.61 inference(ennf_transformation,[],[f543])).
% 1.77/0.61 thf(f543,plain,(
% 1.77/0.61 ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat))) => (zero_zero(nat) = X0))),
% 1.77/0.61 inference(fool_elimination,[],[f542])).
% 1.77/0.61 thf(f542,plain,(
% 1.77/0.61 ! [X0 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) => (zero_zero(nat) = X0))),
% 1.77/0.61 inference(rectify,[],[f228])).
% 1.77/0.61 thf(f228,axiom,(
% 1.77/0.61 ! [X8 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X8),zero_zero(nat)) => (zero_zero(nat) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_bot__nat__0_Oextremum__uniqueI)).
% 1.77/0.61 thf(f2012,plain,(
% 1.77/0.61 spl14_51),
% 1.77/0.61 inference(avatar_split_clause,[],[f1173,f2010])).
% 1.77/0.61 thf(f2010,plain,(
% 1.77/0.61 spl14_51 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1) | (group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_51])])).
% 1.77/0.61 thf(f1173,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1) | (group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f919])).
% 1.77/0.61 thf(f919,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1) | (group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f489])).
% 1.77/0.61 thf(f489,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f488])).
% 1.77/0.61 thf(f488,plain,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1))),
% 1.77/0.61 inference(rectify,[],[f209])).
% 1.77/0.61 thf(f209,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X8) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_add_Ogroup__left__neutral)).
% 1.77/0.61 thf(f2004,plain,(
% 1.77/0.61 spl14_50),
% 1.77/0.61 inference(avatar_split_clause,[],[f1172,f2002])).
% 1.77/0.61 thf(f2002,plain,(
% 1.77/0.61 spl14_50 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1) | (group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_50])])).
% 1.77/0.61 thf(f1172,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1) | (group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f918])).
% 1.77/0.61 thf(f918,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1) | (group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f487])).
% 1.77/0.61 thf(f487,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f486])).
% 1.77/0.61 thf(f486,plain,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1))),
% 1.77/0.61 inference(rectify,[],[f42])).
% 1.77/0.61 thf(f42,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),zero_zero(X0)) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_diff__0__right)).
% 1.77/0.61 thf(f2000,plain,(
% 1.77/0.61 spl14_49),
% 1.77/0.61 inference(avatar_split_clause,[],[f1171,f1998])).
% 1.77/0.61 thf(f1998,plain,(
% 1.77/0.61 spl14_49 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)) | (group_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_49])])).
% 1.77/0.61 thf(f1171,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)) | (group_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f917])).
% 1.77/0.61 thf(f917,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)) | (group_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f485])).
% 1.77/0.61 thf(f485,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f484])).
% 1.77/0.61 thf(f484,plain,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)))),
% 1.77/0.61 inference(rectify,[],[f43])).
% 1.77/0.61 thf(f43,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (group_add(X0) => ! [X8 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X8)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_diff__self)).
% 1.77/0.61 thf(f1996,plain,(
% 1.77/0.61 spl14_48),
% 1.77/0.61 inference(avatar_split_clause,[],[f1165,f1994])).
% 1.77/0.61 thf(f1994,plain,(
% 1.77/0.61 spl14_48 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_48])])).
% 1.77/0.61 thf(f1165,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f911])).
% 1.77/0.61 thf(f911,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)) | (canoni770627133id_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f473])).
% 1.77/0.61 thf(f473,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f472])).
% 1.77/0.61 thf(f472,plain,(
% 1.77/0.61 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1))),
% 1.77/0.61 inference(rectify,[],[f194])).
% 1.77/0.61 thf(f194,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X10 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X10))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_zero__le)).
% 1.77/0.61 thf(f1992,plain,(
% 1.77/0.61 spl14_47),
% 1.77/0.61 inference(avatar_split_clause,[],[f1164,f1990])).
% 1.77/0.61 thf(f1990,plain,(
% 1.77/0.61 spl14_47 <=> ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (canoni770627133id_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_47])])).
% 1.77/0.61 thf(f1164,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (canoni770627133id_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f910])).
% 1.77/0.61 thf(f910,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))) | (canoni770627133id_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f782])).
% 1.77/0.61 thf(f782,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))))),
% 1.77/0.61 inference(flattening,[],[f471])).
% 1.77/0.61 thf(f471,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0] : ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0))))),
% 1.77/0.61 inference(fool_elimination,[],[f470])).
% 1.77/0.61 thf(f470,plain,(
% 1.77/0.61 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X1 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),zero_zero(X0)))),
% 1.77/0.61 inference(rectify,[],[f197])).
% 1.77/0.61 thf(f197,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X3 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),zero_zero(X0)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_not__less__zero)).
% 1.77/0.61 thf(f1988,plain,(
% 1.77/0.61 spl14_46),
% 1.77/0.61 inference(avatar_split_clause,[],[f1120,f1986])).
% 1.77/0.61 thf(f1986,plain,(
% 1.77/0.61 spl14_46 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1) | (cancel1352612707id_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_46])])).
% 1.77/0.61 thf(f1120,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1) | (cancel1352612707id_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f860])).
% 1.77/0.61 thf(f860,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1) | (cancel1352612707id_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f383])).
% 1.77/0.61 thf(f383,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((cancel1352612707id_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f382])).
% 1.77/0.61 thf(f382,plain,(
% 1.77/0.61 ! [X0 : $tType] : (cancel1352612707id_add(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1))),
% 1.77/0.61 inference(rectify,[],[f40])).
% 1.77/0.61 thf(f40,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (cancel1352612707id_add(X0) => ! [X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),zero_zero(X0)) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_diff__zero)).
% 1.77/0.61 thf(f1984,plain,(
% 1.77/0.61 spl14_45),
% 1.77/0.61 inference(avatar_split_clause,[],[f1119,f1982])).
% 1.77/0.61 thf(f1982,plain,(
% 1.77/0.61 spl14_45 <=> ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)) | (cancel1352612707id_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_45])])).
% 1.77/0.61 thf(f1119,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)) | (cancel1352612707id_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f859])).
% 1.77/0.61 thf(f859,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)) | (cancel1352612707id_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f381])).
% 1.77/0.61 thf(f381,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((cancel1352612707id_add(X0) = $true) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)))),
% 1.77/0.61 inference(fool_elimination,[],[f380])).
% 1.77/0.61 thf(f380,plain,(
% 1.77/0.61 ! [X0 : $tType] : (cancel1352612707id_add(X0) => ! [X1 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X1)))),
% 1.77/0.61 inference(rectify,[],[f39])).
% 1.77/0.61 thf(f39,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (cancel1352612707id_add(X0) => ! [X8 : X0] : (zero_zero(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X8)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_cancel__comm__monoid__add__class_Odiff__cancel)).
% 1.77/0.61 thf(f1980,plain,(
% 1.77/0.61 spl14_44),
% 1.77/0.61 inference(avatar_split_clause,[],[f1095,f1978])).
% 1.77/0.61 thf(f1978,plain,(
% 1.77/0.61 spl14_44 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1) | (comm_monoid_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_44])])).
% 1.77/0.61 thf(f1095,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1) | (comm_monoid_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f832])).
% 1.77/0.61 thf(f832,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1) | (comm_monoid_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f333])).
% 1.77/0.61 thf(f333,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f332])).
% 1.77/0.61 thf(f332,plain,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1))),
% 1.77/0.61 inference(rectify,[],[f211])).
% 1.77/0.61 thf(f211,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X8) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_comm__monoid__add__class_Oadd__0)).
% 1.77/0.61 thf(f1976,plain,(
% 1.77/0.61 spl14_43),
% 1.77/0.61 inference(avatar_split_clause,[],[f1094,f1974])).
% 1.77/0.61 thf(f1974,plain,(
% 1.77/0.61 spl14_43 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1) | (comm_monoid_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_43])])).
% 1.77/0.61 thf(f1094,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1) | (comm_monoid_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f831])).
% 1.77/0.61 thf(f831,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1) | (comm_monoid_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f331])).
% 1.77/0.61 thf(f331,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f330])).
% 1.77/0.61 thf(f330,plain,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1))),
% 1.77/0.61 inference(rectify,[],[f210])).
% 1.77/0.61 thf(f210,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),zero_zero(X0)) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_add_Ocomm__neutral)).
% 1.77/0.61 thf(f1972,plain,(
% 1.77/0.61 spl14_42),
% 1.77/0.61 inference(avatar_split_clause,[],[f1085,f1970])).
% 1.77/0.61 thf(f1970,plain,(
% 1.77/0.61 spl14_42 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1) | (monoid_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_42])])).
% 1.77/0.61 thf(f1085,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1) | (monoid_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f822])).
% 1.77/0.61 thf(f822,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1) | (monoid_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f313])).
% 1.77/0.61 thf(f313,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((monoid_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f312])).
% 1.77/0.61 thf(f312,plain,(
% 1.77/0.61 ! [X0 : $tType] : (monoid_add(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1))),
% 1.77/0.61 inference(rectify,[],[f38])).
% 1.77/0.61 thf(f38,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (monoid_add(X0) => ! [X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X8) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add_Oleft__neutral)).
% 1.77/0.61 thf(f1968,plain,(
% 1.77/0.61 spl14_41),
% 1.77/0.61 inference(avatar_split_clause,[],[f1084,f1966])).
% 1.77/0.61 thf(f1966,plain,(
% 1.77/0.61 spl14_41 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1) | (monoid_add(X0) != $true))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_41])])).
% 1.77/0.61 thf(f1084,plain,(
% 1.77/0.61 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1) | (monoid_add(X0) != $true)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f821])).
% 1.77/0.61 thf(f821,plain,(
% 1.77/0.61 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1) | (monoid_add(X0) != $true))),
% 1.77/0.61 inference(ennf_transformation,[],[f311])).
% 1.77/0.61 thf(f311,plain,(
% 1.77/0.61 ! [X0 : $tType] : ((monoid_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1))),
% 1.77/0.61 inference(fool_elimination,[],[f310])).
% 1.77/0.61 thf(f310,plain,(
% 1.77/0.61 ! [X0 : $tType] : (monoid_add(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1))),
% 1.77/0.61 inference(rectify,[],[f37])).
% 1.77/0.61 thf(f37,axiom,(
% 1.77/0.61 ! [X0 : $tType] : (monoid_add(X0) => ! [X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),zero_zero(X0)) = X8))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add_Oright__neutral)).
% 1.77/0.61 thf(f1964,plain,(
% 1.77/0.61 spl14_40 | ~spl14_22 | ~spl14_33),
% 1.77/0.61 inference(avatar_split_clause,[],[f1938,f1925,f1848,f1962])).
% 1.77/0.61 thf(f1925,plain,(
% 1.77/0.61 spl14_33 <=> ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_33])])).
% 1.77/0.61 thf(f1938,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | (~spl14_22 | ~spl14_33)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f1937])).
% 1.77/0.61 thf(f1937,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | (~spl14_22 | ~spl14_33)),
% 1.77/0.61 inference(superposition,[],[f1926,f1849])).
% 1.77/0.61 thf(f1926,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) ) | ~spl14_33),
% 1.77/0.61 inference(avatar_component_clause,[],[f1925])).
% 1.77/0.61 thf(f1958,plain,(
% 1.77/0.61 spl14_39),
% 1.77/0.61 inference(avatar_split_clause,[],[f1224,f1956])).
% 1.77/0.61 thf(f1956,plain,(
% 1.77/0.61 spl14_39 <=> ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) != X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_39])])).
% 1.77/0.61 thf(f1224,plain,(
% 1.77/0.61 ( ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) != X0)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f952])).
% 1.77/0.61 thf(f952,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((zero_zero(nat) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) != X0))),
% 1.77/0.61 inference(ennf_transformation,[],[f794])).
% 1.77/0.61 thf(f794,plain,(
% 1.77/0.61 ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = X0) => (zero_zero(nat) = X1))),
% 1.77/0.61 inference(rectify,[],[f232])).
% 1.77/0.61 thf(f232,axiom,(
% 1.77/0.61 ! [X5 : nat,X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X5),X3) = X5) => (zero_zero(nat) = X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_add__eq__self__zero)).
% 1.77/0.61 thf(f1954,plain,(
% 1.77/0.61 spl14_38),
% 1.77/0.61 inference(avatar_split_clause,[],[f1070,f1952])).
% 1.77/0.61 thf(f1952,plain,(
% 1.77/0.61 spl14_38 <=> ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),zero_zero(nat)),X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_38])])).
% 1.77/0.61 thf(f1070,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),zero_zero(nat)),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f781])).
% 1.77/0.61 thf(f781,plain,(
% 1.77/0.61 ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),zero_zero(nat)),X0))),
% 1.77/0.61 inference(rectify,[],[f61])).
% 1.77/0.61 thf(f61,axiom,(
% 1.77/0.61 ! [X3 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),zero_zero(nat)),X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_diff__0__eq__0)).
% 1.77/0.61 thf(f1950,plain,(
% 1.77/0.61 spl14_37),
% 1.77/0.61 inference(avatar_split_clause,[],[f1069,f1948])).
% 1.77/0.61 thf(f1948,plain,(
% 1.77/0.61 spl14_37 <=> ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_37])])).
% 1.77/0.61 thf(f1069,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f780])).
% 1.77/0.61 thf(f780,plain,(
% 1.77/0.61 ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X0))),
% 1.77/0.61 inference(rectify,[],[f249])).
% 1.77/0.61 thf(f249,axiom,(
% 1.77/0.61 ! [X3 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),zero_zero(nat)),X3))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_mult__0)).
% 1.77/0.61 thf(f1946,plain,(
% 1.77/0.61 spl14_36),
% 1.77/0.61 inference(avatar_split_clause,[],[f1068,f1944])).
% 1.77/0.61 thf(f1944,plain,(
% 1.77/0.61 spl14_36 <=> ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),zero_zero(nat)))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_36])])).
% 1.77/0.61 thf(f1068,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),zero_zero(nat)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f779])).
% 1.77/0.61 thf(f779,plain,(
% 1.77/0.61 ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X0),zero_zero(nat)))),
% 1.77/0.61 inference(rectify,[],[f64])).
% 1.77/0.61 thf(f64,axiom,(
% 1.77/0.61 ! [X5 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times(nat),X5),zero_zero(nat)))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mult__0__right)).
% 1.77/0.61 thf(f1936,plain,(
% 1.77/0.61 spl14_35),
% 1.77/0.61 inference(avatar_split_clause,[],[f1343,f1933])).
% 1.77/0.61 thf(f1933,plain,(
% 1.77/0.61 spl14_35 <=> (vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,p),n) = $true)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_35])])).
% 1.77/0.61 thf(f1343,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,p),n) = $true)),
% 1.77/0.61 inference(cnf_transformation,[],[f765])).
% 1.77/0.61 thf(f765,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,p),n) = $true)),
% 1.77/0.61 inference(fool_elimination,[],[f764])).
% 1.77/0.61 thf(f764,plain,(
% 1.77/0.61 vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,p),n)),
% 1.77/0.61 inference(rectify,[],[f2])).
% 1.77/0.61 thf(f2,axiom,(
% 1.77/0.61 vAPP(nat,$o,vAPP(sTfun(nat,nat),sTfun(nat,$o),number2016821345itions,p),n)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I1_J)).
% 1.77/0.61 thf(f1931,plain,(
% 1.77/0.61 spl14_34),
% 1.77/0.61 inference(avatar_split_clause,[],[f1208,f1929])).
% 1.77/0.61 thf(f1929,plain,(
% 1.77/0.61 spl14_34 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_34])])).
% 1.77/0.61 thf(f1208,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f559])).
% 1.77/0.61 thf(f559,plain,(
% 1.77/0.61 ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0))),
% 1.77/0.61 inference(fool_elimination,[],[f558])).
% 1.77/0.61 thf(f558,plain,(
% 1.77/0.61 ! [X0 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0)),
% 1.77/0.61 inference(rectify,[],[f55])).
% 1.77/0.61 thf(f55,axiom,(
% 1.77/0.61 ! [X8 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X8)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_bot__nat__0_Oextremum)).
% 1.77/0.61 thf(f1927,plain,(
% 1.77/0.61 spl14_33),
% 1.77/0.61 inference(avatar_split_clause,[],[f1203,f1925])).
% 1.77/0.61 thf(f1203,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f785])).
% 1.77/0.61 thf(f785,plain,(
% 1.77/0.61 ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))),
% 1.77/0.61 inference(flattening,[],[f549])).
% 1.77/0.61 thf(f549,plain,(
% 1.77/0.61 ! [X0 : nat] : ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat)))),
% 1.77/0.61 inference(fool_elimination,[],[f548])).
% 1.77/0.61 thf(f548,plain,(
% 1.77/0.61 ! [X0 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),zero_zero(nat))),
% 1.77/0.61 inference(rectify,[],[f221])).
% 1.77/0.61 thf(f221,axiom,(
% 1.77/0.61 ! [X8 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X8),zero_zero(nat))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_bot__nat__0_Oextremum__strict)).
% 1.77/0.61 thf(f1923,plain,(
% 1.77/0.61 spl14_32),
% 1.77/0.61 inference(avatar_split_clause,[],[f1067,f1921])).
% 1.77/0.61 thf(f1921,plain,(
% 1.77/0.61 spl14_32 <=> ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_32])])).
% 1.77/0.61 thf(f1067,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f778])).
% 1.77/0.61 thf(f778,plain,(
% 1.77/0.61 ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0)),
% 1.77/0.61 inference(rectify,[],[f233])).
% 1.77/0.61 thf(f233,axiom,(
% 1.77/0.61 ! [X3 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),zero_zero(nat)),X3) = X3)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_plus__nat_Oadd__0)).
% 1.77/0.61 thf(f1919,plain,(
% 1.77/0.61 spl14_31),
% 1.77/0.61 inference(avatar_split_clause,[],[f1066,f1917])).
% 1.77/0.61 thf(f1917,plain,(
% 1.77/0.61 spl14_31 <=> ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_31])])).
% 1.77/0.61 thf(f1066,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f777])).
% 1.77/0.61 thf(f777,plain,(
% 1.77/0.61 ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0)),
% 1.77/0.61 inference(rectify,[],[f57])).
% 1.77/0.61 thf(f57,axiom,(
% 1.77/0.61 ! [X5 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X5),zero_zero(nat)) = X5)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Nat_Oadd__0__right)).
% 1.77/0.61 thf(f1915,plain,(
% 1.77/0.61 spl14_30 | ~spl14_22 | ~spl14_24),
% 1.77/0.61 inference(avatar_split_clause,[],[f1903,f1885,f1848,f1913])).
% 1.77/0.61 thf(f1913,plain,(
% 1.77/0.61 spl14_30 <=> ! [X0 : nat] : ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_30])])).
% 1.77/0.61 thf(f1885,plain,(
% 1.77/0.61 spl14_24 <=> ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_24])])).
% 1.77/0.61 thf(f1903,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | (~spl14_22 | ~spl14_24)),
% 1.77/0.61 inference(trivial_inequality_removal,[],[f1902])).
% 1.77/0.61 thf(f1902,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | (~spl14_22 | ~spl14_24)),
% 1.77/0.61 inference(superposition,[],[f1886,f1849])).
% 1.77/0.61 thf(f1886,plain,(
% 1.77/0.61 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | ~spl14_24),
% 1.77/0.61 inference(avatar_component_clause,[],[f1885])).
% 1.77/0.61 thf(f1911,plain,(
% 1.77/0.61 spl14_29),
% 1.77/0.61 inference(avatar_split_clause,[],[f1065,f1909])).
% 1.77/0.61 thf(f1909,plain,(
% 1.77/0.61 spl14_29 <=> ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) = X0)),
% 1.77/0.61 introduced(avatar_definition,[new_symbols(naming,[spl14_29])])).
% 1.77/0.61 thf(f1065,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) = X0)) )),
% 1.77/0.61 inference(cnf_transformation,[],[f776])).
% 1.77/0.61 thf(f776,plain,(
% 1.77/0.61 ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) = X0)),
% 1.77/0.61 inference(rectify,[],[f106])).
% 1.77/0.61 thf(f106,axiom,(
% 1.77/0.61 ! [X5 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),zero_zero(nat)) = X5)),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_minus__nat_Odiff__0)).
% 1.77/0.61 thf(f1907,plain,(
% 1.77/0.61 spl14_28),
% 1.77/0.61 inference(avatar_split_clause,[],[f1064,f1905])).
% 1.77/0.61 thf(f1064,plain,(
% 1.77/0.61 ( ! [X0 : nat] : ((zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0))) )),
% 1.77/0.61 inference(cnf_transformation,[],[f775])).
% 1.77/0.61 thf(f775,plain,(
% 1.77/0.61 ! [X0 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0))),
% 1.77/0.61 inference(rectify,[],[f60])).
% 1.77/0.61 thf(f60,axiom,(
% 1.77/0.61 ! [X5 : nat] : (zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X5),X5))),
% 1.77/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_diff__self__eq__0)).
% 1.77/0.61 thf(f1901,plain,(
% 1.77/0.61 spl14_27),
% 1.77/0.61 inference(avatar_split_clause,[],[f1342,f1898])).
% 1.77/0.61 thf(f1342,plain,(
% 1.77/0.61 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),k),n) = $true)),
% 1.77/0.61 inference(cnf_transformation,[],[f763])).
% 1.77/0.62 thf(f763,plain,(
% 1.77/0.62 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),k),n) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f762])).
% 1.77/0.62 thf(f762,plain,(
% 1.77/0.62 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),k),n)),
% 1.77/0.62 inference(rectify,[],[f5])).
% 1.77/0.62 thf(f5,axiom,(
% 1.77/0.62 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),k),n)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062k_A_092_060le_062_An_092_060close_062)).
% 1.77/0.62 thf(f1896,plain,(
% 1.77/0.62 spl14_26),
% 1.77/0.62 inference(avatar_split_clause,[],[f1341,f1893])).
% 1.77/0.62 thf(f1341,plain,(
% 1.77/0.62 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),i),n) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f761])).
% 1.77/0.62 thf(f761,plain,(
% 1.77/0.62 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),i),n) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f760])).
% 1.77/0.62 thf(f760,plain,(
% 1.77/0.62 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),i),n)),
% 1.77/0.62 inference(rectify,[],[f1])).
% 1.77/0.62 thf(f1,axiom,(
% 1.77/0.62 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),i),n)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062i_A_092_060le_062_An_092_060close_062)).
% 1.77/0.62 thf(f1891,plain,(
% 1.77/0.62 spl14_25),
% 1.77/0.62 inference(avatar_split_clause,[],[f1207,f1889])).
% 1.77/0.62 thf(f1889,plain,(
% 1.77/0.62 spl14_25 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0))),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_25])])).
% 1.77/0.62 thf(f1207,plain,(
% 1.77/0.62 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0))) )),
% 1.77/0.62 inference(cnf_transformation,[],[f557])).
% 1.77/0.62 thf(f557,plain,(
% 1.77/0.62 ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0))),
% 1.77/0.62 inference(fool_elimination,[],[f556])).
% 1.77/0.62 thf(f556,plain,(
% 1.77/0.62 ! [X0 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0)),
% 1.77/0.62 inference(rectify,[],[f193])).
% 1.77/0.62 thf(f193,axiom,(
% 1.77/0.62 ! [X3 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X3)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_le__refl)).
% 1.77/0.62 thf(f1887,plain,(
% 1.77/0.62 spl14_24),
% 1.77/0.62 inference(avatar_split_clause,[],[f1201,f1885])).
% 1.77/0.62 thf(f1201,plain,(
% 1.77/0.62 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) )),
% 1.77/0.62 inference(cnf_transformation,[],[f783])).
% 1.77/0.62 thf(f783,plain,(
% 1.77/0.62 ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 1.77/0.62 inference(flattening,[],[f545])).
% 1.77/0.62 thf(f545,plain,(
% 1.77/0.62 ! [X0 : nat] : ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 1.77/0.62 inference(fool_elimination,[],[f544])).
% 1.77/0.62 thf(f544,plain,(
% 1.77/0.62 ! [X0 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0)),
% 1.77/0.62 inference(rectify,[],[f183])).
% 1.77/0.62 thf(f183,axiom,(
% 1.77/0.62 ! [X3 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X3)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_less__irrefl__nat)).
% 1.77/0.62 thf(f1883,plain,(
% 1.77/0.62 ~spl14_23),
% 1.77/0.62 inference(avatar_split_clause,[],[f1060,f1880])).
% 1.77/0.62 thf(f1060,plain,(
% 1.77/0.62 (vAPP(nat,nat,p,i) != zero_zero(nat))),
% 1.77/0.62 inference(cnf_transformation,[],[f6])).
% 1.77/0.62 thf(f6,axiom,(
% 1.77/0.62 (vAPP(nat,nat,p,i) != zero_zero(nat))),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062p_Ai_A_092_060noteq_062_A0_092_060close_062)).
% 1.77/0.62 thf(f1850,plain,(
% 1.77/0.62 spl14_22),
% 1.77/0.62 inference(avatar_split_clause,[],[f277,f1848])).
% 1.77/0.62 thf(f277,plain,(
% 1.77/0.62 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.77/0.62 introduced(fool_axiom,[])).
% 1.77/0.62 thf(f1846,plain,(
% 1.77/0.62 spl14_21),
% 1.77/0.62 inference(avatar_split_clause,[],[f1340,f1843])).
% 1.77/0.62 thf(f1843,plain,(
% 1.77/0.62 spl14_21 <=> (canoni770627133id_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_21])])).
% 1.77/0.62 thf(f1340,plain,(
% 1.77/0.62 (canoni770627133id_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f759])).
% 1.77/0.62 thf(f759,plain,(
% 1.77/0.62 (canoni770627133id_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f758])).
% 1.77/0.62 thf(f758,plain,(
% 1.77/0.62 canoni770627133id_add(nat)),
% 1.77/0.62 inference(rectify,[],[f260])).
% 1.77/0.62 thf(f260,axiom,(
% 1.77/0.62 canoni770627133id_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add)).
% 1.77/0.62 thf(f1841,plain,(
% 1.77/0.62 spl14_20),
% 1.77/0.62 inference(avatar_split_clause,[],[f1339,f1838])).
% 1.77/0.62 thf(f1838,plain,(
% 1.77/0.62 spl14_20 <=> (ordere623563068d_diff(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_20])])).
% 1.77/0.62 thf(f1339,plain,(
% 1.77/0.62 (ordere623563068d_diff(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f757])).
% 1.77/0.62 thf(f757,plain,(
% 1.77/0.62 (ordere623563068d_diff(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f756])).
% 1.77/0.62 thf(f756,plain,(
% 1.77/0.62 ordere623563068d_diff(nat)),
% 1.77/0.62 inference(rectify,[],[f257])).
% 1.77/0.62 thf(f257,axiom,(
% 1.77/0.62 ordere623563068d_diff(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff)).
% 1.77/0.62 thf(f1836,plain,(
% 1.77/0.62 spl14_19),
% 1.77/0.62 inference(avatar_split_clause,[],[f1338,f1833])).
% 1.77/0.62 thf(f1833,plain,(
% 1.77/0.62 spl14_19 <=> (ordere516151231imp_le(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_19])])).
% 1.77/0.62 thf(f1338,plain,(
% 1.77/0.62 (ordere516151231imp_le(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f755])).
% 1.77/0.62 thf(f755,plain,(
% 1.77/0.62 (ordere516151231imp_le(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f754])).
% 1.77/0.62 thf(f754,plain,(
% 1.77/0.62 ordere516151231imp_le(nat)),
% 1.77/0.62 inference(rectify,[],[f255])).
% 1.77/0.62 thf(f255,axiom,(
% 1.77/0.62 ordere516151231imp_le(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le)).
% 1.77/0.62 thf(f1831,plain,(
% 1.77/0.62 spl14_18),
% 1.77/0.62 inference(avatar_split_clause,[],[f1337,f1828])).
% 1.77/0.62 thf(f1828,plain,(
% 1.77/0.62 spl14_18 <=> (ordere236663937imp_le(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_18])])).
% 1.77/0.62 thf(f1337,plain,(
% 1.77/0.62 (ordere236663937imp_le(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f753])).
% 1.77/0.62 thf(f753,plain,(
% 1.77/0.62 (ordere236663937imp_le(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f752])).
% 1.77/0.62 thf(f752,plain,(
% 1.77/0.62 ordere236663937imp_le(nat)),
% 1.77/0.62 inference(rectify,[],[f259])).
% 1.77/0.62 thf(f259,axiom,(
% 1.77/0.62 ordere236663937imp_le(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le)).
% 1.77/0.62 thf(f1826,plain,(
% 1.77/0.62 spl14_17),
% 1.77/0.62 inference(avatar_split_clause,[],[f1336,f1823])).
% 1.77/0.62 thf(f1823,plain,(
% 1.77/0.62 spl14_17 <=> (ordere779506340up_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_17])])).
% 1.77/0.62 thf(f1336,plain,(
% 1.77/0.62 (ordere779506340up_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f751])).
% 1.77/0.62 thf(f751,plain,(
% 1.77/0.62 (ordere779506340up_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f750])).
% 1.77/0.62 thf(f750,plain,(
% 1.77/0.62 ordere779506340up_add(nat)),
% 1.77/0.62 inference(rectify,[],[f261])).
% 1.77/0.62 thf(f261,axiom,(
% 1.77/0.62 ordere779506340up_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add)).
% 1.77/0.62 thf(f1821,plain,(
% 1.77/0.62 spl14_16),
% 1.77/0.62 inference(avatar_split_clause,[],[f1335,f1818])).
% 1.77/0.62 thf(f1818,plain,(
% 1.77/0.62 spl14_16 <=> (cancel1352612707id_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_16])])).
% 1.77/0.62 thf(f1335,plain,(
% 1.77/0.62 (cancel1352612707id_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f749])).
% 1.77/0.62 thf(f749,plain,(
% 1.77/0.62 (cancel1352612707id_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f748])).
% 1.77/0.62 thf(f748,plain,(
% 1.77/0.62 cancel1352612707id_add(nat)),
% 1.77/0.62 inference(rectify,[],[f263])).
% 1.77/0.62 thf(f263,axiom,(
% 1.77/0.62 cancel1352612707id_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add)).
% 1.77/0.62 thf(f1816,plain,(
% 1.77/0.62 spl14_15),
% 1.77/0.62 inference(avatar_split_clause,[],[f1334,f1813])).
% 1.77/0.62 thf(f1813,plain,(
% 1.77/0.62 spl14_15 <=> (cancel146912293up_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_15])])).
% 1.77/0.62 thf(f1334,plain,(
% 1.77/0.62 (cancel146912293up_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f747])).
% 1.77/0.62 thf(f747,plain,(
% 1.77/0.62 (cancel146912293up_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f746])).
% 1.77/0.62 thf(f746,plain,(
% 1.77/0.62 cancel146912293up_add(nat)),
% 1.77/0.62 inference(rectify,[],[f262])).
% 1.77/0.62 thf(f262,axiom,(
% 1.77/0.62 cancel146912293up_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add)).
% 1.77/0.62 thf(f1811,plain,(
% 1.77/0.62 spl14_14),
% 1.77/0.62 inference(avatar_split_clause,[],[f1333,f1808])).
% 1.77/0.62 thf(f1808,plain,(
% 1.77/0.62 spl14_14 <=> (ordere223160158up_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_14])])).
% 1.77/0.62 thf(f1333,plain,(
% 1.77/0.62 (ordere223160158up_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f745])).
% 1.77/0.62 thf(f745,plain,(
% 1.77/0.62 (ordere223160158up_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f744])).
% 1.77/0.62 thf(f744,plain,(
% 1.77/0.62 ordere223160158up_add(nat)),
% 1.77/0.62 inference(rectify,[],[f258])).
% 1.77/0.62 thf(f258,axiom,(
% 1.77/0.62 ordere223160158up_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add)).
% 1.77/0.62 thf(f1806,plain,(
% 1.77/0.62 spl14_13),
% 1.77/0.62 inference(avatar_split_clause,[],[f1332,f1803])).
% 1.77/0.62 thf(f1803,plain,(
% 1.77/0.62 spl14_13 <=> (cancel_semigroup_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_13])])).
% 1.77/0.62 thf(f1332,plain,(
% 1.77/0.62 (cancel_semigroup_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f743])).
% 1.77/0.62 thf(f743,plain,(
% 1.77/0.62 (cancel_semigroup_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f742])).
% 1.77/0.62 thf(f742,plain,(
% 1.77/0.62 cancel_semigroup_add(nat)),
% 1.77/0.62 inference(rectify,[],[f264])).
% 1.77/0.62 thf(f264,axiom,(
% 1.77/0.62 cancel_semigroup_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add)).
% 1.77/0.62 thf(f1801,plain,(
% 1.77/0.62 spl14_12),
% 1.77/0.62 inference(avatar_split_clause,[],[f1331,f1798])).
% 1.77/0.62 thf(f1798,plain,(
% 1.77/0.62 spl14_12 <=> (comm_monoid_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_12])])).
% 1.77/0.62 thf(f1331,plain,(
% 1.77/0.62 (comm_monoid_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f741])).
% 1.77/0.62 thf(f741,plain,(
% 1.77/0.62 (comm_monoid_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f740])).
% 1.77/0.62 thf(f740,plain,(
% 1.77/0.62 comm_monoid_add(nat)),
% 1.77/0.62 inference(rectify,[],[f268])).
% 1.77/0.62 thf(f268,axiom,(
% 1.77/0.62 comm_monoid_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add)).
% 1.77/0.62 thf(f1796,plain,(
% 1.77/0.62 spl14_11),
% 1.77/0.62 inference(avatar_split_clause,[],[f1330,f1793])).
% 1.77/0.62 thf(f1793,plain,(
% 1.77/0.62 spl14_11 <=> (ab_semigroup_mult(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_11])])).
% 1.77/0.62 thf(f1330,plain,(
% 1.77/0.62 (ab_semigroup_mult(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f739])).
% 1.77/0.62 thf(f739,plain,(
% 1.77/0.62 (ab_semigroup_mult(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f738])).
% 1.77/0.62 thf(f738,plain,(
% 1.77/0.62 ab_semigroup_mult(nat)),
% 1.77/0.62 inference(rectify,[],[f265])).
% 1.77/0.62 thf(f265,axiom,(
% 1.77/0.62 ab_semigroup_mult(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult)).
% 1.77/0.62 thf(f1791,plain,(
% 1.77/0.62 spl14_10),
% 1.77/0.62 inference(avatar_split_clause,[],[f1329,f1788])).
% 1.77/0.62 thf(f1788,plain,(
% 1.77/0.62 spl14_10 <=> (ab_semigroup_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_10])])).
% 1.77/0.62 thf(f1329,plain,(
% 1.77/0.62 (ab_semigroup_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f737])).
% 1.77/0.62 thf(f737,plain,(
% 1.77/0.62 (ab_semigroup_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f736])).
% 1.77/0.62 thf(f736,plain,(
% 1.77/0.62 ab_semigroup_add(nat)),
% 1.77/0.62 inference(rectify,[],[f267])).
% 1.77/0.62 thf(f267,axiom,(
% 1.77/0.62 ab_semigroup_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add)).
% 1.77/0.62 thf(f1786,plain,(
% 1.77/0.62 spl14_9),
% 1.77/0.62 inference(avatar_split_clause,[],[f1328,f1783])).
% 1.77/0.62 thf(f1783,plain,(
% 1.77/0.62 spl14_9 <=> (comm_monoid_diff(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_9])])).
% 1.77/0.62 thf(f1328,plain,(
% 1.77/0.62 (comm_monoid_diff(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f735])).
% 1.77/0.62 thf(f735,plain,(
% 1.77/0.62 (comm_monoid_diff(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f734])).
% 1.77/0.62 thf(f734,plain,(
% 1.77/0.62 comm_monoid_diff(nat)),
% 1.77/0.62 inference(rectify,[],[f266])).
% 1.77/0.62 thf(f266,axiom,(
% 1.77/0.62 comm_monoid_diff(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff)).
% 1.77/0.62 thf(f1781,plain,(
% 1.77/0.62 spl14_8),
% 1.77/0.62 inference(avatar_split_clause,[],[f1327,f1778])).
% 1.77/0.62 thf(f1778,plain,(
% 1.77/0.62 spl14_8 <=> (monoid_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_8])])).
% 1.77/0.62 thf(f1327,plain,(
% 1.77/0.62 (monoid_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f733])).
% 1.77/0.62 thf(f733,plain,(
% 1.77/0.62 (monoid_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f732])).
% 1.77/0.62 thf(f732,plain,(
% 1.77/0.62 monoid_add(nat)),
% 1.77/0.62 inference(rectify,[],[f272])).
% 1.77/0.62 thf(f272,axiom,(
% 1.77/0.62 monoid_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add)).
% 1.77/0.62 thf(f1776,plain,(
% 1.77/0.62 spl14_7),
% 1.77/0.62 inference(avatar_split_clause,[],[f1326,f1773])).
% 1.77/0.62 thf(f1773,plain,(
% 1.77/0.62 spl14_7 <=> (wellorder(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_7])])).
% 1.77/0.62 thf(f1326,plain,(
% 1.77/0.62 (wellorder(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f731])).
% 1.77/0.62 thf(f731,plain,(
% 1.77/0.62 (wellorder(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f730])).
% 1.77/0.62 thf(f730,plain,(
% 1.77/0.62 wellorder(nat)),
% 1.77/0.62 inference(rectify,[],[f271])).
% 1.77/0.62 thf(f271,axiom,(
% 1.77/0.62 wellorder(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder)).
% 1.77/0.62 thf(f1771,plain,(
% 1.77/0.62 spl14_6),
% 1.77/0.62 inference(avatar_split_clause,[],[f1325,f1768])).
% 1.77/0.62 thf(f1768,plain,(
% 1.77/0.62 spl14_6 <=> (strict2144017051up_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_6])])).
% 1.77/0.62 thf(f1325,plain,(
% 1.77/0.62 (strict2144017051up_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f729])).
% 1.77/0.62 thf(f729,plain,(
% 1.77/0.62 (strict2144017051up_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f728])).
% 1.77/0.62 thf(f728,plain,(
% 1.77/0.62 strict2144017051up_add(nat)),
% 1.77/0.62 inference(rectify,[],[f256])).
% 1.77/0.62 thf(f256,axiom,(
% 1.77/0.62 strict2144017051up_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add)).
% 1.77/0.62 thf(f1766,plain,(
% 1.77/0.62 spl14_5),
% 1.77/0.62 inference(avatar_split_clause,[],[f1324,f1763])).
% 1.77/0.62 thf(f1763,plain,(
% 1.77/0.62 spl14_5 <=> (semigroup_add(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_5])])).
% 1.77/0.62 thf(f1324,plain,(
% 1.77/0.62 (semigroup_add(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f727])).
% 1.77/0.62 thf(f727,plain,(
% 1.77/0.62 (semigroup_add(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f726])).
% 1.77/0.62 thf(f726,plain,(
% 1.77/0.62 semigroup_add(nat)),
% 1.77/0.62 inference(rectify,[],[f270])).
% 1.77/0.62 thf(f270,axiom,(
% 1.77/0.62 semigroup_add(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add)).
% 1.77/0.62 thf(f1761,plain,(
% 1.77/0.62 spl14_4),
% 1.77/0.62 inference(avatar_split_clause,[],[f1323,f1758])).
% 1.77/0.62 thf(f1758,plain,(
% 1.77/0.62 spl14_4 <=> (semigroup_mult(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_4])])).
% 1.77/0.62 thf(f1323,plain,(
% 1.77/0.62 (semigroup_mult(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f725])).
% 1.77/0.62 thf(f725,plain,(
% 1.77/0.62 (semigroup_mult(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f724])).
% 1.77/0.62 thf(f724,plain,(
% 1.77/0.62 semigroup_mult(nat)),
% 1.77/0.62 inference(rectify,[],[f269])).
% 1.77/0.62 thf(f269,axiom,(
% 1.77/0.62 semigroup_mult(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult)).
% 1.77/0.62 thf(f1756,plain,(
% 1.77/0.62 spl14_3),
% 1.77/0.62 inference(avatar_split_clause,[],[f1322,f1753])).
% 1.77/0.62 thf(f1753,plain,(
% 1.77/0.62 spl14_3 <=> (zero(nat) = $true)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_3])])).
% 1.77/0.62 thf(f1322,plain,(
% 1.77/0.62 (zero(nat) = $true)),
% 1.77/0.62 inference(cnf_transformation,[],[f723])).
% 1.77/0.62 thf(f723,plain,(
% 1.77/0.62 (zero(nat) = $true)),
% 1.77/0.62 inference(fool_elimination,[],[f722])).
% 1.77/0.62 thf(f722,plain,(
% 1.77/0.62 zero(nat)),
% 1.77/0.62 inference(rectify,[],[f273])).
% 1.77/0.62 thf(f273,axiom,(
% 1.77/0.62 zero(nat)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero)).
% 1.77/0.62 thf(f1751,plain,(
% 1.77/0.62 ~spl14_2),
% 1.77/0.62 inference(avatar_split_clause,[],[f1059,f1748])).
% 1.77/0.62 thf(f1059,plain,(
% 1.77/0.62 (i != k)),
% 1.77/0.62 inference(cnf_transformation,[],[f8])).
% 1.77/0.62 thf(f8,axiom,(
% 1.77/0.62 (i != k)),
% 1.77/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062i_A_092_060noteq_062_Ak_092_060close_062)).
% 1.77/0.62 thf(f1746,plain,(
% 1.77/0.62 ~spl14_1),
% 1.77/0.62 inference(avatar_split_clause,[],[f276,f1743])).
% 1.77/0.62 thf(f1743,plain,(
% 1.77/0.62 spl14_1 <=> ($true = $false)),
% 1.77/0.62 introduced(avatar_definition,[new_symbols(naming,[spl14_1])])).
% 1.77/0.62 thf(f276,plain,(
% 1.77/0.62 ($true != $false)),
% 1.77/0.62 introduced(fool_axiom,[])).
% 1.77/0.62 % SZS output end Proof for theBenchmark
% 1.77/0.62 % (10525)------------------------------
% 1.77/0.62 % (10525)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.77/0.62 % (10525)Termination reason: Refutation
% 1.77/0.62
% 1.77/0.62 % (10525)Memory used [KB]: 3325
% 1.77/0.62 % (10525)Time elapsed: 0.221 s
% 1.77/0.62 % (10525)Instructions burned: 596 (million)
% 1.77/0.62 % (10520)Success in time 0.262 s
%------------------------------------------------------------------------------