TSTP Solution File: ITP130^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP130^1 : 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 : n004.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 22:52:45 EDT 2024
% Result : Theorem 3.62s 0.92s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 787
% Syntax : Number of formulae : 2709 ( 590 unt; 115 typ; 0 def)
% Number of atoms : 27350 (4652 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 7363 (2807 ~;2995 |; 272 &; 0 @)
% ( 407 <=>; 882 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 717 ( 716 >; 1 *; 0 +; 0 <<)
% Number of symbols : 521 ( 518 usr; 419 con; 0-6 aty)
% Number of variables : 4237 ( 14 ^3978 !; 231 ?;4237 :)
% ( 14 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
int: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(type_def_7,type,
real: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
real: $tType ).
thf(func_def_1,type,
nat: $tType ).
thf(func_def_2,type,
int: $tType ).
thf(func_def_3,type,
zero_zero_int: int ).
thf(func_def_4,type,
zero_zero_nat: nat ).
thf(func_def_5,type,
zero_zero_real: real ).
thf(func_def_6,type,
ring_1_of_int_int: int > int ).
thf(func_def_7,type,
ring_1_of_int_real: int > real ).
thf(func_def_8,type,
suc: nat > nat ).
thf(func_def_9,type,
nthRoo1352626670d_root: nat > nat > $o ).
thf(func_def_10,type,
ord_less_int: int > int > $o ).
thf(func_def_11,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_12,type,
ord_less_real: real > real > $o ).
thf(func_def_13,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_14,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_15,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_16,type,
power_power_int: int > nat > int ).
thf(func_def_17,type,
power_power_nat: nat > nat > nat ).
thf(func_def_18,type,
power_power_real: real > nat > real ).
thf(func_def_19,type,
divide_divide_int: int > int > int ).
thf(func_def_20,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_21,type,
divide_divide_real: real > real > real ).
thf(func_def_22,type,
ny: real ).
thf(func_def_23,type,
na: int ).
thf(func_def_24,type,
p: nat ).
thf(func_def_25,type,
pm: nat ).
thf(func_def_26,type,
x: int ).
thf(func_def_27,type,
y: int ).
thf(func_def_28,type,
ya: int ).
thf(func_def_32,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_33,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_34,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_35,type,
vOR: $o > $o > $o ).
thf(func_def_36,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vIMP: $o > $o > $o ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
sP0: nat > ( nat > $o ) > $o ).
thf(func_def_43,type,
sP1: ( nat > nat > $o ) > $o ).
thf(func_def_44,type,
sK2: nat > nat ).
thf(func_def_45,type,
sK3: nat > nat ).
thf(func_def_46,type,
sK4: ( nat > $o ) > nat ).
thf(func_def_47,type,
sK5: nat > nat ).
thf(func_def_48,type,
sK6: real > real ).
thf(func_def_49,type,
sK7: real > real ).
thf(func_def_50,type,
sK8: real > int ).
thf(func_def_51,type,
sK9: real > int ).
thf(func_def_52,type,
sK10: real > int ).
thf(func_def_53,type,
sK11: ( nat > $o ) > nat ).
thf(func_def_54,type,
sK12: ( nat > $o ) > nat ).
thf(func_def_55,type,
sK13: ( nat > $o ) > nat ).
thf(func_def_56,type,
sK14: ( nat > $o ) > nat ).
thf(func_def_57,type,
sK15: ( nat > $o ) > nat ).
thf(func_def_58,type,
sK16: ( nat > $o ) > nat ).
thf(func_def_59,type,
sK17: nat > ( nat > $o ) > nat ).
thf(func_def_60,type,
sK18: nat > ( nat > $o ) > nat ).
thf(func_def_61,type,
sK19: ( nat > $o ) > nat ).
thf(func_def_62,type,
sK20: nat > real > real ).
thf(func_def_63,type,
sK21: real > nat > real ).
thf(func_def_64,type,
sK22: real > nat > real ).
thf(func_def_65,type,
sK23: nat > nat > nat ).
thf(func_def_66,type,
sK24: nat > nat ).
thf(func_def_67,type,
sK25: nat > nat > nat ).
thf(func_def_68,type,
sK26: ( nat > nat > $o ) > nat ).
thf(func_def_69,type,
sK27: ( nat > nat > $o ) > nat ).
thf(func_def_70,type,
sK28: ( nat > nat > $o ) > nat ).
thf(func_def_71,type,
sK29: ( nat > nat > $o ) > nat ).
thf(func_def_72,type,
sK30: ( nat > int ) > nat ).
thf(func_def_73,type,
sK31: ( nat > int ) > nat ).
thf(func_def_74,type,
sK32: ( nat > int ) > nat ).
thf(func_def_75,type,
sK33: ( nat > int ) > nat ).
thf(func_def_76,type,
sK34: ( nat > real ) > nat ).
thf(func_def_77,type,
sK35: ( nat > real ) > nat ).
thf(func_def_78,type,
sK36: ( nat > real ) > nat ).
thf(func_def_79,type,
sK37: ( nat > real ) > nat ).
thf(func_def_80,type,
sK38: ( nat > nat ) > nat ).
thf(func_def_81,type,
sK39: ( nat > nat ) > nat ).
thf(func_def_82,type,
sK40: ( nat > nat ) > nat ).
thf(func_def_83,type,
sK41: ( nat > nat ) > nat ).
thf(func_def_84,type,
sK42: ( nat > nat ) > nat ).
thf(func_def_85,type,
sK43: ( nat > nat ) > nat ).
thf(func_def_86,type,
sK44: ( nat > $o ) > nat ).
thf(func_def_87,type,
sK45: nat > ( nat > $o ) > nat ).
thf(func_def_88,type,
sK46: ( nat > nat > $o ) > nat ).
thf(func_def_89,type,
sK47: ( nat > nat > $o ) > nat ).
thf(func_def_90,type,
sK48: ( nat > nat > $o ) > nat ).
thf(func_def_91,type,
sK49: ( nat > nat > $o ) > nat ).
thf(func_def_92,type,
sK50: ( nat > nat > $o ) > nat ).
thf(func_def_93,type,
sK51: ( nat > $o ) > nat > nat ).
thf(func_def_94,type,
sK52: ( nat > $o ) > nat > nat > nat ).
thf(func_def_95,type,
sK53: ( nat > $o ) > nat > nat > nat ).
thf(func_def_96,type,
sK54: nat > ( nat > $o ) > nat ).
thf(func_def_97,type,
sK55: ( nat > $o ) > nat > nat ).
thf(func_def_98,type,
sK56: ( nat > nat > $o ) > nat ).
thf(func_def_99,type,
sK57: ( nat > nat > $o ) > nat ).
thf(func_def_100,type,
sK58: ( nat > nat > $o ) > nat ).
thf(func_def_101,type,
sK59: ( nat > nat > $o ) > nat ).
thf(func_def_103,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_104,type,
sK61: nat > nat > nat ).
thf(func_def_105,type,
sK62: nat > nat > nat ).
thf(func_def_106,type,
sK63: ( nat > $o ) > nat > nat ).
thf(func_def_107,type,
sK64: ( nat > $o ) > nat > nat ).
thf(func_def_108,type,
sK65: ( nat > $o ) > nat > nat ).
thf(func_def_109,type,
sK66: ( nat > $o ) > nat > nat ).
thf(func_def_110,type,
sK67: ( nat > $o ) > nat > nat ).
thf(func_def_111,type,
sK68: ( nat > $o ) > nat > nat ).
thf(func_def_112,type,
sK69: ( nat > $o ) > nat > nat ).
thf(func_def_113,type,
sK70: ( nat > $o ) > nat > nat ).
thf(func_def_114,type,
sK71: nat > nat ).
thf(f14314,plain,
$false,
inference(avatar_sat_refutation,[],[f2319,f2324,f2329,f2334,f2338,f2371,f2376,f2380,f2384,f2389,f2395,f2402,f2407,f2412,f2417,f2421,f2425,f2429,f2433,f2437,f2441,f2445,f2449,f2454,f2462,f2467,f2472,f2482,f2486,f2490,f2494,f2503,f2507,f2515,f2519,f2523,f2527,f2531,f2535,f2539,f2543,f2547,f2551,f2555,f2560,f2565,f2573,f2584,f2588,f2592,f2626,f2630,f2634,f2638,f2643,f2652,f2674,f2678,f2682,f2686,f2690,f2694,f2699,f2704,f2709,f2781,f2798,f2812,f2816,f2820,f2850,f2854,f2858,f2862,f2866,f2870,f2935,f2939,f2943,f2947,f2951,f2955,f3031,f3044,f3069,f3073,f3077,f3081,f3085,f3144,f3148,f3152,f3156,f3200,f3214,f3218,f3223,f3227,f3231,f3291,f3295,f3299,f3303,f3308,f3336,f3340,f3345,f3399,f3403,f3409,f3413,f3417,f3422,f3463,f3467,f3471,f3519,f3530,f3534,f3546,f3610,f3614,f3618,f3622,f3626,f3630,f3645,f3649,f3653,f3657,f3661,f3665,f3669,f3673,f3677,f3790,f3821,f3840,f3859,f3875,f3879,f3883,f3887,f3891,f3969,f3982,f3986,f3990,f3994,f3998,f4002,f4061,f4065,f4099,f4103,f4107,f4111,f4115,f4119,f4124,f4128,f4132,f4136,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4319,f4385,f4389,f4393,f4412,f4435,f4439,f4443,f4447,f4500,f4504,f4515,f4519,f4523,f4560,f4575,f4587,f4591,f4595,f4599,f4603,f4607,f4611,f4615,f4629,f4742,f4746,f4797,f4803,f4812,f4816,f4820,f4824,f4828,f4864,f4868,f4872,f4884,f4902,f4906,f4927,f4944,f4948,f4952,f4978,f4982,f5016,f5020,f5039,f5043,f5055,f5059,f5063,f5067,f5071,f5119,f5123,f5144,f5155,f5174,f5178,f5182,f5186,f5217,f5221,f5226,f5254,f5265,f5281,f5296,f5300,f5304,f5344,f5356,f5360,f5387,f5404,f5409,f5416,f5420,f5424,f5428,f5432,f5436,f5562,f5569,f5574,f5579,f5584,f5589,f5594,f5599,f5604,f5608,f5613,f5617,f5898,f5965,f5969,f5973,f5977,f5985,f6150,f6153,f6156,f6159,f6900,f7153,f7744,f7753,f7757,f7762,f7848,f7852,f7856,f7860,f7866,f7870,f8783,f8866,f8870,f8874,f8878,f8882,f8886,f8892,f8896,f8900,f8904,f8908,f8912,f8916,f8920,f8924,f9134,f9190,f9195,f9199,f9203,f9229,f9235,f9304,f9308,f9312,f9316,f9320,f9324,f9328,f9332,f9333,f9339,f9343,f9347,f9351,f9355,f9359,f9363,f9367,f9372,f9377,f10361,f10472,f10477,f10481,f10714,f10718,f10722,f10726,f10738,f10798,f10802,f10806,f10810,f10814,f10818,f10822,f10826,f10830,f10834,f10838,f10842,f10846,f10850,f10854,f10858,f10862,f10906,f10910,f10914,f10918,f11296,f11801,f11805,f11809,f11813,f11817,f11822,f11826,f11830,f11834,f12820,f12867,f12871,f12875,f12879,f12888,f12894,f12898,f12903,f12917,f12921,f12925,f12929,f12933,f13311,f13315,f13319,f13324,f13328,f13332,f13336,f13340,f13344,f13348,f13352,f13356,f13360,f13364,f13419,f13423,f13892,f13896,f13900,f13905,f13909,f13913,f14292,f14296,f14300,f14310,f14313]) ).
thf(f14313,plain,
( ~ spl60_63
| ~ spl60_402 ),
inference(avatar_contradiction_clause,[],[f14312]) ).
thf(f14312,plain,
( $false
| ~ spl60_63
| ~ spl60_402 ),
inference(trivial_inequality_removal,[],[f14301]) ).
thf(f14301,plain,
( ( $true = $false )
| ~ spl60_63
| ~ spl60_402 ),
inference(superposition,[],[f13904,f2698]) ).
thf(f2698,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) )
| ~ spl60_63 ),
inference(avatar_component_clause,[],[f2696]) ).
thf(f2696,plain,
( spl60_63
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_63])]) ).
thf(f13904,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) )
| ~ spl60_402 ),
inference(avatar_component_clause,[],[f13902]) ).
thf(f13902,plain,
( spl60_402
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_402])]) ).
thf(f14310,plain,
( ~ spl60_63
| ~ spl60_402 ),
inference(avatar_contradiction_clause,[],[f14309]) ).
thf(f14309,plain,
( $false
| ~ spl60_63
| ~ spl60_402 ),
inference(trivial_inequality_removal,[],[f14305]) ).
thf(f14305,plain,
( ( $true = $false )
| ~ spl60_63
| ~ spl60_402 ),
inference(superposition,[],[f2698,f13904]) ).
thf(f14300,plain,
( spl60_407
| ~ spl60_5
| ~ spl60_86 ),
inference(avatar_split_clause,[],[f3099,f3071,f2336,f14298]) ).
thf(f14298,plain,
( spl60_407
<=> ! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_407])]) ).
thf(f2336,plain,
( spl60_5
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_5])]) ).
thf(f3071,plain,
( spl60_86
<=> ! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_86])]) ).
thf(f3099,plain,
( ! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false ) )
| ~ spl60_5
| ~ spl60_86 ),
inference(trivial_inequality_removal,[],[f3098]) ).
thf(f3098,plain,
( ! [X0: int,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false ) )
| ~ spl60_5
| ~ spl60_86 ),
inference(superposition,[],[f3072,f2337]) ).
thf(f2337,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl60_5 ),
inference(avatar_component_clause,[],[f2336]) ).
thf(f3072,plain,
( ! [X0: int,X1: nat] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) )
| ~ spl60_86 ),
inference(avatar_component_clause,[],[f3071]) ).
thf(f14296,plain,
( spl60_406
| ~ spl60_5
| ~ spl60_85 ),
inference(avatar_split_clause,[],[f3090,f3067,f2336,f14294]) ).
thf(f14294,plain,
( spl60_406
<=> ! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_406])]) ).
thf(f3067,plain,
( spl60_85
<=> ! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_85])]) ).
thf(f3090,plain,
( ! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $false ) )
| ~ spl60_5
| ~ spl60_85 ),
inference(trivial_inequality_removal,[],[f3089]) ).
thf(f3089,plain,
( ! [X0: int,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $false ) )
| ~ spl60_5
| ~ spl60_85 ),
inference(superposition,[],[f3068,f2337]) ).
thf(f3068,plain,
( ! [X0: int,X1: nat] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) )
| ~ spl60_85 ),
inference(avatar_component_clause,[],[f3067]) ).
thf(f14292,plain,
( spl60_405
| ~ spl60_55
| ~ spl60_70 ),
inference(avatar_split_clause,[],[f2845,f2818,f2641,f14290]) ).
thf(f14290,plain,
( spl60_405
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_405])]) ).
thf(f2641,plain,
( spl60_55
<=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_55])]) ).
thf(f2818,plain,
( spl60_70
<=> ! [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) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_70])]) ).
thf(f2845,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)) ) )
| ~ spl60_55
| ~ spl60_70 ),
inference(trivial_inequality_removal,[],[f2840]) ).
thf(f2840,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)) ) )
| ~ spl60_55
| ~ spl60_70 ),
inference(superposition,[],[f2819,f2642]) ).
thf(f2642,plain,
( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X0) )
| ~ spl60_55 ),
inference(avatar_component_clause,[],[f2641]) ).
thf(f2819,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
| ~ spl60_70 ),
inference(avatar_component_clause,[],[f2818]) ).
thf(f13913,plain,
( spl60_404
| ~ spl60_23
| ~ spl60_118 ),
inference(avatar_split_clause,[],[f3559,f3528,f2447,f13911]) ).
thf(f13911,plain,
( spl60_404
<=> ! [X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X0),X1)) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_404])]) ).
thf(f2447,plain,
( spl60_23
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_23])]) ).
thf(f3528,plain,
( spl60_118
<=> ! [X0: nat > $o,X1: nat,X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_118])]) ).
thf(f3559,plain,
( ! [X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X0),X1)) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X1,X0) ) )
| ~ spl60_23
| ~ spl60_118 ),
inference(trivial_inequality_removal,[],[f3550]) ).
thf(f3550,plain,
( ! [X0: nat,X1: nat > $o] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X0),X1)) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X1,X0) ) )
| ~ spl60_23
| ~ spl60_118 ),
inference(superposition,[],[f3529,f2448]) ).
thf(f2448,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) )
| ~ spl60_23 ),
inference(avatar_component_clause,[],[f2447]) ).
thf(f3529,plain,
( ! [X3: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)) )
| ( $true != vAPP(nat,$o,X0,X3) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) )
| ~ spl60_118 ),
inference(avatar_component_clause,[],[f3528]) ).
thf(f13909,plain,
( spl60_403
| ~ spl60_45
| ~ spl60_100 ),
inference(avatar_split_clause,[],[f3322,f3289,f2557,f13907]) ).
thf(f13907,plain,
( spl60_403
<=> ! [X0: nat] : ( vAPP(int,real,ring_1_of_int_real,na) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,na))),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_403])]) ).
thf(f2557,plain,
( spl60_45
<=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,na)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_45])]) ).
thf(f3289,plain,
( spl60_100
<=> ! [X0: real,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)),vAPP(nat,nat,suc,X1)) = X0 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_100])]) ).
thf(f3322,plain,
( ! [X0: nat] : ( vAPP(int,real,ring_1_of_int_real,na) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,na))),vAPP(nat,nat,suc,X0)) )
| ~ spl60_45
| ~ spl60_100 ),
inference(trivial_inequality_removal,[],[f3309]) ).
thf(f3309,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(int,real,ring_1_of_int_real,na) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,na))),vAPP(nat,nat,suc,X0)) ) )
| ~ spl60_45
| ~ spl60_100 ),
inference(superposition,[],[f3290,f2559]) ).
thf(f2559,plain,
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,na)) = $true )
| ~ spl60_45 ),
inference(avatar_component_clause,[],[f2557]) ).
thf(f3290,plain,
( ! [X0: real,X1: nat] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)),vAPP(nat,nat,suc,X1)) = X0 ) )
| ~ spl60_100 ),
inference(avatar_component_clause,[],[f3289]) ).
thf(f13905,plain,
( spl60_402
| ~ spl60_14
| ~ spl60_393 ),
inference(avatar_split_clause,[],[f13834,f13350,f2409,f13902]) ).
thf(f2409,plain,
( spl60_14
<=> ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_14])]) ).
thf(f13350,plain,
( spl60_393
<=> ! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_393])]) ).
thf(f13834,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) )
| ~ spl60_14
| ~ spl60_393 ),
inference(trivial_inequality_removal,[],[f13821]) ).
thf(f13821,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) )
| ~ spl60_14
| ~ spl60_393 ),
inference(superposition,[],[f13351,f2411]) ).
thf(f2411,plain,
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm)))) )
| ~ spl60_14 ),
inference(avatar_component_clause,[],[f2409]) ).
thf(f13351,plain,
( ! [X0: int,X1: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) )
| ~ spl60_393 ),
inference(avatar_component_clause,[],[f13350]) ).
thf(f13900,plain,
( spl60_401
| ~ spl60_46
| ~ spl60_100 ),
inference(avatar_split_clause,[],[f3321,f3289,f2562,f13898]) ).
thf(f13898,plain,
( spl60_401
<=> ! [X0: nat] : ( vAPP(int,real,ring_1_of_int_real,ya) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,ya))),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_401])]) ).
thf(f2562,plain,
( spl60_46
<=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,ya)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_46])]) ).
thf(f3321,plain,
( ! [X0: nat] : ( vAPP(int,real,ring_1_of_int_real,ya) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,ya))),vAPP(nat,nat,suc,X0)) )
| ~ spl60_46
| ~ spl60_100 ),
inference(trivial_inequality_removal,[],[f3310]) ).
thf(f3310,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(int,real,ring_1_of_int_real,ya) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,ya))),vAPP(nat,nat,suc,X0)) ) )
| ~ spl60_46
| ~ spl60_100 ),
inference(superposition,[],[f3290,f2564]) ).
thf(f2564,plain,
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,ya)) = $true )
| ~ spl60_46 ),
inference(avatar_component_clause,[],[f2562]) ).
thf(f13896,plain,
( spl60_400
| ~ spl60_43
| ~ spl60_100 ),
inference(avatar_split_clause,[],[f3320,f3289,f2549,f13894]) ).
thf(f13894,plain,
( spl60_400
<=> ! [X0: nat] : ( vAPP(real,real,sK6,zero_zero_real) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(real,real,sK6,zero_zero_real))),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_400])]) ).
thf(f2549,plain,
( spl60_43
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,sK6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_43])]) ).
thf(f3320,plain,
( ! [X0: nat] : ( vAPP(real,real,sK6,zero_zero_real) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(real,real,sK6,zero_zero_real))),vAPP(nat,nat,suc,X0)) )
| ~ spl60_43
| ~ spl60_100 ),
inference(trivial_inequality_removal,[],[f3311]) ).
thf(f3311,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(real,real,sK6,zero_zero_real) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(real,real,sK6,zero_zero_real))),vAPP(nat,nat,suc,X0)) ) )
| ~ spl60_43
| ~ spl60_100 ),
inference(superposition,[],[f3290,f2550]) ).
thf(f2550,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,sK6,X0)) )
| ~ spl60_43 ),
inference(avatar_component_clause,[],[f2549]) ).
thf(f13892,plain,
( spl60_399
| ~ spl60_5
| ~ spl60_84 ),
inference(avatar_split_clause,[],[f3056,f3042,f2336,f13890]) ).
thf(f13890,plain,
( spl60_399
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)) )
| ( $false = vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_399])]) ).
thf(f3042,plain,
( spl60_84
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_84])]) ).
thf(f3056,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_5
| ~ spl60_84 ),
inference(trivial_inequality_removal,[],[f3055]) ).
thf(f3055,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_5
| ~ spl60_84 ),
inference(superposition,[],[f3043,f2337]) ).
thf(f3043,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)) ) )
| ~ spl60_84 ),
inference(avatar_component_clause,[],[f3042]) ).
thf(f13423,plain,
( spl60_398
| ~ spl60_95 ),
inference(avatar_split_clause,[],[f3253,f3212,f13421]) ).
thf(f13421,plain,
( spl60_398
<=> ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_398])]) ).
thf(f3212,plain,
( spl60_95
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_95])]) ).
thf(f3253,plain,
( ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl60_95 ),
inference(equality_proxy_clausification,[],[f3252]) ).
thf(f3252,plain,
( ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( zero_zero_nat = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) ) )
| ~ spl60_95 ),
inference(equality_proxy_clausification,[],[f3251]) ).
thf(f3251,plain,
( ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) ) )
| ~ spl60_95 ),
inference(equality_proxy_clausification,[],[f3236]) ).
thf(f3236,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) ) )
| ~ spl60_95 ),
inference(primitive_instantiation,[],[f3213]) ).
thf(f3213,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0))) ) )
| ~ spl60_95 ),
inference(avatar_component_clause,[],[f3212]) ).
thf(f13419,plain,
spl60_397,
inference(avatar_split_clause,[],[f2173,f13417]) ).
thf(f13417,plain,
( spl60_397
<=> ! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_397])]) ).
thf(f2173,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ) ),
inference(binary_proxy_clausification,[],[f1383]) ).
thf(f1383,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ),
inference(cnf_transformation,[],[f873]) ).
thf(f873,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ),
inference(rectify,[],[f13]) ).
thf(f13,axiom,
! [X1: int,X3: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X1)),vAPP(int,int,ring_1_of_int_int,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_of__int__less__iff) ).
thf(f13364,plain,
spl60_396,
inference(avatar_split_clause,[],[f2172,f13362]) ).
thf(f13362,plain,
( spl60_396
<=> ! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_396])]) ).
thf(f2172,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ) ),
inference(binary_proxy_clausification,[],[f1383]) ).
thf(f13360,plain,
spl60_395,
inference(avatar_split_clause,[],[f2171,f13358]) ).
thf(f13358,plain,
( spl60_395
<=> ! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_395])]) ).
thf(f2171,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ) ),
inference(binary_proxy_clausification,[],[f1384]) ).
thf(f1384,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ),
inference(cnf_transformation,[],[f874]) ).
thf(f874,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ),
inference(rectify,[],[f102]) ).
thf(f102,axiom,
! [X1: int,X3: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X1)),vAPP(int,int,ring_1_of_int_int,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_of__int__le__iff) ).
thf(f13356,plain,
spl60_394,
inference(avatar_split_clause,[],[f2170,f13354]) ).
thf(f13354,plain,
( spl60_394
<=> ! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_394])]) ).
thf(f2170,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) ) ),
inference(binary_proxy_clausification,[],[f1384]) ).
thf(f13352,plain,
spl60_393,
inference(avatar_split_clause,[],[f2169,f13350]) ).
thf(f2169,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f1387]) ).
thf(f1387,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ),
inference(cnf_transformation,[],[f877]) ).
thf(f877,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X1: int,X3: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X1)),vAPP(int,real,ring_1_of_int_real,X3)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_of__int__less__iff) ).
thf(f13348,plain,
spl60_392,
inference(avatar_split_clause,[],[f2168,f13346]) ).
thf(f13346,plain,
( spl60_392
<=> ! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_392])]) ).
thf(f2168,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f1387]) ).
thf(f13344,plain,
spl60_391,
inference(avatar_split_clause,[],[f2167,f13342]) ).
thf(f13342,plain,
( spl60_391
<=> ! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_391])]) ).
thf(f2167,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f1388]) ).
thf(f1388,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ),
inference(cnf_transformation,[],[f878]) ).
thf(f878,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X1: int,X3: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X1)),vAPP(int,real,ring_1_of_int_real,X3)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_of__int__le__iff) ).
thf(f13340,plain,
spl60_390,
inference(avatar_split_clause,[],[f2166,f13338]) ).
thf(f13338,plain,
( spl60_390
<=> ! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_390])]) ).
thf(f2166,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f1388]) ).
thf(f13336,plain,
spl60_389,
inference(avatar_split_clause,[],[f2165,f13334]) ).
thf(f13334,plain,
( spl60_389
<=> ! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$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,suc,X0)),vAPP(nat,nat,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_389])]) ).
thf(f2165,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(binary_proxy_clausification,[],[f1389]) ).
thf(f1389,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(cnf_transformation,[],[f879]) ).
thf(f879,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f217]) ).
thf(f217,axiom,
! [X4: nat,X9: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X4)),vAPP(nat,nat,suc,X9)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_Suc__le__mono) ).
thf(f13332,plain,
spl60_388,
inference(avatar_split_clause,[],[f2164,f13330]) ).
thf(f13330,plain,
( spl60_388
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_388])]) ).
thf(f2164,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(binary_proxy_clausification,[],[f1389]) ).
thf(f13328,plain,
spl60_387,
inference(avatar_split_clause,[],[f1896,f13326]) ).
thf(f13326,plain,
( spl60_387
<=> ! [X2: nat,X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2) )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_387])]) ).
thf(f1896,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2) )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) != X0 ) ),
inference(equality_proxy_clausification,[],[f1895]) ).
thf(f1895,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) ) ),
inference(equality_proxy_clausification,[],[f1891]) ).
thf(f1891,plain,
! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,ring_1_of_int_int,X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2)) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) ) ),
inference(binary_proxy_clausification,[],[f1534]) ).
thf(f1534,plain,
! [X2: nat,X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,ring_1_of_int_int,X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) ),
inference(cnf_transformation,[],[f661]) ).
thf(f661,plain,
! [X0: int,X1: int,X2: nat] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,ring_1_of_int_int,X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) ),
inference(fool_elimination,[],[f660]) ).
thf(f660,plain,
! [X0: int,X1: int,X2: nat] :
( ( vAPP(int,int,ring_1_of_int_int,X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2) )
= ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) = X0 ) ),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
! [X2: int,X0: int,X1: nat] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X0)),X1) = vAPP(int,int,ring_1_of_int_int,X2) )
= ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_of__int__power__eq__of__int__cancel__iff) ).
thf(f13324,plain,
( spl60_386
| ~ spl60_45
| ~ spl60_345 ),
inference(avatar_split_clause,[],[f11399,f10828,f2557,f13321]) ).
thf(f13321,plain,
( spl60_386
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),na) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_386])]) ).
thf(f10828,plain,
( spl60_345
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_345])]) ).
thf(f11399,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),na) )
| ~ spl60_45
| ~ spl60_345 ),
inference(trivial_inequality_removal,[],[f11367]) ).
thf(f11367,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),na) )
| ~ spl60_45
| ~ spl60_345 ),
inference(superposition,[],[f10829,f2559]) ).
thf(f10829,plain,
( ! [X0: int] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $true ) )
| ~ spl60_345 ),
inference(avatar_component_clause,[],[f10828]) ).
thf(f13319,plain,
spl60_385,
inference(avatar_split_clause,[],[f1894,f13317]) ).
thf(f13317,plain,
( spl60_385
<=> ! [X2: nat,X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2) )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_385])]) ).
thf(f1894,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2) )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) = X0 ) ),
inference(equality_proxy_clausification,[],[f1893]) ).
thf(f1893,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) ) ),
inference(equality_proxy_clausification,[],[f1892]) ).
thf(f1892,plain,
! [X2: nat,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,ring_1_of_int_int,X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X1)),X2)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) ) ),
inference(binary_proxy_clausification,[],[f1534]) ).
thf(f13315,plain,
spl60_384,
inference(avatar_split_clause,[],[f1884,f13313]) ).
thf(f13313,plain,
( spl60_384
<=> ! [X2: nat,X0: int,X1: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) = X0 )
| ( vAPP(int,real,ring_1_of_int_real,X0) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_384])]) ).
thf(f1884,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) = X0 )
| ( vAPP(int,real,ring_1_of_int_real,X0) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2) ) ),
inference(equality_proxy_clausification,[],[f1883]) ).
thf(f1883,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) = X0 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2)) ) ),
inference(equality_proxy_clausification,[],[f1879]) ).
thf(f1879,plain,
! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2)) ) ),
inference(binary_proxy_clausification,[],[f1536]) ).
thf(f1536,plain,
! [X2: nat,X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2)) ),
inference(cnf_transformation,[],[f664]) ).
thf(f664,plain,
! [X0: int,X1: int,X2: nat] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2)) ),
inference(fool_elimination,[],[f663]) ).
thf(f663,plain,
! [X0: int,X1: int,X2: nat] :
( ( vAPP(int,real,ring_1_of_int_real,X0) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2) )
= ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) = X0 ) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X2: int,X0: int,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X0)),X1) = vAPP(int,real,ring_1_of_int_real,X2) )
= ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_of__int__power__eq__of__int__cancel__iff) ).
thf(f13311,plain,
spl60_383,
inference(avatar_split_clause,[],[f1882,f13309]) ).
thf(f13309,plain,
( spl60_383
<=> ! [X2: nat,X0: int,X1: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) != X0 )
| ( vAPP(int,real,ring_1_of_int_real,X0) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_383])]) ).
thf(f1882,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) != X0 )
| ( vAPP(int,real,ring_1_of_int_real,X0) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2) ) ),
inference(equality_proxy_clausification,[],[f1881]) ).
thf(f1881,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2) != X0 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2)) ) ),
inference(equality_proxy_clausification,[],[f1880]) ).
thf(f1880,plain,
! [X2: nat,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X1)),X2)) ) ),
inference(binary_proxy_clausification,[],[f1536]) ).
thf(f12933,plain,
( spl60_382
| ~ spl60_120
| ~ spl60_181 ),
inference(avatar_split_clause,[],[f4511,f4502,f3544,f12931]) ).
thf(f12931,plain,
( spl60_382
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_382])]) ).
thf(f3544,plain,
( spl60_120
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_120])]) ).
thf(f4502,plain,
( spl60_181
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_181])]) ).
thf(f4511,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)) )
| ~ spl60_120
| ~ spl60_181 ),
inference(trivial_inequality_removal,[],[f4508]) ).
thf(f4508,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)) ) )
| ~ spl60_120
| ~ spl60_181 ),
inference(superposition,[],[f4503,f3545]) ).
thf(f3545,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,suc,X0)) )
| ~ spl60_120 ),
inference(avatar_component_clause,[],[f3544]) ).
thf(f4503,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 ) )
| ~ spl60_181 ),
inference(avatar_component_clause,[],[f4502]) ).
thf(f12929,plain,
( spl60_381
| ~ spl60_25
| ~ spl60_26
| ~ spl60_155 ),
inference(avatar_split_clause,[],[f4171,f4101,f2464,f2459,f12927]) ).
thf(f12927,plain,
( spl60_381
<=> ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_381])]) ).
thf(f2459,plain,
( spl60_25
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),ya) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_25])]) ).
thf(f2464,plain,
( spl60_26
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_26])]) ).
thf(f4101,plain,
( spl60_155
<=> ! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_155])]) ).
thf(f4171,plain,
( ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) )
| ~ spl60_25
| ~ spl60_26
| ~ spl60_155 ),
inference(trivial_inequality_removal,[],[f4170]) ).
thf(f4170,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) ) )
| ~ spl60_25
| ~ spl60_26
| ~ spl60_155 ),
inference(forward_demodulation,[],[f4161,f2466]) ).
thf(f2466,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) = $true )
| ~ spl60_26 ),
inference(avatar_component_clause,[],[f2464]) ).
thf(f4161,plain,
( ! [X0: nat] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) ) )
| ~ spl60_25
| ~ spl60_155 ),
inference(trivial_inequality_removal,[],[f4156]) ).
thf(f4156,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) ) )
| ~ spl60_25
| ~ spl60_155 ),
inference(superposition,[],[f4102,f2461]) ).
thf(f2461,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),ya) = $true )
| ~ spl60_25 ),
inference(avatar_component_clause,[],[f2459]) ).
thf(f4102,plain,
( ! [X2: nat,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) )
| ~ spl60_155 ),
inference(avatar_component_clause,[],[f4101]) ).
thf(f12925,plain,
( spl60_380
| ~ spl60_26
| ~ spl60_27
| ~ spl60_155 ),
inference(avatar_split_clause,[],[f4169,f4101,f2469,f2464,f12923]) ).
thf(f12923,plain,
( spl60_380
<=> ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_380])]) ).
thf(f2469,plain,
( spl60_27
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_27])]) ).
thf(f4169,plain,
( ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),X0)) )
| ~ spl60_26
| ~ spl60_27
| ~ spl60_155 ),
inference(trivial_inequality_removal,[],[f4168]) ).
thf(f4168,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),X0)) ) )
| ~ spl60_26
| ~ spl60_27
| ~ spl60_155 ),
inference(forward_demodulation,[],[f4162,f2466]) ).
thf(f4162,plain,
( ! [X0: nat] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),X0)) ) )
| ~ spl60_27
| ~ spl60_155 ),
inference(trivial_inequality_removal,[],[f4155]) ).
thf(f4155,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),X0)) ) )
| ~ spl60_27
| ~ spl60_155 ),
inference(superposition,[],[f4102,f2471]) ).
thf(f2471,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),x) )
| ~ spl60_27 ),
inference(avatar_component_clause,[],[f2469]) ).
thf(f12921,plain,
( spl60_379
| ~ spl60_24
| ~ spl60_26
| ~ spl60_155 ),
inference(avatar_split_clause,[],[f4167,f4101,f2464,f2451,f12919]) ).
thf(f12919,plain,
( spl60_379
<=> ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_379])]) ).
thf(f2451,plain,
( spl60_24
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),na) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_24])]) ).
thf(f4167,plain,
( ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0)) )
| ~ spl60_24
| ~ spl60_26
| ~ spl60_155 ),
inference(trivial_inequality_removal,[],[f4166]) ).
thf(f4166,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0)) ) )
| ~ spl60_24
| ~ spl60_26
| ~ spl60_155 ),
inference(forward_demodulation,[],[f4163,f2466]) ).
thf(f4163,plain,
( ! [X0: nat] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0)) ) )
| ~ spl60_24
| ~ spl60_155 ),
inference(trivial_inequality_removal,[],[f4154]) ).
thf(f4154,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0)) ) )
| ~ spl60_24
| ~ spl60_155 ),
inference(superposition,[],[f4102,f2453]) ).
thf(f2453,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),na) = $true )
| ~ spl60_24 ),
inference(avatar_component_clause,[],[f2451]) ).
thf(f12917,plain,
( spl60_378
| ~ spl60_26
| ~ spl60_155 ),
inference(avatar_split_clause,[],[f4165,f4101,f2464,f12915]) ).
thf(f12915,plain,
( spl60_378
<=> ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_378])]) ).
thf(f4165,plain,
( ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) )
| ~ spl60_26
| ~ spl60_155 ),
inference(trivial_inequality_removal,[],[f4164]) ).
thf(f4164,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) ) )
| ~ spl60_26
| ~ spl60_155 ),
inference(duplicate_literal_removal,[],[f4153]) ).
thf(f4153,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) ) )
| ~ spl60_26
| ~ spl60_155 ),
inference(superposition,[],[f4102,f2466]) ).
thf(f12903,plain,
( spl60_377
| ~ spl60_5
| spl60_373 ),
inference(avatar_split_clause,[],[f12890,f12881,f2336,f12900]) ).
thf(f12900,plain,
( spl60_377
<=> ( $false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_377])]) ).
thf(f12881,plain,
( spl60_373
<=> ( $true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_373])]) ).
thf(f12890,plain,
( ( $false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) )
| ~ spl60_5
| spl60_373 ),
inference(trivial_inequality_removal,[],[f12889]) ).
thf(f12889,plain,
( ( $true != $true )
| ( $false = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) )
| ~ spl60_5
| spl60_373 ),
inference(superposition,[],[f12883,f2337]) ).
thf(f12883,plain,
( ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) )
| spl60_373 ),
inference(avatar_component_clause,[],[f12881]) ).
thf(f12898,plain,
( spl60_376
| ~ spl60_22
| ~ spl60_116 ),
inference(avatar_split_clause,[],[f3515,f3469,f2443,f12896]) ).
thf(f12896,plain,
( spl60_376
<=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_376])]) ).
thf(f2443,plain,
( spl60_22
<=> ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_22])]) ).
thf(f3469,plain,
( spl60_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),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_116])]) ).
thf(f3515,plain,
( ! [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),power_power_nat,zero_zero_nat),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ~ spl60_22
| ~ spl60_116 ),
inference(trivial_inequality_removal,[],[f3502]) ).
thf(f3502,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) )
| ~ spl60_22
| ~ spl60_116 ),
inference(superposition,[],[f3470,f2444]) ).
thf(f2444,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true )
| ~ spl60_22 ),
inference(avatar_component_clause,[],[f2443]) ).
thf(f3470,plain,
( ! [X2: nat,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,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ) )
| ~ spl60_116 ),
inference(avatar_component_clause,[],[f3469]) ).
thf(f12894,plain,
( spl60_375
| ~ spl60_22
| ~ spl60_114 ),
inference(avatar_split_clause,[],[f3485,f3461,f2443,f12892]) ).
thf(f12892,plain,
( spl60_375
<=> ! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X1),zero_zero_nat)) )
| ( $true != vAPP(nat,$o,X1,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_375])]) ).
thf(f3461,plain,
( spl60_114
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0)) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_114])]) ).
thf(f3485,plain,
( ! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X1),zero_zero_nat)) )
| ( $true != vAPP(nat,$o,X1,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X1,X0) ) )
| ~ spl60_22
| ~ spl60_114 ),
inference(trivial_inequality_removal,[],[f3473]) ).
thf(f3473,plain,
( ! [X0: nat,X1: nat > $o] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X1),zero_zero_nat)) )
| ( $true != vAPP(nat,$o,X1,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X1,X0) ) )
| ~ spl60_22
| ~ spl60_114 ),
inference(superposition,[],[f3462,f2444]) ).
thf(f3462,plain,
( ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0)) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(nat,$o,X2,X1) ) )
| ~ spl60_114 ),
inference(avatar_component_clause,[],[f3461]) ).
thf(f12888,plain,
( ~ spl60_373
| ~ spl60_374
| ~ spl60_103 ),
inference(avatar_split_clause,[],[f3332,f3301,f12885,f12881]) ).
thf(f12885,plain,
( spl60_374
<=> ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,vEQ(nat)) = vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,vEQ(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_374])]) ).
thf(f3301,plain,
( spl60_103
<=> ! [X0: nat > nat > $o] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_103])]) ).
thf(f3332,plain,
( ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,vEQ(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,vEQ(nat)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) )
| ~ spl60_103 ),
inference(equality_proxy_clausification,[],[f3327]) ).
thf(f3327,plain,
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,vEQ(nat))) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) )
| ~ spl60_103 ),
inference(primitive_instantiation,[],[f3302]) ).
thf(f3302,plain,
( ! [X0: nat > nat > $o] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) )
| ~ spl60_103 ),
inference(avatar_component_clause,[],[f3301]) ).
thf(f12879,plain,
( spl60_372
| ~ spl60_30
| ~ spl60_76 ),
inference(avatar_split_clause,[],[f2923,f2868,f2488,f12877]) ).
thf(f12877,plain,
( spl60_372
<=> ! [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,vAPP(nat,nat,sK3,X0)),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_372])]) ).
thf(f2488,plain,
( spl60_30
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_30])]) ).
thf(f2868,plain,
( spl60_76
<=> ! [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,vAPP(nat,nat,suc,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_76])]) ).
thf(f2923,plain,
( ! [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,vAPP(nat,nat,sK3,X0)),X1) )
| ( zero_zero_nat = X0 ) )
| ~ spl60_30
| ~ spl60_76 ),
inference(superposition,[],[f2869,f2489]) ).
thf(f2489,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_30 ),
inference(avatar_component_clause,[],[f2488]) ).
thf(f2869,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
| ~ spl60_76 ),
inference(avatar_component_clause,[],[f2868]) ).
thf(f12875,plain,
( spl60_371
| ~ spl60_29
| ~ spl60_76 ),
inference(avatar_split_clause,[],[f2922,f2868,f2484,f12873]) ).
thf(f12873,plain,
( spl60_371
<=> ! [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,vAPP(nat,nat,sK2,X0)),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_371])]) ).
thf(f2484,plain,
( spl60_29
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK2,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_29])]) ).
thf(f2922,plain,
( ! [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,vAPP(nat,nat,sK2,X0)),X1) )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29
| ~ spl60_76 ),
inference(superposition,[],[f2869,f2485]) ).
thf(f2485,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK2,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29 ),
inference(avatar_component_clause,[],[f2484]) ).
thf(f12871,plain,
( spl60_370
| ~ spl60_68
| ~ spl60_72 ),
inference(avatar_split_clause,[],[f2885,f2852,f2810,f12869]) ).
thf(f12869,plain,
( spl60_370
<=> ! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( zero_zero_int = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_370])]) ).
thf(f2810,plain,
( spl60_68
<=> ! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_68])]) ).
thf(f2852,plain,
( spl60_72
<=> ! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_72])]) ).
thf(f2885,plain,
( ! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( zero_zero_int = X0 ) )
| ~ spl60_68
| ~ spl60_72 ),
inference(trivial_inequality_removal,[],[f2880]) ).
thf(f2880,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( zero_zero_int = X0 ) )
| ~ spl60_68
| ~ spl60_72 ),
inference(superposition,[],[f2853,f2811]) ).
thf(f2811,plain,
( ! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 ) )
| ~ spl60_68 ),
inference(avatar_component_clause,[],[f2810]) ).
thf(f2853,plain,
( ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) )
| ~ spl60_72 ),
inference(avatar_component_clause,[],[f2852]) ).
thf(f12867,plain,
( spl60_369
| ~ spl60_68
| ~ spl60_71 ),
inference(avatar_split_clause,[],[f2877,f2848,f2810,f12865]) ).
thf(f12865,plain,
( spl60_369
<=> ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( zero_zero_int = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_369])]) ).
thf(f2848,plain,
( spl60_71
<=> ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_71])]) ).
thf(f2877,plain,
( ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( zero_zero_int = X0 ) )
| ~ spl60_68
| ~ spl60_71 ),
inference(trivial_inequality_removal,[],[f2872]) ).
thf(f2872,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( zero_zero_int = X0 ) )
| ~ spl60_68
| ~ spl60_71 ),
inference(superposition,[],[f2849,f2811]) ).
thf(f2849,plain,
( ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) )
| ~ spl60_71 ),
inference(avatar_component_clause,[],[f2848]) ).
thf(f12820,plain,
( spl60_368
| ~ spl60_7
| ~ spl60_104
| ~ spl60_341 ),
inference(avatar_split_clause,[],[f11272,f10812,f3305,f2373,f12817]) ).
thf(f12817,plain,
( spl60_368
<=> ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_368])]) ).
thf(f2373,plain,
( spl60_7
<=> ( zero_zero_real = vAPP(int,real,ring_1_of_int_real,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_7])]) ).
thf(f3305,plain,
( spl60_104
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_104])]) ).
thf(f10812,plain,
( spl60_341
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_341])]) ).
thf(f11272,plain,
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),zero_zero_real) )
| ~ spl60_7
| ~ spl60_104
| ~ spl60_341 ),
inference(trivial_inequality_removal,[],[f11271]) ).
thf(f11271,plain,
( ( $true = $false )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),zero_zero_real) )
| ~ spl60_7
| ~ spl60_104
| ~ spl60_341 ),
inference(forward_demodulation,[],[f11249,f3307]) ).
thf(f3307,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) = $false )
| ~ spl60_104 ),
inference(avatar_component_clause,[],[f3305]) ).
thf(f11249,plain,
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),zero_zero_real) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) = $true )
| ~ spl60_7
| ~ spl60_341 ),
inference(superposition,[],[f10813,f2375]) ).
thf(f2375,plain,
( ( zero_zero_real = vAPP(int,real,ring_1_of_int_real,zero_zero_int) )
| ~ spl60_7 ),
inference(avatar_component_clause,[],[f2373]) ).
thf(f10813,plain,
( ! [X0: int] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true ) )
| ~ spl60_341 ),
inference(avatar_component_clause,[],[f10812]) ).
thf(f11834,plain,
( spl60_367
| ~ spl60_95 ),
inference(avatar_split_clause,[],[f3254,f3212,f11832]) ).
thf(f11832,plain,
( spl60_367
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_367])]) ).
thf(f3254,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_95 ),
inference(equality_proxy_clausification,[],[f3232]) ).
thf(f3232,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) )
| ( zero_zero_nat = X0 ) )
| ~ spl60_95 ),
inference(leibniz_equality_elimination,[],[f3213]) ).
thf(f11830,plain,
( spl60_366
| ~ spl60_53
| ~ spl60_79
| ~ spl60_89 ),
inference(avatar_split_clause,[],[f3139,f3083,f2941,f2632,f11828]) ).
thf(f11828,plain,
( spl60_366
<=> ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(real,int,sK9,zero_zero_real)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_366])]) ).
thf(f2632,plain,
( spl60_53
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK9,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_53])]) ).
thf(f2941,plain,
( spl60_79
<=> ! [X0: int,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X0)),X1) = vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_79])]) ).
thf(f3083,plain,
( spl60_89
<=> ! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_89])]) ).
thf(f3139,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(real,int,sK9,zero_zero_real)),X0))) )
| ~ spl60_53
| ~ spl60_79
| ~ spl60_89 ),
inference(forward_demodulation,[],[f3138,f2942]) ).
thf(f2942,plain,
( ! [X0: int,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X0)),X1) = vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ~ spl60_79 ),
inference(avatar_component_clause,[],[f2941]) ).
thf(f3138,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK9,zero_zero_real))),X0)) )
| ~ spl60_53
| ~ spl60_89 ),
inference(trivial_inequality_removal,[],[f3135]) ).
thf(f3135,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK9,zero_zero_real))),X0)) ) )
| ~ spl60_53
| ~ spl60_89 ),
inference(superposition,[],[f3084,f2633]) ).
thf(f2633,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK9,X0))) )
| ~ spl60_53 ),
inference(avatar_component_clause,[],[f2632]) ).
thf(f3084,plain,
( ! [X0: real,X1: nat] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ) )
| ~ spl60_89 ),
inference(avatar_component_clause,[],[f3083]) ).
thf(f11826,plain,
( spl60_365
| ~ spl60_52
| ~ spl60_79
| ~ spl60_88 ),
inference(avatar_split_clause,[],[f3134,f3079,f2941,f2628,f11824]) ).
thf(f11824,plain,
( spl60_365
<=> ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(real,int,sK8,zero_zero_real)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_365])]) ).
thf(f2628,plain,
( spl60_52
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_52])]) ).
thf(f3079,plain,
( spl60_88
<=> ! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_88])]) ).
thf(f3134,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(real,int,sK8,zero_zero_real)),X0))) )
| ~ spl60_52
| ~ spl60_79
| ~ spl60_88 ),
inference(forward_demodulation,[],[f3128,f2942]) ).
thf(f3128,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,zero_zero_real))),X0)) )
| ~ spl60_52
| ~ spl60_88 ),
inference(trivial_inequality_removal,[],[f3121]) ).
thf(f3121,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,zero_zero_real))),X0)) ) )
| ~ spl60_52
| ~ spl60_88 ),
inference(superposition,[],[f3080,f2629]) ).
thf(f2629,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,X0))) )
| ~ spl60_52 ),
inference(avatar_component_clause,[],[f2628]) ).
thf(f3080,plain,
( ! [X0: real,X1: nat] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ) )
| ~ spl60_88 ),
inference(avatar_component_clause,[],[f3079]) ).
thf(f11822,plain,
( spl60_364
| ~ spl60_265
| ~ spl60_337 ),
inference(avatar_split_clause,[],[f11027,f10796,f5610,f11819]) ).
thf(f11819,plain,
( spl60_364
<=> ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,pm),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_364])]) ).
thf(f5610,plain,
( spl60_265
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),pm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_265])]) ).
thf(f10796,plain,
( spl60_337
<=> ! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_337])]) ).
thf(f11027,plain,
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,pm),zero_zero_nat) )
| ~ spl60_265
| ~ spl60_337 ),
inference(trivial_inequality_removal,[],[f10933]) ).
thf(f10933,plain,
( ( $true = $false )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,pm),zero_zero_nat) )
| ~ spl60_265
| ~ spl60_337 ),
inference(superposition,[],[f10797,f5612]) ).
thf(f5612,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),pm) )
| ~ spl60_265 ),
inference(avatar_component_clause,[],[f5610]) ).
thf(f10797,plain,
( ! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
| ~ spl60_337 ),
inference(avatar_component_clause,[],[f10796]) ).
thf(f11817,plain,
( spl60_363
| ~ spl60_52
| ~ spl60_87 ),
inference(avatar_split_clause,[],[f3114,f3075,f2628,f11815]) ).
thf(f11815,plain,
( spl60_363
<=> ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,zero_zero_real)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_363])]) ).
thf(f3075,plain,
( spl60_87
<=> ! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_87])]) ).
thf(f3114,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,zero_zero_real)))) )
| ~ spl60_52
| ~ spl60_87 ),
inference(trivial_inequality_removal,[],[f3107]) ).
thf(f3107,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,zero_zero_real)))) ) )
| ~ spl60_52
| ~ spl60_87 ),
inference(superposition,[],[f3076,f2629]) ).
thf(f3076,plain,
( ! [X0: real,X1: nat] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)) ) )
| ~ spl60_87 ),
inference(avatar_component_clause,[],[f3075]) ).
thf(f11813,plain,
( spl60_362
| ~ spl60_5
| ~ spl60_82 ),
inference(avatar_split_clause,[],[f3018,f2953,f2336,f11811]) ).
thf(f11811,plain,
( spl60_362
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_362])]) ).
thf(f2953,plain,
( spl60_82
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_82])]) ).
thf(f3018,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_5
| ~ spl60_82 ),
inference(trivial_inequality_removal,[],[f3017]) ).
thf(f3017,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_5
| ~ spl60_82 ),
inference(superposition,[],[f2954,f2337]) ).
thf(f2954,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_82 ),
inference(avatar_component_clause,[],[f2953]) ).
thf(f11809,plain,
( spl60_361
| ~ spl60_5
| ~ spl60_81 ),
inference(avatar_split_clause,[],[f3003,f2949,f2336,f11807]) ).
thf(f11807,plain,
( spl60_361
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_361])]) ).
thf(f2949,plain,
( spl60_81
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_81])]) ).
thf(f3003,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,X0))) ) )
| ~ spl60_5
| ~ spl60_81 ),
inference(trivial_inequality_removal,[],[f3002]) ).
thf(f3002,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,X0))) ) )
| ~ spl60_5
| ~ spl60_81 ),
inference(superposition,[],[f2950,f2337]) ).
thf(f2950,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,X0))) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_81 ),
inference(avatar_component_clause,[],[f2949]) ).
thf(f11805,plain,
( spl60_360
| ~ spl60_5
| ~ spl60_80 ),
inference(avatar_split_clause,[],[f2990,f2945,f2336,f11803]) ).
thf(f11803,plain,
( spl60_360
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_360])]) ).
thf(f2945,plain,
( spl60_80
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_80])]) ).
thf(f2990,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,X0))) ) )
| ~ spl60_5
| ~ spl60_80 ),
inference(trivial_inequality_removal,[],[f2989]) ).
thf(f2989,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,X0))) ) )
| ~ spl60_5
| ~ spl60_80 ),
inference(superposition,[],[f2946,f2337]) ).
thf(f2946,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,X0))) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_80 ),
inference(avatar_component_clause,[],[f2945]) ).
thf(f11801,plain,
( spl60_359
| ~ spl60_5
| ~ spl60_77 ),
inference(avatar_split_clause,[],[f2966,f2933,f2336,f11799]) ).
thf(f11799,plain,
( spl60_359
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_359])]) ).
thf(f2933,plain,
( spl60_77
<=> ! [X2: nat,X0: nat > $o] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,X0))) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_77])]) ).
thf(f2966,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_5
| ~ spl60_77 ),
inference(trivial_inequality_removal,[],[f2965]) ).
thf(f2965,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_5
| ~ spl60_77 ),
inference(superposition,[],[f2934,f2337]) ).
thf(f2934,plain,
( ! [X2: nat,X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_77 ),
inference(avatar_component_clause,[],[f2933]) ).
thf(f11296,plain,
( spl60_358
| ~ spl60_8
| ~ spl60_293 ),
inference(avatar_split_clause,[],[f10863,f8890,f2378,f11294]) ).
thf(f11294,plain,
( spl60_358
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK5,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_358])]) ).
thf(f2378,plain,
( spl60_8
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_8])]) ).
thf(f8890,plain,
( spl60_293
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_293])]) ).
thf(f10863,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK5,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_8
| ~ spl60_293 ),
inference(superposition,[],[f2379,f8891]) ).
thf(f8891,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_293 ),
inference(avatar_component_clause,[],[f8890]) ).
thf(f2379,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 )
| ~ spl60_8 ),
inference(avatar_component_clause,[],[f2378]) ).
thf(f10918,plain,
( spl60_357
| ~ spl60_84 ),
inference(avatar_split_clause,[],[f3064,f3042,f10916]) ).
thf(f10916,plain,
( spl60_357
<=> ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( zero_zero_nat = X0 )
| ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_357])]) ).
thf(f3064,plain,
( ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( zero_zero_nat = X0 )
| ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 ) )
| ~ spl60_84 ),
inference(equality_proxy_clausification,[],[f3063]) ).
thf(f3063,plain,
( ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( zero_zero_nat = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) ) )
| ~ spl60_84 ),
inference(equality_proxy_clausification,[],[f3062]) ).
thf(f3062,plain,
( ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) ) )
| ~ spl60_84 ),
inference(equality_proxy_clausification,[],[f3049]) ).
thf(f3049,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) ) )
| ~ spl60_84 ),
inference(primitive_instantiation,[],[f3043]) ).
thf(f10914,plain,
( spl60_356
| ~ spl60_5
| ~ spl60_76 ),
inference(avatar_split_clause,[],[f2928,f2868,f2336,f10912]) ).
thf(f10912,plain,
( spl60_356
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_356])]) ).
thf(f2928,plain,
( ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) )
| ~ spl60_5
| ~ spl60_76 ),
inference(trivial_inequality_removal,[],[f2927]) ).
thf(f2927,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) )
| ~ spl60_5
| ~ spl60_76 ),
inference(superposition,[],[f2869,f2337]) ).
thf(f10910,plain,
( spl60_355
| ~ spl60_56
| ~ spl60_75 ),
inference(avatar_split_clause,[],[f2918,f2864,f2650,f10908]) ).
thf(f10908,plain,
( spl60_355
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_355])]) ).
thf(f2650,plain,
( spl60_56
<=> ! [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) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_56])]) ).
thf(f2864,plain,
( spl60_75
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_75])]) ).
thf(f2918,plain,
( ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) )
| ~ spl60_56
| ~ spl60_75 ),
inference(trivial_inequality_removal,[],[f2913]) ).
thf(f2913,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) )
| ~ spl60_56
| ~ spl60_75 ),
inference(superposition,[],[f2865,f2651]) ).
thf(f2651,plain,
( ! [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) ) )
| ~ spl60_56 ),
inference(avatar_component_clause,[],[f2650]) ).
thf(f2865,plain,
( ! [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,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) ) )
| ~ spl60_75 ),
inference(avatar_component_clause,[],[f2864]) ).
thf(f10906,plain,
spl60_354,
inference(avatar_split_clause,[],[f2267,f10904]) ).
thf(f10904,plain,
( spl60_354
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_354])]) ).
thf(f2267,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(binary_proxy_clausification,[],[f1321]) ).
thf(f1321,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ),
inference(cnf_transformation,[],[f852]) ).
thf(f852,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ),
inference(rectify,[],[f38]) ).
thf(f38,axiom,
! [X3: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_of__int__0__less__iff) ).
thf(f10862,plain,
spl60_353,
inference(avatar_split_clause,[],[f2266,f10860]) ).
thf(f10860,plain,
( spl60_353
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_353])]) ).
thf(f2266,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(binary_proxy_clausification,[],[f1321]) ).
thf(f10858,plain,
spl60_352,
inference(avatar_split_clause,[],[f2265,f10856]) ).
thf(f10856,plain,
( spl60_352
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_352])]) ).
thf(f2265,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(binary_proxy_clausification,[],[f1322]) ).
thf(f1322,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ),
inference(cnf_transformation,[],[f853]) ).
thf(f853,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ),
inference(rectify,[],[f109]) ).
thf(f109,axiom,
! [X3: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_of__int__0__le__iff) ).
thf(f10854,plain,
spl60_351,
inference(avatar_split_clause,[],[f2264,f10852]) ).
thf(f10852,plain,
( spl60_351
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_351])]) ).
thf(f2264,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(binary_proxy_clausification,[],[f1322]) ).
thf(f10850,plain,
spl60_350,
inference(avatar_split_clause,[],[f2263,f10848]) ).
thf(f10848,plain,
( spl60_350
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_350])]) ).
thf(f2263,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f1323]) ).
thf(f1323,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ),
inference(cnf_transformation,[],[f854]) ).
thf(f854,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ),
inference(rectify,[],[f36]) ).
thf(f36,axiom,
! [X3: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X3)),zero_zero_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_of__int__less__0__iff) ).
thf(f10846,plain,
spl60_349,
inference(avatar_split_clause,[],[f2262,f10844]) ).
thf(f10844,plain,
( spl60_349
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_349])]) ).
thf(f2262,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f1323]) ).
thf(f10842,plain,
spl60_348,
inference(avatar_split_clause,[],[f2261,f10840]) ).
thf(f10840,plain,
( spl60_348
<=> ! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_348])]) ).
thf(f2261,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f1324]) ).
thf(f1324,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ),
inference(cnf_transformation,[],[f855]) ).
thf(f855,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ),
inference(rectify,[],[f107]) ).
thf(f107,axiom,
! [X3: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X3)),zero_zero_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_of__int__le__0__iff) ).
thf(f10838,plain,
spl60_347,
inference(avatar_split_clause,[],[f2260,f10836]) ).
thf(f10836,plain,
( spl60_347
<=> ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_347])]) ).
thf(f2260,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,ring_1_of_int_int,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f1324]) ).
thf(f10834,plain,
spl60_346,
inference(avatar_split_clause,[],[f2259,f10832]) ).
thf(f10832,plain,
( spl60_346
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_346])]) ).
thf(f2259,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1325]) ).
thf(f1325,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ),
inference(cnf_transformation,[],[f856]) ).
thf(f856,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ),
inference(rectify,[],[f37]) ).
thf(f37,axiom,
! [X3: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X3)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_of__int__0__less__iff) ).
thf(f10830,plain,
spl60_345,
inference(avatar_split_clause,[],[f2258,f10828]) ).
thf(f2258,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1325]) ).
thf(f10826,plain,
spl60_344,
inference(avatar_split_clause,[],[f2257,f10824]) ).
thf(f10824,plain,
( spl60_344
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_344])]) ).
thf(f2257,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1326]) ).
thf(f1326,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ),
inference(cnf_transformation,[],[f857]) ).
thf(f857,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ),
inference(rectify,[],[f108]) ).
thf(f108,axiom,
! [X3: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X3)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_of__int__0__le__iff) ).
thf(f10822,plain,
spl60_343,
inference(avatar_split_clause,[],[f2256,f10820]) ).
thf(f10820,plain,
( spl60_343
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_343])]) ).
thf(f2256,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1326]) ).
thf(f10818,plain,
spl60_342,
inference(avatar_split_clause,[],[f2255,f10816]) ).
thf(f10816,plain,
( spl60_342
<=> ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $false )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_342])]) ).
thf(f2255,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $false )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1327]) ).
thf(f1327,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ),
inference(cnf_transformation,[],[f858]) ).
thf(f858,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ),
inference(rectify,[],[f35]) ).
thf(f35,axiom,
! [X3: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X3)),zero_zero_real) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),zero_zero_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_of__int__less__0__iff) ).
thf(f10814,plain,
spl60_341,
inference(avatar_split_clause,[],[f2254,f10812]) ).
thf(f2254,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1327]) ).
thf(f10810,plain,
spl60_340,
inference(avatar_split_clause,[],[f2253,f10808]) ).
thf(f10808,plain,
( spl60_340
<=> ! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_340])]) ).
thf(f2253,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1328]) ).
thf(f1328,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ),
inference(cnf_transformation,[],[f859]) ).
thf(f859,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ),
inference(rectify,[],[f106]) ).
thf(f106,axiom,
! [X3: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X3)),zero_zero_real) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_of__int__le__0__iff) ).
thf(f10806,plain,
spl60_339,
inference(avatar_split_clause,[],[f2252,f10804]) ).
thf(f10804,plain,
( spl60_339
<=> ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_339])]) ).
thf(f2252,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1328]) ).
thf(f10802,plain,
spl60_338,
inference(avatar_split_clause,[],[f2070,f10800]) ).
thf(f10800,plain,
( spl60_338
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_338])]) ).
thf(f2070,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(not_proxy_clausification,[],[f2067]) ).
thf(f2067,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1402]) ).
thf(f1402,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f463]) ).
thf(f463,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)) ),
inference(fool_elimination,[],[f462]) ).
thf(f462,plain,
! [X0: nat,X1: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) ),
inference(rectify,[],[f231]) ).
thf(f231,axiom,
! [X9: nat,X4: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X4)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_not__less__eq__eq) ).
thf(f10798,plain,
spl60_337,
inference(avatar_split_clause,[],[f2069,f10796]) ).
thf(f2069,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(not_proxy_clausification,[],[f2068]) ).
thf(f2068,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X1)),X0) )
| ( $true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1402]) ).
thf(f10738,plain,
( ~ spl60_336
| ~ spl60_8
| ~ spl60_302 ),
inference(avatar_split_clause,[],[f9260,f9127,f2378,f10735]) ).
thf(f10735,plain,
( spl60_336
<=> ( pm = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,pm),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_336])]) ).
thf(f9127,plain,
( spl60_302
<=> ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,pm),zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_302])]) ).
thf(f9260,plain,
( ( pm != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,pm),zero_zero_nat) )
| ~ spl60_8
| ~ spl60_302 ),
inference(superposition,[],[f2379,f9129]) ).
thf(f9129,plain,
( ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,pm),zero_zero_nat)) )
| ~ spl60_302 ),
inference(avatar_component_clause,[],[f9127]) ).
thf(f10726,plain,
( spl60_335
| ~ spl60_29
| ~ spl60_83 ),
inference(avatar_split_clause,[],[f3035,f3029,f2484,f10724]) ).
thf(f10724,plain,
( spl60_335
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0) )
| ( X1 = X2 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_335])]) ).
thf(f3029,plain,
( spl60_83
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_83])]) ).
thf(f3035,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0) )
| ( X1 = X2 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29
| ~ spl60_83 ),
inference(superposition,[],[f3030,f2485]) ).
thf(f3030,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) )
| ( X0 = X2 ) )
| ~ spl60_83 ),
inference(avatar_component_clause,[],[f3029]) ).
thf(f10722,plain,
( spl60_334
| ~ spl60_5
| ~ spl60_70 ),
inference(avatar_split_clause,[],[f2844,f2818,f2336,f10720]) ).
thf(f10720,plain,
( spl60_334
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_334])]) ).
thf(f2844,plain,
( ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
| ~ spl60_5
| ~ spl60_70 ),
inference(trivial_inequality_removal,[],[f2843]) ).
thf(f2843,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
| ~ spl60_5
| ~ spl60_70 ),
inference(superposition,[],[f2819,f2337]) ).
thf(f10718,plain,
spl60_333,
inference(avatar_split_clause,[],[f1867,f10716]) ).
thf(f10716,plain,
( spl60_333
<=> ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X1) )
| ( X0 = X2 )
| ( zero_zero_real = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_333])]) ).
thf(f1867,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X1) )
| ( X0 = X2 )
| ( zero_zero_real = X1 ) ),
inference(equality_proxy_clausification,[],[f1866]) ).
thf(f1866,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X1) )
| ( X0 = X2 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) ) ),
inference(equality_proxy_clausification,[],[f1865]) ).
thf(f1865,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) ) ),
inference(binary_proxy_clausification,[],[f1864]) ).
thf(f1864,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X1) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2)) ) ),
inference(equality_proxy_clausification,[],[f1863]) ).
thf(f1863,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X1)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2)) ) ),
inference(binary_proxy_clausification,[],[f1538]) ).
thf(f1538,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2)) ),
inference(cnf_transformation,[],[f667]) ).
thf(f667,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2)) ),
inference(fool_elimination,[],[f666]) ).
thf(f666,plain,
! [X0: real,X1: real,X2: real] :
( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X1) )
= ( X0 = X2 ) )
| ( zero_zero_real = X1 ) ),
inference(rectify,[],[f210]) ).
thf(f210,axiom,
! [X23: real,X38: real,X0: real] :
( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X23),X38) = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X38) )
= ( X0 = X23 ) )
| ( zero_zero_real = X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_divide__cancel__right) ).
thf(f10714,plain,
spl60_332,
inference(avatar_split_clause,[],[f1856,f10712]) ).
thf(f10712,plain,
( spl60_332
<=> ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2) )
| ( X1 = X2 )
| ( zero_zero_real = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_332])]) ).
thf(f1856,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2) )
| ( X1 = X2 )
| ( zero_zero_real = X0 ) ),
inference(equality_proxy_clausification,[],[f1855]) ).
thf(f1855,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2) )
| ( X1 = X2 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) ) ),
inference(equality_proxy_clausification,[],[f1854]) ).
thf(f1854,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) ) ),
inference(binary_proxy_clausification,[],[f1853]) ).
thf(f1853,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2)) ) ),
inference(equality_proxy_clausification,[],[f1852]) ).
thf(f1852,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f1539]) ).
thf(f1539,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2)) ),
inference(cnf_transformation,[],[f669]) ).
thf(f669,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2)) ),
inference(fool_elimination,[],[f668]) ).
thf(f668,plain,
! [X0: real,X1: real,X2: real] :
( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2) )
= ( X1 = X2 ) )
| ( zero_zero_real = X0 ) ),
inference(rectify,[],[f212]) ).
thf(f212,axiom,
! [X38: real,X23: real,X0: real] :
( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X38),X23) = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X38),X0) )
= ( X0 = X23 ) )
| ( zero_zero_real = X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_divide__cancel__left) ).
thf(f10481,plain,
( spl60_331
| ~ spl60_51
| ~ spl60_83 ),
inference(avatar_split_clause,[],[f3034,f3029,f2624,f10479]) ).
thf(f10479,plain,
( spl60_331
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(nat,nat,suc,X0)) )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_331])]) ).
thf(f2624,plain,
( spl60_51
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_51])]) ).
thf(f3034,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(nat,nat,suc,X0)) )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X1 ) )
| ~ spl60_51
| ~ spl60_83 ),
inference(superposition,[],[f3030,f2625]) ).
thf(f2625,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) )
| ~ spl60_51 ),
inference(avatar_component_clause,[],[f2624]) ).
thf(f10477,plain,
( spl60_330
| ~ spl60_56
| ~ spl60_67 ),
inference(avatar_split_clause,[],[f2807,f2796,f2650,f10475]) ).
thf(f10475,plain,
( spl60_330
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,suc,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_330])]) ).
thf(f2796,plain,
( spl60_67
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_67])]) ).
thf(f2807,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,suc,X0)) ) )
| ~ spl60_56
| ~ spl60_67 ),
inference(trivial_inequality_removal,[],[f2802]) ).
thf(f2802,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,suc,X0)) ) )
| ~ spl60_56
| ~ spl60_67 ),
inference(superposition,[],[f2797,f2651]) ).
thf(f2797,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 ) )
| ~ spl60_67 ),
inference(avatar_component_clause,[],[f2796]) ).
thf(f10472,plain,
( spl60_329
| ~ spl60_5
| ~ spl60_67 ),
inference(avatar_split_clause,[],[f2805,f2796,f2336,f10470]) ).
thf(f10470,plain,
( spl60_329
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_329])]) ).
thf(f2805,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) )
| ~ spl60_5
| ~ spl60_67 ),
inference(trivial_inequality_removal,[],[f2804]) ).
thf(f2804,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) )
| ~ spl60_5
| ~ spl60_67 ),
inference(superposition,[],[f2797,f2337]) ).
thf(f10361,plain,
( spl60_328
| ~ spl60_8
| ~ spl60_287 ),
inference(avatar_split_clause,[],[f9000,f8864,f2378,f10359]) ).
thf(f10359,plain,
( spl60_328
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK24,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_328])]) ).
thf(f8864,plain,
( spl60_287
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_287])]) ).
thf(f9000,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK24,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_8
| ~ spl60_287 ),
inference(superposition,[],[f2379,f8865]) ).
thf(f8865,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_287 ),
inference(avatar_component_clause,[],[f8864]) ).
thf(f9377,plain,
( spl60_327
| ~ spl60_27
| ~ spl60_65
| ~ spl60_86
| ~ spl60_96 ),
inference(avatar_split_clause,[],[f3270,f3216,f3071,f2706,f2469,f9374]) ).
thf(f9374,plain,
( spl60_327
<=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))),na) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_327])]) ).
thf(f2706,plain,
( spl60_65
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))),na) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_65])]) ).
thf(f3216,plain,
( spl60_96
<=> ! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_96])]) ).
thf(f3270,plain,
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))),na) )
| ~ spl60_27
| ~ spl60_65
| ~ spl60_86
| ~ spl60_96 ),
inference(trivial_inequality_removal,[],[f3269]) ).
thf(f3269,plain,
( ( $true != $true )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))),na) )
| ~ spl60_27
| ~ spl60_65
| ~ spl60_86
| ~ spl60_96 ),
inference(forward_demodulation,[],[f3262,f3101]) ).
thf(f3101,plain,
( ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),X0)) )
| ~ spl60_27
| ~ spl60_86 ),
inference(trivial_inequality_removal,[],[f3096]) ).
thf(f3096,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),X0)) ) )
| ~ spl60_27
| ~ spl60_86 ),
inference(superposition,[],[f3072,f2471]) ).
thf(f3262,plain,
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))),na) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))) )
| ~ spl60_65
| ~ spl60_96 ),
inference(trivial_inequality_removal,[],[f3259]) ).
thf(f3259,plain,
( ( $true != $true )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))),na) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))) )
| ~ spl60_65
| ~ spl60_96 ),
inference(superposition,[],[f3217,f2708]) ).
thf(f2708,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))),na) )
| ~ spl60_65 ),
inference(avatar_component_clause,[],[f2706]) ).
thf(f3217,plain,
( ! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) )
| ~ spl60_96 ),
inference(avatar_component_clause,[],[f3216]) ).
thf(f9372,plain,
( spl60_326
| ~ spl60_24
| ~ spl60_63
| ~ spl60_96 ),
inference(avatar_split_clause,[],[f3268,f3216,f2696,f2451,f9369]) ).
thf(f9369,plain,
( spl60_326
<=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_326])]) ).
thf(f3268,plain,
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) )
| ~ spl60_24
| ~ spl60_63
| ~ spl60_96 ),
inference(trivial_inequality_removal,[],[f3267]) ).
thf(f3267,plain,
( ( $true != $true )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) )
| ~ spl60_24
| ~ spl60_63
| ~ spl60_96 ),
inference(forward_demodulation,[],[f3263,f2453]) ).
thf(f3263,plain,
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),na) != $true )
| ~ spl60_63
| ~ spl60_96 ),
inference(trivial_inequality_removal,[],[f3258]) ).
thf(f3258,plain,
( ( $true != $true )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),na) != $true )
| ~ spl60_63
| ~ spl60_96 ),
inference(superposition,[],[f3217,f2698]) ).
thf(f9367,plain,
( spl60_325
| ~ spl60_46
| ~ spl60_79
| ~ spl60_88 ),
inference(avatar_split_clause,[],[f3133,f3079,f2941,f2562,f9365]) ).
thf(f9365,plain,
( spl60_325
<=> ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_325])]) ).
thf(f3133,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0))) )
| ~ spl60_46
| ~ spl60_79
| ~ spl60_88 ),
inference(forward_demodulation,[],[f3130,f2942]) ).
thf(f3130,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),X0)) )
| ~ spl60_46
| ~ spl60_88 ),
inference(trivial_inequality_removal,[],[f3119]) ).
thf(f3119,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),X0)) ) )
| ~ spl60_46
| ~ spl60_88 ),
inference(superposition,[],[f3080,f2564]) ).
thf(f9363,plain,
( spl60_324
| ~ spl60_45
| ~ spl60_79
| ~ spl60_88 ),
inference(avatar_split_clause,[],[f3132,f3079,f2941,f2557,f9361]) ).
thf(f9361,plain,
( spl60_324
<=> ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_324])]) ).
thf(f3132,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0))) )
| ~ spl60_45
| ~ spl60_79
| ~ spl60_88 ),
inference(forward_demodulation,[],[f3131,f2942]) ).
thf(f3131,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,na)),X0)) )
| ~ spl60_45
| ~ spl60_88 ),
inference(trivial_inequality_removal,[],[f3118]) ).
thf(f3118,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,na)),X0)) ) )
| ~ spl60_45
| ~ spl60_88 ),
inference(superposition,[],[f3080,f2559]) ).
thf(f9359,plain,
( spl60_323
| ~ spl60_43
| ~ spl60_88 ),
inference(avatar_split_clause,[],[f3129,f3079,f2549,f9357]) ).
thf(f9357,plain,
( spl60_323
<=> ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,sK6,zero_zero_real)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_323])]) ).
thf(f3129,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,sK6,zero_zero_real)),X0)) )
| ~ spl60_43
| ~ spl60_88 ),
inference(trivial_inequality_removal,[],[f3120]) ).
thf(f3120,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,sK6,zero_zero_real)),X0)) ) )
| ~ spl60_43
| ~ spl60_88 ),
inference(superposition,[],[f3080,f2550]) ).
thf(f9355,plain,
( spl60_322
| ~ spl60_45
| ~ spl60_87 ),
inference(avatar_split_clause,[],[f3117,f3075,f2557,f9353]) ).
thf(f9353,plain,
( spl60_322
<=> ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,na))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_322])]) ).
thf(f3117,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,na))) )
| ~ spl60_45
| ~ spl60_87 ),
inference(trivial_inequality_removal,[],[f3104]) ).
thf(f3104,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,na))) ) )
| ~ spl60_45
| ~ spl60_87 ),
inference(superposition,[],[f3076,f2559]) ).
thf(f9351,plain,
( spl60_321
| ~ spl60_46
| ~ spl60_87 ),
inference(avatar_split_clause,[],[f3116,f3075,f2562,f9349]) ).
thf(f9349,plain,
( spl60_321
<=> ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,ya))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_321])]) ).
thf(f3116,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,ya))) )
| ~ spl60_46
| ~ spl60_87 ),
inference(trivial_inequality_removal,[],[f3105]) ).
thf(f3105,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(int,real,ring_1_of_int_real,ya))) ) )
| ~ spl60_46
| ~ spl60_87 ),
inference(superposition,[],[f3076,f2564]) ).
thf(f9347,plain,
( spl60_320
| ~ spl60_43
| ~ spl60_87 ),
inference(avatar_split_clause,[],[f3115,f3075,f2549,f9345]) ).
thf(f9345,plain,
( spl60_320
<=> ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(real,real,sK6,zero_zero_real))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_320])]) ).
thf(f3115,plain,
( ! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(real,real,sK6,zero_zero_real))) )
| ~ spl60_43
| ~ spl60_87 ),
inference(trivial_inequality_removal,[],[f3106]) ).
thf(f3106,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X0),vAPP(real,real,sK6,zero_zero_real))) ) )
| ~ spl60_43
| ~ spl60_87 ),
inference(superposition,[],[f3076,f2550]) ).
thf(f9343,plain,
( spl60_319
| ~ spl60_84 ),
inference(avatar_split_clause,[],[f3065,f3042,f9341]) ).
thf(f9341,plain,
( spl60_319
<=> ! [X0: nat] :
( ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_319])]) ).
thf(f3065,plain,
( ! [X0: nat] :
( ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_84 ),
inference(equality_proxy_clausification,[],[f3045]) ).
thf(f3045,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( zero_zero_nat = X0 ) )
| ~ spl60_84 ),
inference(leibniz_equality_elimination,[],[f3043]) ).
thf(f9339,plain,
( spl60_318
| ~ spl60_7
| ~ spl60_79 ),
inference(avatar_split_clause,[],[f2979,f2941,f2373,f9337]) ).
thf(f9337,plain,
( spl60_318
<=> ! [X0: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) = vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_318])]) ).
thf(f2979,plain,
( ! [X0: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) = vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) )
| ~ spl60_7
| ~ spl60_79 ),
inference(superposition,[],[f2942,f2375]) ).
thf(f9333,plain,
( spl60_303
| ~ spl60_146
| ~ spl60_305 ),
inference(avatar_split_clause,[],[f9251,f9192,f3979,f9131]) ).
thf(f9131,plain,
( spl60_303
<=> ( pm = vAPP(nat,nat,suc,zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_303])]) ).
thf(f3979,plain,
( spl60_146
<=> ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,sK5,pm)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_146])]) ).
thf(f9192,plain,
( spl60_305
<=> ( zero_zero_nat = vAPP(nat,nat,sK5,pm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_305])]) ).
thf(f9251,plain,
( ( pm = vAPP(nat,nat,suc,zero_zero_nat) )
| ~ spl60_146
| ~ spl60_305 ),
inference(superposition,[],[f3981,f9194]) ).
thf(f9194,plain,
( ( zero_zero_nat = vAPP(nat,nat,sK5,pm) )
| ~ spl60_305 ),
inference(avatar_component_clause,[],[f9192]) ).
thf(f3981,plain,
( ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,sK5,pm)) )
| ~ spl60_146 ),
inference(avatar_component_clause,[],[f3979]) ).
thf(f9332,plain,
( spl60_317
| ~ spl60_6
| ~ spl60_78 ),
inference(avatar_split_clause,[],[f2976,f2937,f2368,f9330]) ).
thf(f9330,plain,
( spl60_317
<=> ! [X0: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) = vAPP(int,int,ring_1_of_int_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_317])]) ).
thf(f2368,plain,
( spl60_6
<=> ( zero_zero_int = vAPP(int,int,ring_1_of_int_int,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_6])]) ).
thf(f2937,plain,
( spl60_78
<=> ! [X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X0)),X1) = vAPP(int,int,ring_1_of_int_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_78])]) ).
thf(f2976,plain,
( ! [X0: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) = vAPP(int,int,ring_1_of_int_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) )
| ~ spl60_6
| ~ spl60_78 ),
inference(superposition,[],[f2938,f2370]) ).
thf(f2370,plain,
( ( zero_zero_int = vAPP(int,int,ring_1_of_int_int,zero_zero_int) )
| ~ spl60_6 ),
inference(avatar_component_clause,[],[f2368]) ).
thf(f2938,plain,
( ! [X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X0)),X1) = vAPP(int,int,ring_1_of_int_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ~ spl60_78 ),
inference(avatar_component_clause,[],[f2937]) ).
thf(f9328,plain,
( spl60_316
| ~ spl60_55
| ~ spl60_75 ),
inference(avatar_split_clause,[],[f2919,f2864,f2641,f9326]) ).
thf(f9326,plain,
( spl60_316
<=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_316])]) ).
thf(f2919,plain,
( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),vAPP(nat,nat,suc,X0)) )
| ~ spl60_55
| ~ spl60_75 ),
inference(trivial_inequality_removal,[],[f2912]) ).
thf(f2912,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),vAPP(nat,nat,suc,X0)) ) )
| ~ spl60_55
| ~ spl60_75 ),
inference(superposition,[],[f2865,f2642]) ).
thf(f9324,plain,
( spl60_315
| ~ spl60_29
| ~ spl60_67 ),
inference(avatar_split_clause,[],[f2799,f2796,f2484,f9322]) ).
thf(f9322,plain,
( spl60_315
<=> ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_315])]) ).
thf(f2799,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29
| ~ spl60_67 ),
inference(superposition,[],[f2797,f2485]) ).
thf(f9320,plain,
( spl60_314
| ~ spl60_5
| ~ spl60_62 ),
inference(avatar_split_clause,[],[f2790,f2692,f2336,f9318]) ).
thf(f9318,plain,
( spl60_314
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_314])]) ).
thf(f2692,plain,
( spl60_62
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_62])]) ).
thf(f2790,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)) ) )
| ~ spl60_5
| ~ spl60_62 ),
inference(trivial_inequality_removal,[],[f2789]) ).
thf(f2789,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)) ) )
| ~ spl60_5
| ~ spl60_62 ),
inference(superposition,[],[f2693,f2337]) ).
thf(f2693,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) )
| ~ spl60_62 ),
inference(avatar_component_clause,[],[f2692]) ).
thf(f9316,plain,
( spl60_313
| ~ spl60_5
| ~ spl60_61 ),
inference(avatar_split_clause,[],[f2773,f2688,f2336,f9314]) ).
thf(f9314,plain,
( spl60_313
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_313])]) ).
thf(f2688,plain,
( spl60_61
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_61])]) ).
thf(f2773,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) ) )
| ~ spl60_5
| ~ spl60_61 ),
inference(trivial_inequality_removal,[],[f2772]) ).
thf(f2772,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) ) )
| ~ spl60_5
| ~ spl60_61 ),
inference(superposition,[],[f2689,f2337]) ).
thf(f2689,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_61 ),
inference(avatar_component_clause,[],[f2688]) ).
thf(f9312,plain,
( spl60_312
| ~ spl60_5
| ~ spl60_60 ),
inference(avatar_split_clause,[],[f2754,f2684,f2336,f9310]) ).
thf(f9310,plain,
( spl60_312
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_312])]) ).
thf(f2684,plain,
( spl60_60
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_60])]) ).
thf(f2754,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_5
| ~ spl60_60 ),
inference(trivial_inequality_removal,[],[f2753]) ).
thf(f2753,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_5
| ~ spl60_60 ),
inference(superposition,[],[f2685,f2337]) ).
thf(f2685,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_60 ),
inference(avatar_component_clause,[],[f2684]) ).
thf(f9308,plain,
( spl60_311
| ~ spl60_5
| ~ spl60_58 ),
inference(avatar_split_clause,[],[f2733,f2676,f2336,f9306]) ).
thf(f9306,plain,
( spl60_311
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_311])]) ).
thf(f2676,plain,
( spl60_58
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_58])]) ).
thf(f2733,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_5
| ~ spl60_58 ),
inference(trivial_inequality_removal,[],[f2732]) ).
thf(f2732,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_5
| ~ spl60_58 ),
inference(superposition,[],[f2677,f2337]) ).
thf(f2677,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_58 ),
inference(avatar_component_clause,[],[f2676]) ).
thf(f9304,plain,
( spl60_310
| ~ spl60_5
| ~ spl60_57 ),
inference(avatar_split_clause,[],[f2718,f2672,f2336,f9302]) ).
thf(f9302,plain,
( spl60_310
<=> ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK4,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_310])]) ).
thf(f2672,plain,
( spl60_57
<=> ! [X2: nat,X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK4,X0)) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_57])]) ).
thf(f2718,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK4,X0)) ) )
| ~ spl60_5
| ~ spl60_57 ),
inference(trivial_inequality_removal,[],[f2717]) ).
thf(f2717,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK4,X0)) ) )
| ~ spl60_5
| ~ spl60_57 ),
inference(superposition,[],[f2673,f2337]) ).
thf(f2673,plain,
( ! [X2: nat,X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK4,X0)) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl60_57 ),
inference(avatar_component_clause,[],[f2672]) ).
thf(f9235,plain,
( spl60_309
| ~ spl60_303
| ~ spl60_308 ),
inference(avatar_split_clause,[],[f9231,f9227,f9131,f9233]) ).
thf(f9233,plain,
( spl60_309
<=> ! [X0: nat,X1: nat] :
( ( pm = X0 )
| ( pm != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( zero_zero_nat = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_309])]) ).
thf(f9227,plain,
( spl60_308
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_308])]) ).
thf(f9231,plain,
( ! [X0: nat,X1: nat] :
( ( pm = X0 )
| ( pm != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( zero_zero_nat = X1 ) )
| ~ spl60_303
| ~ spl60_308 ),
inference(forward_demodulation,[],[f9230,f9133]) ).
thf(f9133,plain,
( ( pm = vAPP(nat,nat,suc,zero_zero_nat) )
| ~ spl60_303 ),
inference(avatar_component_clause,[],[f9131]) ).
thf(f9230,plain,
( ! [X0: nat,X1: nat] :
( ( pm != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X1 ) )
| ~ spl60_303
| ~ spl60_308 ),
inference(forward_demodulation,[],[f9228,f9133]) ).
thf(f9228,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X1 ) )
| ~ spl60_308 ),
inference(avatar_component_clause,[],[f9227]) ).
thf(f9229,plain,
spl60_308,
inference(avatar_split_clause,[],[f2076,f9227]) ).
thf(f2076,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X1 ) ),
inference(equality_proxy_clausification,[],[f2075]) ).
thf(f2075,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) ) ),
inference(equality_proxy_clausification,[],[f2074]) ).
thf(f2074,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) ) ),
inference(binary_proxy_clausification,[],[f2073]) ).
thf(f2073,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ) ),
inference(equality_proxy_clausification,[],[f2072]) ).
thf(f2072,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ) ),
inference(binary_proxy_clausification,[],[f1401]) ).
thf(f1401,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ),
inference(cnf_transformation,[],[f461]) ).
thf(f461,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ),
inference(fool_elimination,[],[f460]) ).
thf(f460,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
= ( vAPP(nat,nat,suc,zero_zero_nat) = X0 ) )
| ( zero_zero_nat = X1 ) ),
inference(rectify,[],[f90]) ).
thf(f90,axiom,
! [X2: nat,X9: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X9) = vAPP(nat,nat,suc,zero_zero_nat) )
= ( vAPP(nat,nat,suc,zero_zero_nat) = X2 ) )
| ( zero_zero_nat = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_nat__power__eq__Suc__0__iff) ).
thf(f9203,plain,
( spl60_307
| ~ spl60_22
| ~ spl60_99 ),
inference(avatar_split_clause,[],[f3287,f3229,f2443,f9201]) ).
thf(f9201,plain,
( spl60_307
<=> ! [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,X1),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_307])]) ).
thf(f3229,plain,
( spl60_99
<=> ! [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) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_99])]) ).
thf(f3287,plain,
( ! [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,X1),zero_zero_nat) ) )
| ~ spl60_22
| ~ spl60_99 ),
inference(trivial_inequality_removal,[],[f3275]) ).
thf(f3275,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$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,X1),zero_zero_nat) ) )
| ~ spl60_22
| ~ spl60_99 ),
inference(superposition,[],[f3230,f2444]) ).
thf(f3230,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$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) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
| ~ spl60_99 ),
inference(avatar_component_clause,[],[f3229]) ).
thf(f9199,plain,
( spl60_306
| ~ spl60_81 ),
inference(avatar_split_clause,[],[f3007,f2949,f9197]) ).
thf(f9197,plain,
( spl60_306
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_306])]) ).
thf(f3007,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) )
| ~ spl60_81 ),
inference(equality_proxy_clausification,[],[f3006]) ).
thf(f3006,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_81 ),
inference(equality_proxy_clausification,[],[f3005]) ).
thf(f3005,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_81 ),
inference(equality_proxy_clausification,[],[f2998]) ).
thf(f2998,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_81 ),
inference(primitive_instantiation,[],[f2950]) ).
thf(f9195,plain,
( spl60_305
| ~ spl60_250
| ~ spl60_303 ),
inference(avatar_split_clause,[],[f9181,f9131,f5418,f9192]) ).
thf(f5418,plain,
( spl60_250
<=> ! [X0: nat] :
( ( pm != vAPP(nat,nat,suc,X0) )
| ( vAPP(nat,nat,sK5,pm) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_250])]) ).
thf(f9181,plain,
( ( zero_zero_nat = vAPP(nat,nat,sK5,pm) )
| ~ spl60_250
| ~ spl60_303 ),
inference(trivial_inequality_removal,[],[f9174]) ).
thf(f9174,plain,
( ( pm != pm )
| ( zero_zero_nat = vAPP(nat,nat,sK5,pm) )
| ~ spl60_250
| ~ spl60_303 ),
inference(superposition,[],[f5419,f9133]) ).
thf(f5419,plain,
( ! [X0: nat] :
( ( pm != vAPP(nat,nat,suc,X0) )
| ( vAPP(nat,nat,sK5,pm) = X0 ) )
| ~ spl60_250 ),
inference(avatar_component_clause,[],[f5418]) ).
thf(f9190,plain,
( spl60_304
| ~ spl60_80 ),
inference(avatar_split_clause,[],[f2994,f2945,f9188]) ).
thf(f9188,plain,
( spl60_304
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_304])]) ).
thf(f2994,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) )
| ~ spl60_80 ),
inference(equality_proxy_clausification,[],[f2993]) ).
thf(f2993,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_80 ),
inference(equality_proxy_clausification,[],[f2992]) ).
thf(f2992,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_80 ),
inference(equality_proxy_clausification,[],[f2985]) ).
thf(f2985,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_80 ),
inference(primitive_instantiation,[],[f2946]) ).
thf(f9134,plain,
( spl60_302
| spl60_303
| ~ spl60_113
| ~ spl60_185 ),
inference(avatar_split_clause,[],[f4567,f4558,f3419,f9131,f9127]) ).
thf(f3419,plain,
( spl60_113
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),pm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_113])]) ).
thf(f4558,plain,
( spl60_185
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) = X1 )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_185])]) ).
thf(f4567,plain,
( ( pm = vAPP(nat,nat,suc,zero_zero_nat) )
| ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,pm),zero_zero_nat)) )
| ~ spl60_113
| ~ spl60_185 ),
inference(trivial_inequality_removal,[],[f4561]) ).
thf(f4561,plain,
( ( $true != $true )
| ( pm = vAPP(nat,nat,suc,zero_zero_nat) )
| ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,pm),zero_zero_nat)) )
| ~ spl60_113
| ~ spl60_185 ),
inference(superposition,[],[f4559,f3421]) ).
thf(f3421,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),pm) )
| ~ spl60_113 ),
inference(avatar_component_clause,[],[f3419]) ).
thf(f4559,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) = X1 ) )
| ~ spl60_185 ),
inference(avatar_component_clause,[],[f4558]) ).
thf(f8924,plain,
( spl60_301
| ~ spl60_22
| ~ spl60_94 ),
inference(avatar_split_clause,[],[f3209,f3198,f2443,f8922]) ).
thf(f8922,plain,
( spl60_301
<=> ! [X0: nat] : ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_301])]) ).
thf(f3198,plain,
( spl60_94
<=> ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_94])]) ).
thf(f3209,plain,
( ! [X0: nat] : ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat)) )
| ~ spl60_22
| ~ spl60_94 ),
inference(trivial_inequality_removal,[],[f3204]) ).
thf(f3204,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X0),vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat)) ) )
| ~ spl60_22
| ~ spl60_94 ),
inference(superposition,[],[f3199,f2444]) ).
thf(f3199,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) )
| ~ spl60_94 ),
inference(avatar_component_clause,[],[f3198]) ).
thf(f8920,plain,
( spl60_300
| ~ spl60_26
| ~ spl60_86 ),
inference(avatar_split_clause,[],[f3103,f3071,f2464,f8918]) ).
thf(f8918,plain,
( spl60_300
<=> ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_300])]) ).
thf(f3103,plain,
( ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) )
| ~ spl60_26
| ~ spl60_86 ),
inference(trivial_inequality_removal,[],[f3094]) ).
thf(f3094,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0)) ) )
| ~ spl60_26
| ~ spl60_86 ),
inference(superposition,[],[f3072,f2466]) ).
thf(f8916,plain,
( spl60_299
| ~ spl60_24
| ~ spl60_86 ),
inference(avatar_split_clause,[],[f3102,f3071,f2451,f8914]) ).
thf(f8914,plain,
( spl60_299
<=> ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_299])]) ).
thf(f3102,plain,
( ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0)) )
| ~ spl60_24
| ~ spl60_86 ),
inference(trivial_inequality_removal,[],[f3095]) ).
thf(f3095,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,na),X0)) ) )
| ~ spl60_24
| ~ spl60_86 ),
inference(superposition,[],[f3072,f2453]) ).
thf(f8912,plain,
( spl60_298
| ~ spl60_27
| ~ spl60_86 ),
inference(avatar_split_clause,[],[f3101,f3071,f2469,f8910]) ).
thf(f8910,plain,
( spl60_298
<=> ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_298])]) ).
thf(f8908,plain,
( spl60_297
| ~ spl60_25
| ~ spl60_86 ),
inference(avatar_split_clause,[],[f3100,f3071,f2459,f8906]) ).
thf(f8906,plain,
( spl60_297
<=> ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_297])]) ).
thf(f3100,plain,
( ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) )
| ~ spl60_25
| ~ spl60_86 ),
inference(trivial_inequality_removal,[],[f3097]) ).
thf(f3097,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) ) )
| ~ spl60_25
| ~ spl60_86 ),
inference(superposition,[],[f3072,f2461]) ).
thf(f8904,plain,
( spl60_296
| ~ spl60_32
| ~ spl60_85 ),
inference(avatar_split_clause,[],[f3093,f3067,f2500,f8902]) ).
thf(f8902,plain,
( spl60_296
<=> ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_296])]) ).
thf(f2500,plain,
( spl60_32
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),ya) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_32])]) ).
thf(f3093,plain,
( ! [X0: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) )
| ~ spl60_32
| ~ spl60_85 ),
inference(trivial_inequality_removal,[],[f3086]) ).
thf(f3086,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),X0)) ) )
| ~ spl60_32
| ~ spl60_85 ),
inference(superposition,[],[f3068,f2502]) ).
thf(f2502,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),ya) = $true )
| ~ spl60_32 ),
inference(avatar_component_clause,[],[f2500]) ).
thf(f8900,plain,
( spl60_295
| ~ spl60_82 ),
inference(avatar_split_clause,[],[f3027,f2953,f8898]) ).
thf(f8898,plain,
( spl60_295
<=> ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_295])]) ).
thf(f3027,plain,
( ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl60_82 ),
inference(equality_proxy_clausification,[],[f3008]) ).
thf(f3008,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl60_82 ),
inference(leibniz_equality_elimination,[],[f2954]) ).
thf(f8896,plain,
( spl60_294
| ~ spl60_77 ),
inference(avatar_split_clause,[],[f2975,f2933,f8894]) ).
thf(f8894,plain,
( spl60_294
<=> ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_294])]) ).
thf(f2975,plain,
( ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl60_77 ),
inference(equality_proxy_clausification,[],[f2956]) ).
thf(f2956,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl60_77 ),
inference(leibniz_equality_elimination,[],[f2934]) ).
thf(f8892,plain,
( spl60_293
| ~ spl60_29
| ~ spl60_278 ),
inference(avatar_split_clause,[],[f7805,f7755,f2484,f8890]) ).
thf(f7755,plain,
( spl60_278
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK5,vAPP(nat,nat,suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_278])]) ).
thf(f7805,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29
| ~ spl60_278 ),
inference(superposition,[],[f7756,f2485]) ).
thf(f7756,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK5,vAPP(nat,nat,suc,X0))) )
| ~ spl60_278 ),
inference(avatar_component_clause,[],[f7755]) ).
thf(f8886,plain,
( spl60_292
| ~ spl60_62 ),
inference(avatar_split_clause,[],[f2794,f2692,f8884]) ).
thf(f8884,plain,
( spl60_292
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( zero_zero_nat = X0 )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_292])]) ).
thf(f2794,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( zero_zero_nat = X0 )
| ( X0 != X1 ) )
| ~ spl60_62 ),
inference(equality_proxy_clausification,[],[f2793]) ).
thf(f2793,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_62 ),
inference(equality_proxy_clausification,[],[f2792]) ).
thf(f2792,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_62 ),
inference(equality_proxy_clausification,[],[f2785]) ).
thf(f2785,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK19,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_62 ),
inference(primitive_instantiation,[],[f2693]) ).
thf(f8882,plain,
( spl60_291
| ~ spl60_61 ),
inference(avatar_split_clause,[],[f2777,f2688,f8880]) ).
thf(f8880,plain,
( spl60_291
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_291])]) ).
thf(f2777,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) )
| ~ spl60_61 ),
inference(equality_proxy_clausification,[],[f2776]) ).
thf(f2776,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_61 ),
inference(equality_proxy_clausification,[],[f2775]) ).
thf(f2775,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_61 ),
inference(equality_proxy_clausification,[],[f2768]) ).
thf(f2768,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_61 ),
inference(primitive_instantiation,[],[f2689]) ).
thf(f8878,plain,
( spl60_290
| ~ spl60_60 ),
inference(avatar_split_clause,[],[f2762,f2684,f8876]) ).
thf(f8876,plain,
( spl60_290
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_290])]) ).
thf(f2762,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( X0 = X1 ) )
| ~ spl60_60 ),
inference(equality_proxy_clausification,[],[f2761]) ).
thf(f2761,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_60 ),
inference(equality_proxy_clausification,[],[f2760]) ).
thf(f2760,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_60 ),
inference(equality_proxy_clausification,[],[f2747]) ).
thf(f2747,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_60 ),
inference(primitive_instantiation,[],[f2685]) ).
thf(f8874,plain,
( spl60_289
| ~ spl60_58 ),
inference(avatar_split_clause,[],[f2741,f2676,f8872]) ).
thf(f8872,plain,
( spl60_289
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_289])]) ).
thf(f2741,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( X0 = X1 ) )
| ~ spl60_58 ),
inference(equality_proxy_clausification,[],[f2740]) ).
thf(f2740,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_58 ),
inference(equality_proxy_clausification,[],[f2739]) ).
thf(f2739,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_58 ),
inference(equality_proxy_clausification,[],[f2726]) ).
thf(f2726,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_58 ),
inference(primitive_instantiation,[],[f2677]) ).
thf(f8870,plain,
( spl60_288
| ~ spl60_57 ),
inference(avatar_split_clause,[],[f2722,f2672,f8868]) ).
thf(f8868,plain,
( spl60_288
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK4,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 != X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_288])]) ).
thf(f2722,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK4,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 != X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_57 ),
inference(equality_proxy_clausification,[],[f2721]) ).
thf(f2721,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK4,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_57 ),
inference(equality_proxy_clausification,[],[f2720]) ).
thf(f2720,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK4,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_57 ),
inference(equality_proxy_clausification,[],[f2713]) ).
thf(f2713,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK4,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl60_57 ),
inference(primitive_instantiation,[],[f2673]) ).
thf(f8866,plain,
( spl60_287
| ~ spl60_29
| ~ spl60_277 ),
inference(avatar_split_clause,[],[f7766,f7751,f2484,f8864]) ).
thf(f7751,plain,
( spl60_277
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK24,vAPP(nat,nat,suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_277])]) ).
thf(f7766,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29
| ~ spl60_277 ),
inference(superposition,[],[f7752,f2485]) ).
thf(f7752,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK24,vAPP(nat,nat,suc,X0))) )
| ~ spl60_277 ),
inference(avatar_component_clause,[],[f7751]) ).
thf(f8783,plain,
( spl60_286
| ~ spl60_119
| ~ spl60_173 ),
inference(avatar_split_clause,[],[f4419,f4387,f3532,f8781]) ).
thf(f8781,plain,
( spl60_286
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_286])]) ).
thf(f3532,plain,
( spl60_119
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_119])]) ).
thf(f4387,plain,
( spl60_173
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_173])]) ).
thf(f4419,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,suc,X0)) )
| ~ spl60_119
| ~ spl60_173 ),
inference(trivial_inequality_removal,[],[f4414]) ).
thf(f4414,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,suc,X0)) ) )
| ~ spl60_119
| ~ spl60_173 ),
inference(superposition,[],[f4388,f3533]) ).
thf(f3533,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),vAPP(nat,nat,suc,X0)) )
| ~ spl60_119 ),
inference(avatar_component_clause,[],[f3532]) ).
thf(f4388,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) )
| ~ spl60_173 ),
inference(avatar_component_clause,[],[f4387]) ).
thf(f7870,plain,
( spl60_285
| ~ spl60_41
| ~ spl60_83 ),
inference(avatar_split_clause,[],[f3033,f3029,f2541,f7868]) ).
thf(f7868,plain,
( spl60_285
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(nat,nat,suc,zero_zero_nat)) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_285])]) ).
thf(f2541,plain,
( spl60_41
<=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_41])]) ).
thf(f3033,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(nat,nat,suc,zero_zero_nat)) != X0 )
| ( X0 = X1 ) )
| ~ spl60_41
| ~ spl60_83 ),
inference(superposition,[],[f3030,f2542]) ).
thf(f2542,plain,
( ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 )
| ~ spl60_41 ),
inference(avatar_component_clause,[],[f2541]) ).
thf(f7866,plain,
( spl60_284
| ~ spl60_5
| ~ spl60_50 ),
inference(avatar_split_clause,[],[f2619,f2590,f2336,f7864]) ).
thf(f7864,plain,
( spl60_284
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_284])]) ).
thf(f2590,plain,
( spl60_50
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_50])]) ).
thf(f2619,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) ) )
| ~ spl60_5
| ~ spl60_50 ),
inference(trivial_inequality_removal,[],[f2618]) ).
thf(f2618,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) ) )
| ~ spl60_5
| ~ spl60_50 ),
inference(superposition,[],[f2591,f2337]) ).
thf(f2591,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_50 ),
inference(avatar_component_clause,[],[f2590]) ).
thf(f7860,plain,
( spl60_283
| ~ spl60_5
| ~ spl60_49 ),
inference(avatar_split_clause,[],[f2609,f2586,f2336,f7858]) ).
thf(f7858,plain,
( spl60_283
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK12,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_283])]) ).
thf(f2586,plain,
( spl60_49
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK12,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_49])]) ).
thf(f2609,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK12,X0)) ) )
| ~ spl60_5
| ~ spl60_49 ),
inference(trivial_inequality_removal,[],[f2608]) ).
thf(f2608,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK12,X0)) ) )
| ~ spl60_5
| ~ spl60_49 ),
inference(superposition,[],[f2587,f2337]) ).
thf(f2587,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK12,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_49 ),
inference(avatar_component_clause,[],[f2586]) ).
thf(f7856,plain,
( spl60_282
| ~ spl60_5
| ~ spl60_48 ),
inference(avatar_split_clause,[],[f2599,f2582,f2336,f7854]) ).
thf(f7854,plain,
( spl60_282
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_282])]) ).
thf(f2582,plain,
( spl60_48
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_48])]) ).
thf(f2599,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) )
| ~ spl60_5
| ~ spl60_48 ),
inference(trivial_inequality_removal,[],[f2598]) ).
thf(f2598,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) )
| ~ spl60_5
| ~ spl60_48 ),
inference(superposition,[],[f2583,f2337]) ).
thf(f2583,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl60_48 ),
inference(avatar_component_clause,[],[f2582]) ).
thf(f7852,plain,
( spl60_281
| ~ spl60_30
| ~ spl60_42 ),
inference(avatar_split_clause,[],[f2577,f2545,f2488,f7850]) ).
thf(f7850,plain,
( spl60_281
<=> ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK3,X0)) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_281])]) ).
thf(f2545,plain,
( spl60_42
<=> ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_42])]) ).
thf(f2577,plain,
( ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK3,X0)) )
| ( zero_zero_nat = X0 ) )
| ~ spl60_30
| ~ spl60_42 ),
inference(superposition,[],[f2546,f2489]) ).
thf(f2546,plain,
( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X0) )
| ~ spl60_42 ),
inference(avatar_component_clause,[],[f2545]) ).
thf(f7848,plain,
( spl60_280
| ~ spl60_29
| ~ spl60_42 ),
inference(avatar_split_clause,[],[f2576,f2545,f2484,f7846]) ).
thf(f7846,plain,
( spl60_280
<=> ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK2,X0)) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_280])]) ).
thf(f2576,plain,
( ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK2,X0)) )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29
| ~ spl60_42 ),
inference(superposition,[],[f2546,f2485]) ).
thf(f7762,plain,
( spl60_279
| ~ spl60_250
| ~ spl60_274 ),
inference(avatar_split_clause,[],[f7562,f6897,f5418,f7759]) ).
thf(f7759,plain,
( spl60_279
<=> ( vAPP(nat,nat,sK5,pm) = vAPP(nat,nat,sK24,pm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_279])]) ).
thf(f6897,plain,
( spl60_274
<=> ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,sK24,pm)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_274])]) ).
thf(f7562,plain,
( ( vAPP(nat,nat,sK5,pm) = vAPP(nat,nat,sK24,pm) )
| ~ spl60_250
| ~ spl60_274 ),
inference(trivial_inequality_removal,[],[f7561]) ).
thf(f7561,plain,
( ( pm != pm )
| ( vAPP(nat,nat,sK5,pm) = vAPP(nat,nat,sK24,pm) )
| ~ spl60_250
| ~ spl60_274 ),
inference(superposition,[],[f5419,f6899]) ).
thf(f6899,plain,
( ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,sK24,pm)) )
| ~ spl60_274 ),
inference(avatar_component_clause,[],[f6897]) ).
thf(f7757,plain,
( spl60_278
| ~ spl60_119
| ~ spl60_145 ),
inference(avatar_split_clause,[],[f3976,f3967,f3532,f7755]) ).
thf(f3967,plain,
( spl60_145
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_145])]) ).
thf(f3976,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK5,vAPP(nat,nat,suc,X0))) )
| ~ spl60_119
| ~ spl60_145 ),
inference(trivial_inequality_removal,[],[f3971]) ).
thf(f3971,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK5,vAPP(nat,nat,suc,X0))) ) )
| ~ spl60_119
| ~ spl60_145 ),
inference(superposition,[],[f3968,f3533]) ).
thf(f3968,plain,
( ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0 ) )
| ~ spl60_145 ),
inference(avatar_component_clause,[],[f3967]) ).
thf(f7753,plain,
( spl60_277
| ~ spl60_23
| ~ spl60_67 ),
inference(avatar_split_clause,[],[f2808,f2796,f2447,f7751]) ).
thf(f2808,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK24,vAPP(nat,nat,suc,X0))) )
| ~ spl60_23
| ~ spl60_67 ),
inference(trivial_inequality_removal,[],[f2801]) ).
thf(f2801,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK24,vAPP(nat,nat,suc,X0))) ) )
| ~ spl60_23
| ~ spl60_67 ),
inference(superposition,[],[f2797,f2448]) ).
thf(f7744,plain,
( spl60_276
| spl60_273
| ~ spl60_60 ),
inference(avatar_split_clause,[],[f2763,f2684,f5983,f7741]) ).
thf(f7741,plain,
( spl60_276
<=> ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_276])]) ).
thf(f5983,plain,
( spl60_273
<=> ! [X0: nat] : ( zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_273])]) ).
thf(f2763,plain,
( ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) )
| ~ spl60_60 ),
inference(equality_proxy_clausification,[],[f2744]) ).
thf(f2744,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) )
| ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) )
| ~ spl60_60 ),
inference(leibniz_equality_elimination,[],[f2685]) ).
thf(f7153,plain,
( ~ spl60_275
| ~ spl60_8
| ~ spl60_274 ),
inference(avatar_split_clause,[],[f7008,f6897,f2378,f7150]) ).
thf(f7150,plain,
( spl60_275
<=> ( pm = vAPP(nat,nat,sK24,pm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_275])]) ).
thf(f7008,plain,
( ( pm != vAPP(nat,nat,sK24,pm) )
| ~ spl60_8
| ~ spl60_274 ),
inference(superposition,[],[f2379,f6899]) ).
thf(f6900,plain,
( spl60_274
| ~ spl60_67
| ~ spl60_265 ),
inference(avatar_split_clause,[],[f5951,f5610,f2796,f6897]) ).
thf(f5951,plain,
( ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,sK24,pm)) )
| ~ spl60_67
| ~ spl60_265 ),
inference(trivial_inequality_removal,[],[f5902]) ).
thf(f5902,plain,
( ( $true != $true )
| ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,sK24,pm)) )
| ~ spl60_67
| ~ spl60_265 ),
inference(superposition,[],[f2797,f5612]) ).
thf(f6159,plain,
( ~ spl60_5
| ~ spl60_170
| ~ spl60_179
| ~ spl60_273 ),
inference(avatar_contradiction_clause,[],[f6158]) ).
thf(f6158,plain,
( $false
| ~ spl60_5
| ~ spl60_170
| ~ spl60_179
| ~ spl60_273 ),
inference(trivial_inequality_removal,[],[f6157]) ).
thf(f6157,plain,
( ( $true = $false )
| ~ spl60_5
| ~ spl60_170
| ~ spl60_179
| ~ spl60_273 ),
inference(forward_demodulation,[],[f6050,f4381]) ).
thf(f4381,plain,
( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),zero_zero_nat),X0) )
| ~ spl60_5
| ~ spl60_170 ),
inference(trivial_inequality_removal,[],[f4380]) ).
thf(f4380,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),zero_zero_nat),X0) ) )
| ~ spl60_5
| ~ spl60_170 ),
inference(superposition,[],[f4302,f2337]) ).
thf(f4302,plain,
( ! [X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),zero_zero_nat),X1) )
| ~ spl60_170 ),
inference(avatar_component_clause,[],[f4301]) ).
thf(f4301,plain,
( spl60_170
<=> ! [X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),zero_zero_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_170])]) ).
thf(f6050,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),zero_zero_nat),X0) )
| ~ spl60_179
| ~ spl60_273 ),
inference(superposition,[],[f4446,f5984]) ).
thf(f5984,plain,
( ! [X0: nat] : ( zero_zero_nat = X0 )
| ~ spl60_273 ),
inference(avatar_component_clause,[],[f5983]) ).
thf(f4446,plain,
( ! [X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),vAPP(nat,nat,suc,X1)),X1) )
| ~ spl60_179 ),
inference(avatar_component_clause,[],[f4445]) ).
thf(f4445,plain,
( spl60_179
<=> ! [X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),vAPP(nat,nat,suc,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_179])]) ).
thf(f6156,plain,
( ~ spl60_5
| ~ spl60_111
| ~ spl60_120
| ~ spl60_273 ),
inference(avatar_contradiction_clause,[],[f6155]) ).
thf(f6155,plain,
( $false
| ~ spl60_5
| ~ spl60_111
| ~ spl60_120
| ~ spl60_273 ),
inference(trivial_inequality_removal,[],[f6154]) ).
thf(f6154,plain,
( ( $true = $false )
| ~ spl60_5
| ~ spl60_111
| ~ spl60_120
| ~ spl60_273 ),
inference(forward_demodulation,[],[f6043,f3433]) ).
thf(f3433,plain,
( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),zero_zero_nat) )
| ~ spl60_5
| ~ spl60_111 ),
inference(trivial_inequality_removal,[],[f3432]) ).
thf(f3432,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),zero_zero_nat) ) )
| ~ spl60_5
| ~ spl60_111 ),
inference(superposition,[],[f3412,f2337]) ).
thf(f3412,plain,
( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),zero_zero_nat) )
| ~ spl60_111 ),
inference(avatar_component_clause,[],[f3411]) ).
thf(f3411,plain,
( spl60_111
<=> ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_111])]) ).
thf(f6043,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),zero_zero_nat) )
| ~ spl60_120
| ~ spl60_273 ),
inference(superposition,[],[f3545,f5984]) ).
thf(f6153,plain,
( ~ spl60_5
| ~ spl60_111
| ~ spl60_119
| ~ spl60_273 ),
inference(avatar_contradiction_clause,[],[f6152]) ).
thf(f6152,plain,
( $false
| ~ spl60_5
| ~ spl60_111
| ~ spl60_119
| ~ spl60_273 ),
inference(trivial_inequality_removal,[],[f6151]) ).
thf(f6151,plain,
( ( $true = $false )
| ~ spl60_5
| ~ spl60_111
| ~ spl60_119
| ~ spl60_273 ),
inference(forward_demodulation,[],[f6042,f3433]) ).
thf(f6042,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),zero_zero_nat) )
| ~ spl60_119
| ~ spl60_273 ),
inference(superposition,[],[f3533,f5984]) ).
thf(f6150,plain,
( ~ spl60_9
| ~ spl60_273 ),
inference(avatar_contradiction_clause,[],[f6149]) ).
thf(f6149,plain,
( $false
| ~ spl60_9
| ~ spl60_273 ),
inference(trivial_inequality_removal,[],[f6032]) ).
thf(f6032,plain,
( ( zero_zero_nat != zero_zero_nat )
| ~ spl60_9
| ~ spl60_273 ),
inference(superposition,[],[f2383,f5984]) ).
thf(f2383,plain,
( ! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) )
| ~ spl60_9 ),
inference(avatar_component_clause,[],[f2382]) ).
thf(f2382,plain,
( spl60_9
<=> ! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_9])]) ).
thf(f5985,plain,
( spl60_272
| spl60_273
| ~ spl60_58 ),
inference(avatar_split_clause,[],[f2742,f2676,f5983,f5979]) ).
thf(f5979,plain,
( spl60_272
<=> ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_272])]) ).
thf(f2742,plain,
( ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) )
| ~ spl60_58 ),
inference(equality_proxy_clausification,[],[f2723]) ).
thf(f2723,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) )
| ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) )
| ~ spl60_58 ),
inference(leibniz_equality_elimination,[],[f2677]) ).
thf(f5977,plain,
( spl60_271
| ~ spl60_50 ),
inference(avatar_split_clause,[],[f2622,f2590,f5975]) ).
thf(f5975,plain,
( spl60_271
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_271])]) ).
thf(f2622,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) )
| ~ spl60_50 ),
inference(equality_proxy_clausification,[],[f2621]) ).
thf(f2621,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_50 ),
inference(equality_proxy_clausification,[],[f2616]) ).
thf(f2616,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_50 ),
inference(primitive_instantiation,[],[f2591]) ).
thf(f5973,plain,
( spl60_270
| ~ spl60_49 ),
inference(avatar_split_clause,[],[f2612,f2586,f5971]) ).
thf(f5971,plain,
( spl60_270
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK12,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_270])]) ).
thf(f2612,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK12,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) )
| ~ spl60_49 ),
inference(equality_proxy_clausification,[],[f2611]) ).
thf(f2611,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK12,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_49 ),
inference(equality_proxy_clausification,[],[f2606]) ).
thf(f2606,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK12,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_49 ),
inference(primitive_instantiation,[],[f2587]) ).
thf(f5969,plain,
( spl60_269
| ~ spl60_48 ),
inference(avatar_split_clause,[],[f2602,f2582,f5967]) ).
thf(f5967,plain,
( spl60_269
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK11,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_269])]) ).
thf(f2602,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK11,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) )
| ~ spl60_48 ),
inference(equality_proxy_clausification,[],[f2601]) ).
thf(f2601,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK11,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_48 ),
inference(equality_proxy_clausification,[],[f2596]) ).
thf(f2596,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK11,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl60_48 ),
inference(primitive_instantiation,[],[f2583]) ).
thf(f5965,plain,
spl60_268,
inference(avatar_split_clause,[],[f2114,f5963]) ).
thf(f5963,plain,
( spl60_268
<=> ! [X0: real,X1: real] :
( ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) )
| ( zero_zero_real = X1 )
| ( zero_zero_real = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_268])]) ).
thf(f2114,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) )
| ( zero_zero_real = X1 )
| ( zero_zero_real = X0 ) ),
inference(equality_proxy_clausification,[],[f2113]) ).
thf(f2113,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) )
| ( zero_zero_real = X1 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) ) ),
inference(equality_proxy_clausification,[],[f2112]) ).
thf(f2112,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) ) ),
inference(binary_proxy_clausification,[],[f2111]) ).
thf(f2111,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1)) ) ),
inference(equality_proxy_clausification,[],[f2110]) ).
thf(f2110,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1)) ) ),
inference(binary_proxy_clausification,[],[f1397]) ).
thf(f1397,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1)) ),
inference(cnf_transformation,[],[f453]) ).
thf(f453,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1)) ),
inference(fool_elimination,[],[f452]) ).
thf(f452,plain,
! [X0: real,X1: real] :
( ( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1) )
= ( zero_zero_real = X1 ) )
| ( zero_zero_real = X0 ) ),
inference(rectify,[],[f211]) ).
thf(f211,axiom,
! [X23: real,X0: real] :
( ( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X23),X0) )
= ( zero_zero_real = X0 ) )
| ( zero_zero_real = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_divide__eq__0__iff) ).
thf(f5898,plain,
spl60_267,
inference(avatar_split_clause,[],[f2099,f5896]) ).
thf(f5896,plain,
( spl60_267
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( zero_zero_nat != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_267])]) ).
thf(f2099,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( zero_zero_nat != X1 ) ),
inference(equality_proxy_clausification,[],[f2097]) ).
thf(f2097,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) ) ),
inference(binary_proxy_clausification,[],[f2096]) ).
thf(f2096,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(equality_proxy_clausification,[],[f2091]) ).
thf(f2091,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(binary_proxy_clausification,[],[f1672]) ).
thf(f1672,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ),
inference(definition_unfolding,[],[f1399,f1287]) ).
thf(f1287,plain,
ord_less_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),
inference(cnf_transformation,[],[f331]) ).
thf(f331,plain,
ord_less_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),
inference(fool_elimination,[],[f330]) ).
thf(f330,plain,
( ord_less_nat
= ( ^ [X0: nat] : vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)) ) ),
inference(rectify,[],[f257]) ).
thf(f257,axiom,
( ord_less_nat
= ( ^ [X41: nat] : vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_less__eq__Suc__le) ).
thf(f1399,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ),
inference(cnf_transformation,[],[f457]) ).
thf(f457,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ),
inference(fool_elimination,[],[f456]) ).
thf(f456,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
= ( zero_zero_nat = X1 ) )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
inference(rectify,[],[f294]) ).
thf(f294,axiom,
! [X9: nat,X4: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X9),X4) )
= ( zero_zero_nat = X4 ) )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Euclidean__Division_Odiv__eq__0__iff) ).
thf(f5617,plain,
spl60_266,
inference(avatar_split_clause,[],[f2087,f5615]) ).
thf(f5615,plain,
( spl60_266
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_266])]) ).
thf(f2087,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f2086]) ).
thf(f2086,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(binary_proxy_clausification,[],[f2084]) ).
thf(f2084,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1)) ) ),
inference(equality_proxy_clausification,[],[f2083]) ).
thf(f2083,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1)) ) ),
inference(binary_proxy_clausification,[],[f1673]) ).
thf(f1673,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1)) ),
inference(definition_unfolding,[],[f1400,f1287]) ).
thf(f1400,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)) ),
inference(cnf_transformation,[],[f459]) ).
thf(f459,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)) ),
inference(fool_elimination,[],[f458]) ).
thf(f458,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
& ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
! [X23: nat,X4: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X23),X4) )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4) )
& ( zero_zero_nat = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_power__eq__0__iff) ).
thf(f5613,plain,
( spl60_265
| ~ spl60_113
| ~ spl60_173 ),
inference(avatar_split_clause,[],[f4420,f4387,f3419,f5610]) ).
thf(f4420,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),pm) )
| ~ spl60_113
| ~ spl60_173 ),
inference(trivial_inequality_removal,[],[f4413]) ).
thf(f4413,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),pm) )
| ~ spl60_113
| ~ spl60_173 ),
inference(superposition,[],[f4388,f3421]) ).
thf(f5608,plain,
( spl60_264
| ~ spl60_120
| ~ spl60_151 ),
inference(avatar_split_clause,[],[f4040,f4000,f3544,f5606]) ).
thf(f5606,plain,
( spl60_264
<=> ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_264])]) ).
thf(f4000,plain,
( spl60_151
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_151])]) ).
thf(f4040,plain,
( ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,X0)) )
| ~ spl60_120
| ~ spl60_151 ),
inference(trivial_inequality_removal,[],[f4037]) ).
thf(f4037,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,X0)) ) )
| ~ spl60_120
| ~ spl60_151 ),
inference(superposition,[],[f4001,f3545]) ).
thf(f4001,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) ) )
| ~ spl60_151 ),
inference(avatar_component_clause,[],[f4000]) ).
thf(f5604,plain,
( spl60_263
| ~ spl60_24
| ~ spl60_74 ),
inference(avatar_split_clause,[],[f2907,f2860,f2451,f5601]) ).
thf(f5601,plain,
( spl60_263
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,na)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_263])]) ).
thf(f2860,plain,
( spl60_74
<=> ! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_74])]) ).
thf(f2907,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,na)) )
| ~ spl60_24
| ~ spl60_74 ),
inference(trivial_inequality_removal,[],[f2900]) ).
thf(f2900,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,na)) )
| ~ spl60_24
| ~ spl60_74 ),
inference(superposition,[],[f2861,f2453]) ).
thf(f2861,plain,
( ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) )
| ~ spl60_74 ),
inference(avatar_component_clause,[],[f2860]) ).
thf(f5599,plain,
( spl60_262
| ~ spl60_27
| ~ spl60_74 ),
inference(avatar_split_clause,[],[f2906,f2860,f2469,f5596]) ).
thf(f5596,plain,
( spl60_262
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_262])]) ).
thf(f2906,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,x)) )
| ~ spl60_27
| ~ spl60_74 ),
inference(trivial_inequality_removal,[],[f2901]) ).
thf(f2901,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,x)) )
| ~ spl60_27
| ~ spl60_74 ),
inference(superposition,[],[f2861,f2471]) ).
thf(f5594,plain,
( spl60_261
| ~ spl60_25
| ~ spl60_74 ),
inference(avatar_split_clause,[],[f2905,f2860,f2459,f5591]) ).
thf(f5591,plain,
( spl60_261
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,ya)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_261])]) ).
thf(f2905,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,ya)) )
| ~ spl60_25
| ~ spl60_74 ),
inference(trivial_inequality_removal,[],[f2902]) ).
thf(f2902,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,ya)) )
| ~ spl60_25
| ~ spl60_74 ),
inference(superposition,[],[f2861,f2461]) ).
thf(f5589,plain,
( spl60_260
| ~ spl60_24
| ~ spl60_73 ),
inference(avatar_split_clause,[],[f2896,f2856,f2451,f5586]) ).
thf(f5586,plain,
( spl60_260
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,na)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_260])]) ).
thf(f2856,plain,
( spl60_73
<=> ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_73])]) ).
thf(f2896,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,na)) )
| ~ spl60_24
| ~ spl60_73 ),
inference(trivial_inequality_removal,[],[f2889]) ).
thf(f2889,plain,
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,na)) )
| ~ spl60_24
| ~ spl60_73 ),
inference(superposition,[],[f2857,f2453]) ).
thf(f2857,plain,
( ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) )
| ~ spl60_73 ),
inference(avatar_component_clause,[],[f2856]) ).
thf(f5584,plain,
( spl60_259
| ~ spl60_27
| ~ spl60_73 ),
inference(avatar_split_clause,[],[f2895,f2856,f2469,f5581]) ).
thf(f5581,plain,
( spl60_259
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_259])]) ).
thf(f2895,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,x)) )
| ~ spl60_27
| ~ spl60_73 ),
inference(trivial_inequality_removal,[],[f2890]) ).
thf(f2890,plain,
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,x)) )
| ~ spl60_27
| ~ spl60_73 ),
inference(superposition,[],[f2857,f2471]) ).
thf(f5579,plain,
( spl60_258
| ~ spl60_25
| ~ spl60_73 ),
inference(avatar_split_clause,[],[f2894,f2856,f2459,f5576]) ).
thf(f5576,plain,
( spl60_258
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,ya)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_258])]) ).
thf(f2894,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,ya)) )
| ~ spl60_25
| ~ spl60_73 ),
inference(trivial_inequality_removal,[],[f2891]) ).
thf(f2891,plain,
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,ya)) )
| ~ spl60_25
| ~ spl60_73 ),
inference(superposition,[],[f2857,f2461]) ).
thf(f5574,plain,
( spl60_257
| ~ spl60_32
| ~ spl60_71 ),
inference(avatar_split_clause,[],[f2878,f2848,f2500,f5571]) ).
thf(f5571,plain,
( spl60_257
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,ya)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_257])]) ).
thf(f2878,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,ya)) )
| ~ spl60_32
| ~ spl60_71 ),
inference(trivial_inequality_removal,[],[f2871]) ).
thf(f2871,plain,
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,ya)) )
| ~ spl60_32
| ~ spl60_71 ),
inference(superposition,[],[f2849,f2502]) ).
thf(f5569,plain,
( spl60_256
| ~ spl60_42
| ~ spl60_56 ),
inference(avatar_split_clause,[],[f2670,f2650,f2545,f5567]) ).
thf(f5567,plain,
( spl60_256
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_256])]) ).
thf(f2670,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X0)) )
| ~ spl60_42
| ~ spl60_56 ),
inference(trivial_inequality_removal,[],[f2653]) ).
thf(f2653,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X0)) ) )
| ~ spl60_42
| ~ spl60_56 ),
inference(superposition,[],[f2546,f2651]) ).
thf(f5562,plain,
( spl60_255
| ~ spl60_5
| ~ spl60_42 ),
inference(avatar_split_clause,[],[f2579,f2545,f2336,f5560]) ).
thf(f5560,plain,
( spl60_255
<=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_255])]) ).
thf(f2579,plain,
( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X0) )
| ~ spl60_5
| ~ spl60_42 ),
inference(trivial_inequality_removal,[],[f2578]) ).
thf(f2578,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X0) ) )
| ~ spl60_5
| ~ spl60_42 ),
inference(superposition,[],[f2546,f2337]) ).
thf(f5436,plain,
( spl60_254
| ~ spl60_29
| ~ spl60_36 ),
inference(avatar_split_clause,[],[f2574,f2521,f2484,f5434]) ).
thf(f5434,plain,
( spl60_254
<=> ! [X0: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_254])]) ).
thf(f2521,plain,
( spl60_36
<=> ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_36])]) ).
thf(f2574,plain,
( ! [X0: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29
| ~ spl60_36 ),
inference(superposition,[],[f2522,f2485]) ).
thf(f2522,plain,
( ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) )
| ~ spl60_36 ),
inference(avatar_component_clause,[],[f2521]) ).
thf(f5432,plain,
( spl60_253
| ~ spl60_29
| ~ spl60_35 ),
inference(avatar_split_clause,[],[f2568,f2517,f2484,f5430]) ).
thf(f5430,plain,
( spl60_253
<=> ! [X0: nat] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_253])]) ).
thf(f2517,plain,
( spl60_35
<=> ! [X0: nat] : ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_35])]) ).
thf(f2568,plain,
( ! [X0: nat] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29
| ~ spl60_35 ),
inference(superposition,[],[f2518,f2485]) ).
thf(f2518,plain,
( ! [X0: nat] : ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(nat,nat,suc,X0)) )
| ~ spl60_35 ),
inference(avatar_component_clause,[],[f2517]) ).
thf(f5428,plain,
( spl60_252
| ~ spl60_29
| ~ spl60_34 ),
inference(avatar_split_clause,[],[f2566,f2513,f2484,f5426]) ).
thf(f5426,plain,
( spl60_252
<=> ! [X0: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_252])]) ).
thf(f2513,plain,
( spl60_34
<=> ! [X0: nat] : ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_34])]) ).
thf(f2566,plain,
( ! [X0: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( zero_zero_nat = X0 ) )
| ~ spl60_29
| ~ spl60_34 ),
inference(superposition,[],[f2514,f2485]) ).
thf(f2514,plain,
( ! [X0: nat] : ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(nat,nat,suc,X0)) )
| ~ spl60_34 ),
inference(avatar_component_clause,[],[f2513]) ).
thf(f5424,plain,
spl60_251,
inference(avatar_split_clause,[],[f2193,f5422]) ).
thf(f5422,plain,
( spl60_251
<=> ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_251])]) ).
thf(f2193,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ),
inference(equality_proxy_clausification,[],[f2190]) ).
thf(f2190,plain,
! [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,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ),
inference(binary_proxy_clausification,[],[f1342]) ).
thf(f1342,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f369]) ).
thf(f369,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ),
inference(fool_elimination,[],[f368]) ).
thf(f368,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat)
= ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f225]) ).
thf(f225,axiom,
! [X23: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X23),zero_zero_nat)
= ( zero_zero_nat = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_bot__nat__0_Oextremum__unique) ).
thf(f5420,plain,
( spl60_250
| ~ spl60_140
| ~ spl60_146 ),
inference(avatar_split_clause,[],[f5166,f3979,f3873,f5418]) ).
thf(f3873,plain,
( spl60_140
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,suc,X1) != vAPP(nat,nat,suc,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_140])]) ).
thf(f5166,plain,
( ! [X0: nat] :
( ( pm != vAPP(nat,nat,suc,X0) )
| ( vAPP(nat,nat,sK5,pm) = X0 ) )
| ~ spl60_140
| ~ spl60_146 ),
inference(superposition,[],[f3874,f3981]) ).
thf(f3874,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) != vAPP(nat,nat,suc,X0) )
| ( X0 = X1 ) )
| ~ spl60_140 ),
inference(avatar_component_clause,[],[f3873]) ).
thf(f5416,plain,
spl60_249,
inference(avatar_split_clause,[],[f2192,f5414]) ).
thf(f5414,plain,
( spl60_249
<=> ! [X0: nat] :
( ( zero_zero_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_249])]) ).
thf(f2192,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ),
inference(equality_proxy_clausification,[],[f2191]) ).
thf(f2191,plain,
! [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,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ),
inference(binary_proxy_clausification,[],[f1342]) ).
thf(f5409,plain,
spl60_248,
inference(avatar_split_clause,[],[f1643,f5406]) ).
thf(f5406,plain,
( spl60_248
<=> ( vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc) = 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,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_248])]) ).
thf(f1643,plain,
vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc) = 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,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))),
inference(definition_unfolding,[],[f1288,f1287]) ).
thf(f1288,plain,
ord_less_nat = vAPP(sTfun(nat,sTfun(nat,$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,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))),
inference(cnf_transformation,[],[f333]) ).
thf(f333,plain,
ord_less_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,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))),
inference(fool_elimination,[],[f332]) ).
thf(f332,plain,
( ord_less_nat
= ( ^ [X0: nat,X1: nat] :
( ( X0 != X1 )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(rectify,[],[f243]) ).
thf(f243,axiom,
( ord_less_nat
= ( ^ [X35: nat,X41: nat] :
( ( X35 != X41 )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X41) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_nat__less__le) ).
thf(f5404,plain,
spl60_247,
inference(avatar_split_clause,[],[f1641,f5401]) ).
thf(f5401,plain,
( spl60_247
<=> ( ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,$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)),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc)))),vEQ(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_247])]) ).
thf(f1641,plain,
ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,$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)),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc)))),vEQ(nat)),
inference(definition_unfolding,[],[f1286,f1287]) ).
thf(f1286,plain,
ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,$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)),
inference(cnf_transformation,[],[f329]) ).
thf(f329,plain,
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,$o))),bCOMB,vOR)),ord_less_nat))),vEQ(nat)),
inference(fool_elimination,[],[f328]) ).
thf(f328,plain,
( ord_less_eq_nat
= ( ^ [X0: nat,X1: nat] :
( ( X0 = X1 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(rectify,[],[f241]) ).
thf(f241,axiom,
( ord_less_eq_nat
= ( ^ [X35: nat,X41: nat] :
( ( X35 = X41 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X41) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_le__eq__less__or__eq) ).
thf(f5387,plain,
spl60_246,
inference(avatar_split_clause,[],[f1735,f5385]) ).
thf(f5385,plain,
( spl60_246
<=> ! [X2: nat,X0: nat > nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK40,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK40,X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_246])]) ).
thf(f1735,plain,
! [X2: nat,X0: nat > nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK40,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK40,X0)))) ) ),
inference(definition_unfolding,[],[f1560,f1287,f1287,f1287]) ).
thf(f1560,plain,
! [X2: nat,X0: nat > nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK40,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK40,X0)))) ) ),
inference(cnf_transformation,[],[f1243]) ).
thf(f1243,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK40,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK40,X0)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f1074,f1242]) ).
thf(f1242,plain,
! [X0: nat > nat] :
( ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK40,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK40,X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f1074,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(flattening,[],[f1073]) ).
thf(f1073,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(ennf_transformation,[],[f709]) ).
thf(f709,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ) ),
inference(fool_elimination,[],[f708]) ).
thf(f708,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ),
inference(rectify,[],[f66]) ).
thf(f66,axiom,
! [X20: nat > nat,X4: nat,X22: nat] :
( ! [X21: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X20,X21)),vAPP(nat,nat,X20,vAPP(nat,nat,suc,X21)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X22)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X20,X4)),vAPP(nat,nat,X20,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_lift__Suc__mono__less) ).
thf(f5360,plain,
spl60_245,
inference(avatar_split_clause,[],[f2309,f5358]) ).
thf(f5358,plain,
( spl60_245
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_245])]) ).
thf(f2309,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(trivial_inequality_removal,[],[f2308]) ).
thf(f2308,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(forward_demodulation,[],[f1760,f1374]) ).
thf(f1374,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true ),
inference(cnf_transformation,[],[f427]) ).
thf(f427,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true ),
inference(fool_elimination,[],[f426]) ).
thf(f426,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0),
inference(rectify,[],[f227]) ).
thf(f227,axiom,
! [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_less__eq__nat_Osimps_I1_J) ).
thf(f1760,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1618,f1287,f1287,f1287]) ).
thf(f1618,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1143]) ).
thf(f1143,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(flattening,[],[f1142]) ).
thf(f1142,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f779]) ).
thf(f779,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ) ) ) ),
inference(fool_elimination,[],[f778]) ).
thf(f778,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ) ) ),
inference(rectify,[],[f179]) ).
thf(f179,axiom,
! [X23: nat,X0: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X23),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X23)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X23),X4)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_power__strict__mono) ).
thf(f5356,plain,
spl60_244,
inference(avatar_split_clause,[],[f1749,f5354]) ).
thf(f5354,plain,
( spl60_244
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_244])]) ).
thf(f1749,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1580,f1287,f1287,f1287]) ).
thf(f1580,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1106]) ).
thf(f1106,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f1105]) ).
thf(f1105,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f741]) ).
thf(f741,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) ),
inference(fool_elimination,[],[f740]) ).
thf(f740,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(rectify,[],[f129]) ).
thf(f129,axiom,
! [X10: nat,X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X10)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X10),X9)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X10),X4))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_nat__power__less__imp__less) ).
thf(f5344,plain,
spl60_243,
inference(avatar_split_clause,[],[f1761,f5342]) ).
thf(f5342,plain,
( spl60_243
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_243])]) ).
thf(f1761,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1619,f1287,f1287,f1287]) ).
thf(f1619,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1145]) ).
thf(f1145,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(flattening,[],[f1144]) ).
thf(f1144,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f781]) ).
thf(f781,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X2) ) ) ),
inference(fool_elimination,[],[f780]) ).
thf(f780,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X2) ) ),
inference(rectify,[],[f43]) ).
thf(f43,axiom,
! [X10: nat,X11: nat,X16: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X10),X11)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X11),X16)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X10)),X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_less__trans__Suc) ).
thf(f5304,plain,
spl60_242,
inference(avatar_split_clause,[],[f1592,f5302]) ).
thf(f5302,plain,
( spl60_242
<=> ! [X2: nat > nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK49,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_242])]) ).
thf(f1592,plain,
! [X2: nat > nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK49,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1256]) ).
thf(f1256,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2))) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK49,X2)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK48,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK49,X2)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK48,X2)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47,sK48,sK49,sK50])],[f1252,f1255,f1254,f1253]) ).
thf(f1253,plain,
! [X2: nat > nat > $o] :
( ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2))) ) ),
introduced(choice_axiom,[]) ).
thf(f1254,plain,
! [X2: nat > nat > $o] :
( ? [X4: nat,X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK49,X2)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK48,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK49,X2)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK48,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1255,plain,
! [X2: nat > nat > $o] :
( ? [X7: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X7),X7) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f1252,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
| ? [X4: nat,X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) ) )
| ? [X7: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X7),X7) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f1126]) ).
thf(f1126,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ? [X7: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X7),vAPP(nat,nat,suc,X7)) )
| ? [X4: nat,X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) ) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1125]) ).
thf(f1125,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ? [X7: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X7),vAPP(nat,nat,suc,X7)) )
| ? [X4: nat,X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) ) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f761]) ).
thf(f761,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ! [X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),X3) )
=> ( ! [X4: nat,X5: nat,X6: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) ) ) )
=> ( ! [X7: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X7),vAPP(nat,nat,suc,X7)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) ) ) ) ) ),
inference(fool_elimination,[],[f760]) ).
thf(f760,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( ! [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),X3)
=> ( ! [X4: nat,X5: nat,X6: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) ) )
=> ( ! [X7: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X7),vAPP(nat,nat,suc,X7))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) ) ) ) ),
inference(rectify,[],[f228]) ).
thf(f228,axiom,
! [X9: nat,X4: nat,X39: nat > nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4)
=> ( ! [X30: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X39,X30),X30)
=> ( ! [X30: nat,X31: nat,X25: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X39,X30),X31)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X39,X31),X25)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X39,X30),X25) ) )
=> ( ! [X21: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X39,X21),vAPP(nat,nat,suc,X21))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X39,X9),X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_transitive__stepwise__le) ).
thf(f5300,plain,
spl60_241,
inference(avatar_split_clause,[],[f1591,f5298]) ).
thf(f5298,plain,
( spl60_241
<=> ! [X2: nat > nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK48,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK49,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_241])]) ).
thf(f1591,plain,
! [X2: nat > nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK48,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK49,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1256]) ).
thf(f5296,plain,
spl60_240,
inference(avatar_split_clause,[],[f1590,f5294]) ).
thf(f5294,plain,
( spl60_240
<=> ! [X2: nat > nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK48,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_240])]) ).
thf(f1590,plain,
! [X2: nat > nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X2))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK48,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK50,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1256]) ).
thf(f5281,plain,
spl60_239,
inference(avatar_split_clause,[],[f1701,f5279]) ).
thf(f5279,plain,
( spl60_239
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_239])]) ).
thf(f1701,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1491,f1287,f1287]) ).
thf(f1491,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1006]) ).
thf(f1006,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f1005]) ).
thf(f1005,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f597]) ).
thf(f597,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)) ) ) ),
inference(fool_elimination,[],[f596]) ).
thf(f596,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)) ) ),
inference(rectify,[],[f312]) ).
thf(f312,axiom,
! [X0: nat,X23: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X23)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X23),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_div__positive) ).
thf(f5265,plain,
spl60_238,
inference(avatar_split_clause,[],[f2311,f5263]) ).
thf(f5263,plain,
( spl60_238
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_238])]) ).
thf(f2311,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(trivial_inequality_removal,[],[f2310]) ).
thf(f2310,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(forward_demodulation,[],[f1762,f1374]) ).
thf(f1762,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(definition_unfolding,[],[f1622,f1287,f1287]) ).
thf(f1622,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(cnf_transformation,[],[f1151]) ).
thf(f1151,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(flattening,[],[f1150]) ).
thf(f1150,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(ennf_transformation,[],[f787]) ).
thf(f787,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f786]) ).
thf(f786,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ),
inference(rectify,[],[f176]) ).
thf(f176,axiom,
! [X23: nat,X4: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X23),X4)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X4))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X23),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_power__less__imp__less__base) ).
thf(f5254,plain,
spl60_237,
inference(avatar_split_clause,[],[f1714,f5252]) ).
thf(f5252,plain,
( spl60_237
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_237])]) ).
thf(f1714,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1505,f1287,f1287]) ).
thf(f1505,plain,
! [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),sK23,X1),X0)) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1212]) ).
thf(f1212,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) ) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f1023,f1211]) ).
thf(f1211,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,suc,X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
=> ( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1023,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,suc,X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(flattening,[],[f1022]) ).
thf(f1022,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,suc,X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f625]) ).
thf(f625,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( ( vAPP(nat,nat,suc,X0) != X1 )
=> ~ ! [X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
=> ( vAPP(nat,nat,suc,X2) != X1 ) ) ) ),
inference(fool_elimination,[],[f624]) ).
thf(f624,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( ( vAPP(nat,nat,suc,X0) != X1 )
=> ~ ! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2)
=> ( vAPP(nat,nat,suc,X2) != X1 ) ) ) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
! [X10: nat,X16: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X10),X16)
=> ( ( vAPP(nat,nat,suc,X10) != X16 )
=> ~ ! [X14: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X10),X14)
=> ( vAPP(nat,nat,suc,X14) != X16 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Nat_OlessE) ).
thf(f5226,plain,
spl60_236,
inference(avatar_split_clause,[],[f1774,f5224]) ).
thf(f5224,plain,
( spl60_236
<=> ! [X0: nat,X3: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0)),X0) = X3 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_236])]) ).
thf(f1774,plain,
! [X3: real,X0: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0)),X0) = X3 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(equality_resolution,[],[f1698]) ).
thf(f1698,plain,
! [X3: real,X0: nat,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0) = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0) != X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1490,f1287]) ).
thf(f1490,plain,
! [X3: real,X0: nat,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0) = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0) != X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1210]) ).
thf(f1210,plain,
! [X0: nat,X1: real] :
( ( ! [X3: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0) = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0) != X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)),X0) = X1 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)) ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f1004,f1209]) ).
thf(f1209,plain,
! [X0: nat,X1: real] :
( ? [X2: real] :
( ! [X3: real] :
( ( X2 = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0) != X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
=> ( ! [X3: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0) = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0) != X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)),X0) = X1 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1004,plain,
! [X0: nat,X1: real] :
( ? [X2: real] :
( ! [X3: real] :
( ( X2 = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0) != X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f1003]) ).
thf(f1003,plain,
! [X0: nat,X1: real] :
( ? [X2: real] :
( ! [X3: real] :
( ( X2 = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0) != X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f595]) ).
thf(f595,plain,
! [X0: nat,X1: real] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ? [X2: real] :
( ! [X3: real] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0) = X1 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
=> ( X2 = X3 ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) ) ) ),
inference(fool_elimination,[],[f594]) ).
thf(f594,plain,
! [X0: nat,X1: real] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ? [X2: real] :
( ! [X3: real] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X0) = X1 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) )
=> ( X2 = X3 ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) ) ) ),
inference(rectify,[],[f187]) ).
thf(f187,axiom,
! [X4: nat,X23: real] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X23)
=> ? [X30: real] :
( ! [X36: real] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X36),X4) = X23 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X36) )
=> ( X30 = X36 ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X30),X4) = X23 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X30) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_realpow__pos__nth__unique) ).
thf(f5221,plain,
spl60_235,
inference(avatar_split_clause,[],[f1751,f5219]) ).
thf(f5219,plain,
( spl60_235
<=> ! [X2: nat,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_235])]) ).
thf(f1751,plain,
! [X2: nat,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(definition_unfolding,[],[f1585,f1287]) ).
thf(f1585,plain,
! [X2: nat,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1116]) ).
thf(f1116,plain,
! [X0: real,X1: real,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(flattening,[],[f1115]) ).
thf(f1115,plain,
! [X0: real,X1: real,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f751]) ).
thf(f751,plain,
! [X0: real,X1: real,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) ) ) ) ),
inference(fool_elimination,[],[f750]) ).
thf(f750,plain,
! [X0: real,X1: real,X2: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) ) ) ),
inference(rectify,[],[f177]) ).
thf(f177,axiom,
! [X23: real,X0: real,X4: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X23),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X23)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),X4)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_power__strict__mono) ).
thf(f5217,plain,
spl60_234,
inference(avatar_split_clause,[],[f1750,f5215]) ).
thf(f5215,plain,
( spl60_234
<=> ! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_234])]) ).
thf(f1750,plain,
! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(definition_unfolding,[],[f1581,f1287]) ).
thf(f1581,plain,
! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(cnf_transformation,[],[f1108]) ).
thf(f1108,plain,
! [X0: int,X1: int,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(flattening,[],[f1107]) ).
thf(f1107,plain,
! [X0: int,X1: int,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(ennf_transformation,[],[f743]) ).
thf(f743,plain,
! [X0: int,X1: int,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) ) ) ),
inference(fool_elimination,[],[f742]) ).
thf(f742,plain,
! [X0: int,X1: int,X2: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) ) ),
inference(rectify,[],[f178]) ).
thf(f178,axiom,
! [X23: int,X0: int,X4: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X23),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X23)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X23),X4)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_power__strict__mono) ).
thf(f5186,plain,
spl60_233,
inference(avatar_split_clause,[],[f1733,f5184]) ).
thf(f5184,plain,
( spl60_233
<=> ! [X2: nat,X0: nat > real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK35,X0))),vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK35,X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_233])]) ).
thf(f1733,plain,
! [X2: nat,X0: nat > real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK35,X0))),vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK35,X0)))) ) ),
inference(definition_unfolding,[],[f1555,f1287]) ).
thf(f1555,plain,
! [X2: nat,X0: nat > real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK35,X0))),vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK35,X0)))) ) ),
inference(cnf_transformation,[],[f1233]) ).
thf(f1233,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK35,X0))),vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK35,X0)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f1065,f1232]) ).
thf(f1232,plain,
! [X0: nat > real] :
( ? [X3: nat] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))) )
=> ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK35,X0))),vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK35,X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f1065,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(flattening,[],[f1064]) ).
thf(f1064,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(ennf_transformation,[],[f699]) ).
thf(f699,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) ) ) ),
inference(fool_elimination,[],[f698]) ).
thf(f698,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) ) ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X20: nat > real,X4: nat,X22: nat] :
( ! [X21: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X20,X21)),vAPP(nat,real,X20,vAPP(nat,nat,suc,X21)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X22)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,X20,X4)),vAPP(nat,real,X20,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_lift__Suc__mono__less) ).
thf(f5182,plain,
spl60_232,
inference(avatar_split_clause,[],[f1731,f5180]) ).
thf(f5180,plain,
( spl60_232
<=> ! [X2: nat,X0: nat > int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK31,X0))),vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK31,X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_232])]) ).
thf(f1731,plain,
! [X2: nat,X0: nat > int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK31,X0))),vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK31,X0)))) ) ),
inference(definition_unfolding,[],[f1551,f1287]) ).
thf(f1551,plain,
! [X2: nat,X0: nat > int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK31,X0))),vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK31,X0)))) ) ),
inference(cnf_transformation,[],[f1225]) ).
thf(f1225,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK31,X0))),vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK31,X0)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f1058,f1224]) ).
thf(f1224,plain,
! [X0: nat > int] :
( ? [X3: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK31,X0))),vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK31,X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f1058,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(flattening,[],[f1057]) ).
thf(f1057,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(ennf_transformation,[],[f691]) ).
thf(f691,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) ) ) ),
inference(fool_elimination,[],[f690]) ).
thf(f690,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) ) ),
inference(rectify,[],[f65]) ).
thf(f65,axiom,
! [X20: nat > int,X4: nat,X22: nat] :
( ! [X21: nat] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X20,X21)),vAPP(nat,int,X20,vAPP(nat,nat,suc,X21)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X22)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,X20,X4)),vAPP(nat,int,X20,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_lift__Suc__mono__less) ).
thf(f5178,plain,
spl60_231,
inference(avatar_split_clause,[],[f1724,f5176]) ).
thf(f5176,plain,
( spl60_231
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_231])]) ).
thf(f1724,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X1) ) ),
inference(definition_unfolding,[],[f1519,f1287,f1287]) ).
thf(f1519,plain,
! [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),sK25,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(cnf_transformation,[],[f1216]) ).
thf(f1216,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f1039,f1215]) ).
thf(f1215,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,suc,X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
=> ( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1039,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,suc,X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(ennf_transformation,[],[f651]) ).
thf(f651,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) )
=> ~ ! [X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
=> ( vAPP(nat,nat,suc,X2) != X1 ) ) ),
inference(fool_elimination,[],[f650]) ).
thf(f650,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1)
=> ~ ! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2)
=> ( vAPP(nat,nat,suc,X2) != X1 ) ) ),
inference(rectify,[],[f54]) ).
thf(f54,axiom,
! [X10: nat,X16: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X10)),X16)
=> ~ ! [X14: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X10),X14)
=> ( vAPP(nat,nat,suc,X14) != X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Suc__lessE) ).
thf(f5174,plain,
spl60_230,
inference(avatar_split_clause,[],[f1720,f5172]) ).
thf(f5172,plain,
( spl60_230
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_230])]) ).
thf(f1720,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ),
inference(definition_unfolding,[],[f1513,f1287,f1287]) ).
thf(f1513,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ),
inference(cnf_transformation,[],[f1031]) ).
thf(f1031,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ),
inference(ennf_transformation,[],[f639]) ).
thf(f639,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ),
inference(fool_elimination,[],[f638]) ).
thf(f638,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ),
inference(rectify,[],[f140]) ).
thf(f140,axiom,
! [X4: nat,X16: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X16),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X4),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_power__gt__expt) ).
thf(f5155,plain,
spl60_229,
inference(avatar_split_clause,[],[f1759,f5153]) ).
thf(f5153,plain,
( spl60_229
<=> ! [X2: nat > nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_229])]) ).
thf(f1759,plain,
! [X2: nat > nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1617,f1287]) ).
thf(f1617,plain,
! [X2: nat > nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1274]) ).
thf(f1274,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f1167,f1273]) ).
thf(f1273,plain,
! [X2: nat > nat > $o] :
( ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK59,X2))) ) ),
introduced(choice_axiom,[]) ).
thf(f1167,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ( $true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(definition_folding,[],[f1141,f1166]) ).
thf(f1166,plain,
! [X2: nat > nat > $o] :
( ? [X4: nat,X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1141,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ? [X4: nat,X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(flattening,[],[f1140]) ).
thf(f1140,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) )
| ? [X4: nat,X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f777]) ).
thf(f777,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( ! [X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
=> ( ! [X4: nat,X5: nat,X6: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X6) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) ) ) ) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) ) ) ) ),
inference(fool_elimination,[],[f776]) ).
thf(f776,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( ! [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X3),vAPP(nat,nat,suc,X3))
=> ( ! [X4: nat,X5: nat,X6: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X6)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) ) ) ) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X0),X1) ) ) ),
inference(rectify,[],[f42]) ).
thf(f42,axiom,
! [X10: nat,X11: nat,X12: nat > nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X10),X11)
=> ( ! [X13: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X13),vAPP(nat,nat,suc,X13))
=> ( ! [X13: nat,X14: nat,X15: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X13),X14)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X15)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X13),X14)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X14),X15)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X13),X15) ) ) ) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X10),X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_less__Suc__induct) ).
thf(f5144,plain,
spl60_228,
inference(avatar_split_clause,[],[f1715,f5142]) ).
thf(f5142,plain,
( spl60_228
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_228])]) ).
thf(f1715,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1507,f1287,f1287]) ).
thf(f1507,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1025]) ).
thf(f1025,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(flattening,[],[f1024]) ).
thf(f1024,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f627]) ).
thf(f627,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( ( vAPP(nat,nat,suc,X0) != X1 )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) ) ) ),
inference(fool_elimination,[],[f626]) ).
thf(f626,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( ( vAPP(nat,nat,suc,X0) != X1 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(rectify,[],[f53]) ).
thf(f53,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4)
=> ( ( vAPP(nat,nat,suc,X9) != X4 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X9)),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Suc__lessI) ).
thf(f5123,plain,
spl60_227,
inference(avatar_split_clause,[],[f1736,f5121]) ).
thf(f5121,plain,
( spl60_227
<=> ! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK42,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK43,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_227])]) ).
thf(f1736,plain,
! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK42,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK43,X0))) ) ),
inference(definition_unfolding,[],[f1563,f1287]) ).
thf(f1563,plain,
! [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,sK42,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK43,X0))) ) ),
inference(cnf_transformation,[],[f1247]) ).
thf(f1247,plain,
! [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,sK42,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK43,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK42,X0)),vAPP(sTfun(nat,nat),nat,sK43,X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43])],[f1078,f1246]) ).
thf(f1246,plain,
! [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,sK42,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK43,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK42,X0)),vAPP(sTfun(nat,nat),nat,sK43,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1078,plain,
! [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) ) ) ),
inference(flattening,[],[f1077]) ).
thf(f1077,plain,
! [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) ) ) ),
inference(ennf_transformation,[],[f713]) ).
thf(f713,plain,
! [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,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ) ),
inference(fool_elimination,[],[f712]) ).
thf(f712,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ! [X3: nat,X4: nat] :
( vAPP(nat,$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,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ),
inference(rectify,[],[f238]) ).
thf(f238,axiom,
! [X20: nat > nat,X10: nat,X11: nat] :
( ! [X13: nat,X14: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X13),X14)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X20,X13)),vAPP(nat,nat,X20,X14)) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X10),X11)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X20,X10)),vAPP(nat,nat,X20,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_less__mono__imp__le__mono) ).
thf(f5119,plain,
spl60_226,
inference(avatar_split_clause,[],[f1702,f5117]) ).
thf(f5117,plain,
( spl60_226
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_226])]) ).
thf(f1702,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1492,f1287,f1287]) ).
thf(f1492,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1007]) ).
thf(f1007,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f599]) ).
thf(f599,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ),
inference(fool_elimination,[],[f598]) ).
thf(f598,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ),
inference(rectify,[],[f78]) ).
thf(f78,axiom,
! [X23: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X23)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X23),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_zero__less__power) ).
thf(f5071,plain,
spl60_225,
inference(avatar_split_clause,[],[f1728,f5069]) ).
thf(f5069,plain,
( spl60_225
<=> ! [X2: real,X0: real,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_225])]) ).
thf(f1728,plain,
! [X2: real,X0: real,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) ) ),
inference(definition_unfolding,[],[f1543,f1287]) ).
thf(f1543,plain,
! [X2: real,X0: real,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) ) ),
inference(cnf_transformation,[],[f1045]) ).
thf(f1045,plain,
! [X0: real,X1: nat,X2: real] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) ) ),
inference(flattening,[],[f1044]) ).
thf(f1044,plain,
! [X0: real,X1: nat,X2: real] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) ) ),
inference(ennf_transformation,[],[f677]) ).
thf(f677,plain,
! [X0: real,X1: nat,X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( X0 = X2 ) ) ) ) ),
inference(fool_elimination,[],[f676]) ).
thf(f676,plain,
! [X0: real,X1: nat,X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( X0 = X2 ) ) ) ) ),
inference(rectify,[],[f160]) ).
thf(f160,axiom,
! [X23: real,X4: nat,X0: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),X4) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X4) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X23)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> ( X0 = X23 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_power__eq__imp__eq__base) ).
thf(f5067,plain,
spl60_224,
inference(avatar_split_clause,[],[f1727,f5065]) ).
thf(f5065,plain,
( spl60_224
<=> ! [X2: int,X0: int,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_224])]) ).
thf(f1727,plain,
! [X2: int,X0: int,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) ) ),
inference(definition_unfolding,[],[f1542,f1287]) ).
thf(f1542,plain,
! [X2: int,X0: int,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) ) ),
inference(cnf_transformation,[],[f1043]) ).
thf(f1043,plain,
! [X0: int,X1: nat,X2: int] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) ) ),
inference(flattening,[],[f1042]) ).
thf(f1042,plain,
! [X0: int,X1: nat,X2: int] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) ) ),
inference(ennf_transformation,[],[f675]) ).
thf(f675,plain,
! [X0: int,X1: nat,X2: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( X0 = X2 ) ) ) ) ),
inference(fool_elimination,[],[f674]) ).
thf(f674,plain,
! [X0: int,X1: nat,X2: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( X0 = X2 ) ) ) ) ),
inference(rectify,[],[f161]) ).
thf(f161,axiom,
! [X23: int,X4: nat,X0: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X23),X4) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X4) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X23)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> ( X0 = X23 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_power__eq__imp__eq__base) ).
thf(f5063,plain,
spl60_223,
inference(avatar_split_clause,[],[f1726,f5061]) ).
thf(f5061,plain,
( spl60_223
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_223])]) ).
thf(f1726,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(definition_unfolding,[],[f1522,f1287,f1287]) ).
thf(f1522,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(cnf_transformation,[],[f1041]) ).
thf(f1041,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(ennf_transformation,[],[f655]) ).
thf(f655,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(fool_elimination,[],[f654]) ).
thf(f654,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
inference(rectify,[],[f44]) ).
thf(f44,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X9)),vAPP(nat,nat,suc,X4))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Suc__less__SucD) ).
thf(f5059,plain,
spl60_222,
inference(avatar_split_clause,[],[f1719,f5057]) ).
thf(f5057,plain,
( spl60_222
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_222])]) ).
thf(f1719,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1511,f1287,f1287]) ).
thf(f1511,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1029]) ).
thf(f1029,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f635]) ).
thf(f635,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(fool_elimination,[],[f634]) ).
thf(f634,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X9)),vAPP(nat,nat,suc,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Suc__mono) ).
thf(f5055,plain,
spl60_221,
inference(avatar_split_clause,[],[f1549,f5053]) ).
thf(f5053,plain,
( spl60_221
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_221])]) ).
thf(f1549,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1221]) ).
thf(f1221,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27,sK28,sK29])],[f1217,f1220,f1219,f1218]) ).
thf(f1218,plain,
! [X0: nat > nat > $o] :
( ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1219,plain,
! [X0: nat > nat > $o] :
( ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X5)) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1220,plain,
! [X0: nat > nat > $o] :
( ? [X6: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),zero_zero_nat) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),zero_zero_nat) ) ),
introduced(choice_axiom,[]) ).
thf(f1217,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) ) )
| ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X5)) )
| ? [X6: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),zero_zero_nat) ) ),
inference(rectify,[],[f1055]) ).
thf(f1055,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) ) )
| ? [X4: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X4)) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero_nat) ) ),
inference(flattening,[],[f1054]) ).
thf(f1054,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) ) )
| ? [X4: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X4)) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero_nat) ) ),
inference(ennf_transformation,[],[f687]) ).
thf(f687,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero_nat) )
=> ( ! [X4: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X4)) )
=> ( ! [X5: nat,X6: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ) ),
inference(fool_elimination,[],[f686]) ).
thf(f686,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero_nat)
=> ( ! [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X4))
=> ( ! [X5: nat,X6: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ),
inference(rectify,[],[f147]) ).
thf(f147,axiom,
! [X12: nat > nat > $o,X9: nat,X4: nat] :
( ! [X30: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X30),zero_zero_nat)
=> ( ! [X31: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,zero_zero_nat),vAPP(nat,nat,suc,X31))
=> ( ! [X30: nat,X31: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X30),X31)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,vAPP(nat,nat,suc,X30)),vAPP(nat,nat,suc,X31)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X9),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_diff__induct) ).
thf(f5043,plain,
spl60_220,
inference(avatar_split_clause,[],[f1688,f5041]) ).
thf(f5041,plain,
( spl60_220
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_220])]) ).
thf(f1688,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1432,f1287,f1287]) ).
thf(f1432,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f935]) ).
thf(f935,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(flattening,[],[f934]) ).
thf(f934,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f890]) ).
thf(f890,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
=> ( X0 = X1 ) ) ),
inference(flattening,[],[f511]) ).
thf(f511,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f510]) ).
thf(f510,plain,
! [X0: nat,X1: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f45]) ).
thf(f45,axiom,
! [X4: nat,X9: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X9)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),vAPP(nat,nat,suc,X9))
=> ( X4 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_less__antisym) ).
thf(f5039,plain,
spl60_219,
inference(avatar_split_clause,[],[f2152,f5037]) ).
thf(f5037,plain,
( spl60_219
<=> ! [X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) = vAPP(int,int,ring_1_of_int_int,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_219])]) ).
thf(f2152,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) = vAPP(int,int,ring_1_of_int_int,X1) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f2151]) ).
thf(f2151,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) = vAPP(int,int,ring_1_of_int_int,X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2147]) ).
thf(f2147,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1392]) ).
thf(f1392,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ),
inference(cnf_transformation,[],[f443]) ).
thf(f443,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ),
inference(fool_elimination,[],[f442]) ).
thf(f442,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) = vAPP(int,int,ring_1_of_int_int,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X1: int,X3: int] :
( ( vAPP(int,int,ring_1_of_int_int,X3) = vAPP(int,int,ring_1_of_int_int,X1) )
= ( X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_of__int__eq__iff) ).
thf(f5020,plain,
spl60_218,
inference(avatar_split_clause,[],[f1725,f5018]) ).
thf(f5018,plain,
( spl60_218
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_218])]) ).
thf(f1725,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X1) ) ),
inference(definition_unfolding,[],[f1521,f1287,f1287]) ).
thf(f1521,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(cnf_transformation,[],[f1040]) ).
thf(f1040,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(ennf_transformation,[],[f653]) ).
thf(f653,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(fool_elimination,[],[f652]) ).
thf(f652,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X9)),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Suc__lessD) ).
thf(f5016,plain,
spl60_217,
inference(avatar_split_clause,[],[f1717,f5014]) ).
thf(f5014,plain,
( spl60_217
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_217])]) ).
thf(f1717,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1509,f1287,f1287]) ).
thf(f1509,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1027]) ).
thf(f1027,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f631]) ).
thf(f631,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) ) ),
inference(fool_elimination,[],[f630]) ).
thf(f630,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f51]) ).
thf(f51,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),vAPP(nat,nat,suc,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__SucI) ).
thf(f4982,plain,
spl60_216,
inference(avatar_split_clause,[],[f1753,f4980]) ).
thf(f4980,plain,
( spl60_216
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)),X1) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_216])]) ).
thf(f1753,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)),X1) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(definition_unfolding,[],[f1601,f1287]) ).
thf(f1601,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)),X1) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1262]) ).
thf(f1262,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)) ) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f1132,f1261]) ).
thf(f1261,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,X3) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
=> ( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1132,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,X3) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1131]) ).
thf(f1131,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,X3) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f767]) ).
thf(f767,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,X2,X1) )
=> ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1) )
=> ( ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
=> ( $true = vAPP(nat,$o,X2,X3) ) ) ) )
=> ( $true = vAPP(nat,$o,X2,X0) ) ) ) ),
inference(fool_elimination,[],[f766]) ).
thf(f766,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,X2,X1)
=> ( ! [X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1)
=> ( vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3))
=> vAPP(nat,$o,X2,X3) ) ) )
=> vAPP(nat,$o,X2,X0) ) ) ),
inference(rectify,[],[f253]) ).
thf(f253,axiom,
! [X10: nat,X11: nat,X12: nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X10),X11)
=> ( vAPP(nat,$o,X12,X11)
=> ( ! [X21: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X10),X21)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X21),X11)
=> ( vAPP(nat,$o,X12,vAPP(nat,nat,suc,X21))
=> vAPP(nat,$o,X12,X21) ) ) )
=> vAPP(nat,$o,X12,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_inc__induct) ).
thf(f4978,plain,
spl60_215,
inference(avatar_split_clause,[],[f1752,f4976]) ).
thf(f4976,plain,
( spl60_215
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)),X1) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_215])]) ).
thf(f1752,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)),X1) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(definition_unfolding,[],[f1597,f1287]) ).
thf(f1597,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)),X1) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1260]) ).
thf(f1260,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0))) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)) ) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f1130,f1259]) ).
thf(f1259,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
& ( $true = vAPP(nat,$o,X2,X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
=> ( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0))) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1130,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
& ( $true = vAPP(nat,$o,X2,X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1129]) ).
thf(f1129,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
& ( $true = vAPP(nat,$o,X2,X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f765]) ).
thf(f765,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,X2,X0) )
=> ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1) )
=> ( ( $true = vAPP(nat,$o,X2,X3) )
=> ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) ) ) ) )
=> ( $true = vAPP(nat,$o,X2,X1) ) ) ) ),
inference(fool_elimination,[],[f764]) ).
thf(f764,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,X2,X0)
=> ( ! [X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X1)
=> ( vAPP(nat,$o,X2,X3)
=> vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) ) ) )
=> vAPP(nat,$o,X2,X1) ) ) ),
inference(rectify,[],[f252]) ).
thf(f252,axiom,
! [X10: nat,X11: nat,X12: nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X10),X11)
=> ( vAPP(nat,$o,X12,X10)
=> ( ! [X21: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X10),X21)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X21),X11)
=> ( vAPP(nat,$o,X12,X21)
=> vAPP(nat,$o,X12,vAPP(nat,nat,suc,X21)) ) ) )
=> vAPP(nat,$o,X12,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_dec__induct) ).
thf(f4952,plain,
spl60_214,
inference(avatar_split_clause,[],[f2150,f4950]) ).
thf(f4950,plain,
( spl60_214
<=> ! [X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) != vAPP(int,int,ring_1_of_int_int,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_214])]) ).
thf(f2150,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) != vAPP(int,int,ring_1_of_int_int,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f2149]) ).
thf(f2149,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,ring_1_of_int_int,X0) != vAPP(int,int,ring_1_of_int_int,X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2148]) ).
thf(f2148,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,ring_1_of_int_int,X0)),vAPP(int,int,ring_1_of_int_int,X1)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1392]) ).
thf(f4948,plain,
spl60_213,
inference(avatar_split_clause,[],[f1748,f4946]) ).
thf(f4946,plain,
( spl60_213
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_213])]) ).
thf(f1748,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1579,f1287]) ).
thf(f1579,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1104]) ).
thf(f1104,plain,
! [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),divide_divide_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f1103]) ).
thf(f1103,plain,
! [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),divide_divide_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f739]) ).
thf(f739,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X0)) ) ) ),
inference(fool_elimination,[],[f738]) ).
thf(f738,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X2),X0)) ) ),
inference(rectify,[],[f297]) ).
thf(f297,axiom,
! [X9: nat,X4: nat,X16: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X9)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X16),X4)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X16),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_div__le__mono2) ).
thf(f4944,plain,
spl60_212,
inference(avatar_split_clause,[],[f1737,f4942]) ).
thf(f4942,plain,
( spl60_212
<=> ! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,nat),nat,sK42,X0)),vAPP(sTfun(nat,nat),nat,sK43,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_212])]) ).
thf(f1737,plain,
! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,nat),nat,sK42,X0)),vAPP(sTfun(nat,nat),nat,sK43,X0)) ) ),
inference(definition_unfolding,[],[f1562,f1287]) ).
thf(f1562,plain,
! [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,sK42,X0)),vAPP(sTfun(nat,nat),nat,sK43,X0)) ) ),
inference(cnf_transformation,[],[f1247]) ).
thf(f4927,plain,
spl60_211,
inference(avatar_split_clause,[],[f1548,f4925]) ).
thf(f4925,plain,
( spl60_211
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_211])]) ).
thf(f1548,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK26,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1221]) ).
thf(f4906,plain,
spl60_210,
inference(avatar_split_clause,[],[f1756,f4904]) ).
thf(f4904,plain,
( spl60_210
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_210])]) ).
thf(f1756,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1610,f1287]) ).
thf(f1610,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1268]) ).
thf(f1268,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) )
| ( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) )
& ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f1165,f1267]) ).
thf(f1267,plain,
! [X1: nat,X2: nat > $o] :
( ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,X3) )
& ( vAPP(nat,nat,suc,X3) = X1 ) )
=> ( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) )
& ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1165,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,X3) )
& ( vAPP(nat,nat,suc,X3) = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(definition_folding,[],[f1139,f1164]) ).
thf(f1164,plain,
! [X2: nat > $o,X1: nat] :
( ? [X4: nat] :
( ( $true != vAPP(nat,$o,X2,X4) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X1) ) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1139,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ? [X4: nat] :
( ( $true != vAPP(nat,$o,X2,X4) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X1) ) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,X3) )
& ( vAPP(nat,nat,suc,X3) = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(flattening,[],[f1138]) ).
thf(f1138,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ? [X4: nat] :
( ( $true != vAPP(nat,$o,X2,X4) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X1) ) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,X3) )
& ( vAPP(nat,nat,suc,X3) = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f775]) ).
thf(f775,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( ! [X3: nat] :
( ( vAPP(nat,nat,suc,X3) = X1 )
=> ( $true = vAPP(nat,$o,X2,X3) ) )
=> ( ! [X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X1) )
=> ( ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4)) )
=> ( $true = vAPP(nat,$o,X2,X4) ) ) )
=> ( $true = vAPP(nat,$o,X2,X0) ) ) ) ),
inference(fool_elimination,[],[f774]) ).
thf(f774,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( ! [X3: nat] :
( ( vAPP(nat,nat,suc,X3) = X1 )
=> vAPP(nat,$o,X2,X3) )
=> ( ! [X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X1)
=> ( vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4))
=> vAPP(nat,$o,X2,X4) ) )
=> vAPP(nat,$o,X2,X0) ) ) ),
inference(rectify,[],[f41]) ).
thf(f41,axiom,
! [X10: nat,X11: nat,X12: nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X10),X11)
=> ( ! [X13: nat] :
( ( vAPP(nat,nat,suc,X13) = X11 )
=> vAPP(nat,$o,X12,X13) )
=> ( ! [X13: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X13),X11)
=> ( vAPP(nat,$o,X12,vAPP(nat,nat,suc,X13))
=> vAPP(nat,$o,X12,X13) ) )
=> vAPP(nat,$o,X12,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_strict__inc__induct) ).
thf(f4902,plain,
spl60_209,
inference(avatar_split_clause,[],[f1755,f4900]) ).
thf(f4900,plain,
( spl60_209
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) )
| ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_209])]) ).
thf(f1755,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) )
| ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1611,f1287]) ).
thf(f1611,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) )
| ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK55,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1268]) ).
thf(f4884,plain,
spl60_208,
inference(avatar_split_clause,[],[f2146,f4882]) ).
thf(f4882,plain,
( spl60_208
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,real,ring_1_of_int_real,X0) != vAPP(int,real,ring_1_of_int_real,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_208])]) ).
thf(f2146,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,real,ring_1_of_int_real,X0) != vAPP(int,real,ring_1_of_int_real,X1) ) ),
inference(equality_proxy_clausification,[],[f2145]) ).
thf(f2145,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ),
inference(equality_proxy_clausification,[],[f2141]) ).
thf(f2141,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f1393]) ).
thf(f1393,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ),
inference(cnf_transformation,[],[f445]) ).
thf(f445,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ),
inference(fool_elimination,[],[f444]) ).
thf(f444,plain,
! [X0: int,X1: int] :
( ( vAPP(int,real,ring_1_of_int_real,X0) = vAPP(int,real,ring_1_of_int_real,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X1: int,X3: int] :
( ( vAPP(int,real,ring_1_of_int_real,X3) = vAPP(int,real,ring_1_of_int_real,X1) )
= ( X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_of__int__eq__iff) ).
thf(f4872,plain,
spl60_207,
inference(avatar_split_clause,[],[f1628,f4870]) ).
thf(f4870,plain,
( spl60_207
<=> ! [X0: real,X3: real,X2: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_207])]) ).
thf(f1628,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f1163]) ).
thf(f1163,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(flattening,[],[f1162]) ).
thf(f1162,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f799]) ).
thf(f799,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) ) ) ) ) ),
inference(fool_elimination,[],[f798]) ).
thf(f798,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) ) ) ) ),
inference(rectify,[],[f279]) ).
thf(f279,axiom,
! [X19: real,X2: real,X1: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X19)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X19)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X3)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X19),X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_frac__le) ).
thf(f4868,plain,
spl60_206,
inference(avatar_split_clause,[],[f1627,f4866]) ).
thf(f4866,plain,
( spl60_206
<=> ! [X0: real,X3: real,X2: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_206])]) ).
thf(f1627,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f1161]) ).
thf(f1161,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(flattening,[],[f1160]) ).
thf(f1160,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f797]) ).
thf(f797,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) ) ) ) ) ),
inference(fool_elimination,[],[f796]) ).
thf(f796,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) ) ) ) ),
inference(rectify,[],[f280]) ).
thf(f280,axiom,
! [X2: real,X19: real,X1: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X19)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X3)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X19),X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_frac__less) ).
thf(f4864,plain,
spl60_205,
inference(avatar_split_clause,[],[f1626,f4862]) ).
thf(f4862,plain,
( spl60_205
<=> ! [X0: real,X3: real,X2: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_205])]) ).
thf(f1626,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f1159]) ).
thf(f1159,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(flattening,[],[f1158]) ).
thf(f1158,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f795]) ).
thf(f795,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) ) ) ) ) ),
inference(fool_elimination,[],[f794]) ).
thf(f794,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) ) ) ) ),
inference(rectify,[],[f281]) ).
thf(f281,axiom,
! [X2: real,X19: real,X1: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X19)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X3)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X19),X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_frac__less2) ).
thf(f4828,plain,
spl60_204,
inference(avatar_split_clause,[],[f1700,f4826]) ).
thf(f4826,plain,
( spl60_204
<=> ! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_204])]) ).
thf(f1700,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1488,f1287]) ).
thf(f1488,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1210]) ).
thf(f4824,plain,
spl60_203,
inference(avatar_split_clause,[],[f1699,f4822]) ).
thf(f4822,plain,
( spl60_203
<=> ! [X0: nat,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)),X0) = X1 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_203])]) ).
thf(f1699,plain,
! [X0: nat,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)),X0) = X1 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1489,f1287]) ).
thf(f1489,plain,
! [X0: nat,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK22,X1),X0)),X0) = X1 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1210]) ).
thf(f4820,plain,
spl60_202,
inference(avatar_split_clause,[],[f2144,f4818]) ).
thf(f4818,plain,
( spl60_202
<=> ! [X0: int,X1: int] :
( ( X0 != X1 )
| ( vAPP(int,real,ring_1_of_int_real,X0) = vAPP(int,real,ring_1_of_int_real,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_202])]) ).
thf(f2144,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ( vAPP(int,real,ring_1_of_int_real,X0) = vAPP(int,real,ring_1_of_int_real,X1) ) ),
inference(equality_proxy_clausification,[],[f2143]) ).
thf(f2143,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ),
inference(equality_proxy_clausification,[],[f2142]) ).
thf(f2142,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),vAPP(int,real,ring_1_of_int_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f1393]) ).
thf(f4816,plain,
spl60_201,
inference(avatar_split_clause,[],[f1697,f4814]) ).
thf(f4814,plain,
( spl60_201
<=> ! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_201])]) ).
thf(f1697,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1486,f1287]) ).
thf(f1486,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1208]) ).
thf(f1208,plain,
! [X0: nat,X1: real] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)),X0) = X1 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)) ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f1002,f1207]) ).
thf(f1207,plain,
! [X0: nat,X1: real] :
( ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
=> ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)),X0) = X1 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1002,plain,
! [X0: nat,X1: real] :
( ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f1001]) ).
thf(f1001,plain,
! [X0: nat,X1: real] :
( ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f593]) ).
thf(f593,plain,
! [X0: nat,X1: real] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) ) ) ),
inference(fool_elimination,[],[f592]) ).
thf(f592,plain,
! [X0: nat,X1: real] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) = X1 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) ) ) ),
inference(rectify,[],[f186]) ).
thf(f186,axiom,
! [X4: nat,X23: real] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X23)
=> ? [X24: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X24),X4) = X23 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_realpow__pos__nth) ).
thf(f4812,plain,
spl60_200,
inference(avatar_split_clause,[],[f1696,f4810]) ).
thf(f4810,plain,
( spl60_200
<=> ! [X0: nat,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)),X0) = X1 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_200])]) ).
thf(f1696,plain,
! [X0: nat,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)),X0) = X1 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1487,f1287]) ).
thf(f1487,plain,
! [X0: nat,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),sK21,X1),X0)),X0) = X1 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1208]) ).
thf(f4803,plain,
spl60_199,
inference(avatar_split_clause,[],[f1693,f4801]) ).
thf(f4801,plain,
( spl60_199
<=> ! [X0: nat > $o,X1: nat,X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_199])]) ).
thf(f1693,plain,
! [X3: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(definition_unfolding,[],[f1447,f1287]) ).
thf(f1447,plain,
! [X3: nat,X0: nat > $o,X1: 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,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1200]) ).
thf(f1200,plain,
! [X0: nat > $o,X1: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),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,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),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),sK17,X1),X0)),X1) ) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f946,f1199]) ).
thf(f1199,plain,
! [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,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
=> ( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),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,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),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),sK17,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f946,plain,
! [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,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(flattening,[],[f945]) ).
thf(f945,plain,
! [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,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f893]) ).
thf(f893,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
=> ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,X2) )
& ! [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,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) ) ) ),
inference(flattening,[],[f525]) ).
thf(f525,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
=> ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,X2) )
& ! [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,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) ) ) ),
inference(fool_elimination,[],[f524]) ).
thf(f524,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,X1)
=> ( ~ vAPP(nat,$o,X0,zero_zero_nat)
=> ? [X2: nat] :
( vAPP(nat,$o,X0,X2)
& ! [X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2)
=> ~ vAPP(nat,$o,X0,X3) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) ) ),
inference(rectify,[],[f249]) ).
thf(f249,axiom,
! [X12: nat > $o,X4: nat] :
( vAPP(nat,$o,X12,X4)
=> ( ~ vAPP(nat,$o,X12,zero_zero_nat)
=> ? [X15: nat] :
( vAPP(nat,$o,X12,X15)
& ! [X45: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X45),X15)
=> ~ vAPP(nat,$o,X12,X45) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X15),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_ex__least__nat__le) ).
thf(f4797,plain,
spl60_198,
inference(avatar_split_clause,[],[f1754,f4795]) ).
thf(f4795,plain,
( spl60_198
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)),X1) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_198])]) ).
thf(f1754,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)),X1) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ),
inference(definition_unfolding,[],[f1607,f1287]) ).
thf(f1607,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)),X1) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f1266]) ).
thf(f1266,plain,
! [X0: nat > $o,X1: nat] :
( ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)),X1) ) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f1264,f1265]) ).
thf(f1265,plain,
! [X0: nat > $o,X1: nat] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1264,plain,
! [X0: nat > $o,X1: nat] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ),
inference(rectify,[],[f1263]) ).
thf(f1263,plain,
! [X2: nat > $o,X1: nat] :
( ? [X4: nat] :
( ( $true != vAPP(nat,$o,X2,X4) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X1) ) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X2) ) ),
inference(nnf_transformation,[],[f1164]) ).
thf(f4746,plain,
spl60_197,
inference(avatar_split_clause,[],[f1694,f4744]) ).
thf(f4744,plain,
( spl60_197
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)),X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_197])]) ).
thf(f1694,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)),X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(definition_unfolding,[],[f1449,f1287]) ).
thf(f1449,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)),X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1202]) ).
thf(f1202,plain,
! [X0: nat > $o,X1: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0))) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)),X1) ) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f948,f1201]) ).
thf(f1201,plain,
! [X0: nat > $o,X1: nat] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
=> ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0))) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f948,plain,
! [X0: nat > $o,X1: nat] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(flattening,[],[f947]) ).
thf(f947,plain,
! [X0: nat > $o,X1: nat] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f894]) ).
thf(f894,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
=> ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ! [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,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ) ) ),
inference(flattening,[],[f527]) ).
thf(f527,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
=> ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ! [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,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ) ) ),
inference(fool_elimination,[],[f526]) ).
thf(f526,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,X1)
=> ( ~ vAPP(nat,$o,X0,zero_zero_nat)
=> ? [X2: nat] :
( vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))
& ! [X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2)
=> ~ vAPP(nat,$o,X0,X3) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ) ),
inference(rectify,[],[f261]) ).
thf(f261,axiom,
! [X12: nat > $o,X4: nat] :
( vAPP(nat,$o,X12,X4)
=> ( ~ vAPP(nat,$o,X12,zero_zero_nat)
=> ? [X15: nat] :
( vAPP(nat,$o,X12,vAPP(nat,nat,suc,X15))
& ! [X45: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X45),X15)
=> ~ vAPP(nat,$o,X12,X45) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X15),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_ex__least__nat__less) ).
thf(f4742,plain,
spl60_196,
inference(avatar_split_clause,[],[f1568,f4740]) ).
thf(f4740,plain,
( spl60_196
<=> ! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_196])]) ).
thf(f1568,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f1082]) ).
thf(f1082,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(flattening,[],[f1081]) ).
thf(f1081,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f717]) ).
thf(f717,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)) ) ) ) ),
inference(fool_elimination,[],[f716]) ).
thf(f716,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)) ) ) ),
inference(rectify,[],[f307]) ).
thf(f307,axiom,
! [X23: int,X50: int,X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X23)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X50)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X50),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X23),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X23),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_zdiv__mono2) ).
thf(f4629,plain,
spl60_195,
inference(avatar_split_clause,[],[f1758,f4627]) ).
thf(f4627,plain,
( spl60_195
<=> ! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_195])]) ).
thf(f1758,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(definition_unfolding,[],[f1612,f1287]) ).
thf(f1612,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1272]) ).
thf(f1272,plain,
! [X0: nat > nat > $o] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)) ) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57,sK58])],[f1270,f1271]) ).
thf(f1271,plain,
! [X0: nat > nat > $o] :
( ? [X1: nat,X2: nat,X3: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X2),X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1270,plain,
! [X0: nat > nat > $o] :
( ? [X1: nat,X2: nat,X3: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X2),X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(rectify,[],[f1269]) ).
thf(f1269,plain,
! [X2: nat > nat > $o] :
( ? [X4: nat,X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X2,X4),X5) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X2) ) ),
inference(nnf_transformation,[],[f1166]) ).
thf(f4615,plain,
spl60_194,
inference(avatar_split_clause,[],[f1757,f4613]) ).
thf(f4613,plain,
( spl60_194
<=> ! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_194])]) ).
thf(f1757,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(definition_unfolding,[],[f1613,f1287]) ).
thf(f1613,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1272]) ).
thf(f4611,plain,
spl60_193,
inference(avatar_split_clause,[],[f1691,f4609]) ).
thf(f4609,plain,
( spl60_193
<=> ! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X3),vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_193])]) ).
thf(f1691,plain,
! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X3),vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(definition_unfolding,[],[f1445,f1287]) ).
thf(f1445,plain,
! [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,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1198]) ).
thf(f1198,plain,
! [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,sK16,X0)) ) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK16,X0)) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f944,f1197]) ).
thf(f1197,plain,
! [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) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true ) )
=> ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK16,X0)) ) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK16,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f944,plain,
! [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) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(flattening,[],[f943]) ).
thf(f943,plain,
! [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) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(ennf_transformation,[],[f892]) ).
thf(f892,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
=> ( ! [X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true )
=> ( ( $true != vAPP(nat,$o,X0,X2) )
=> ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) ) ) )
=> ( $true = vAPP(nat,$o,X0,X1) ) ) ),
inference(flattening,[],[f523]) ).
thf(f523,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
=> ( ! [X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true )
=> ( ( $true != vAPP(nat,$o,X0,X2) )
=> ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) ) ) )
=> ( $true = vAPP(nat,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f522]) ).
thf(f522,plain,
! [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) ) ),
inference(rectify,[],[f126]) ).
thf(f126,axiom,
! [X12: nat > $o,X4: nat] :
( vAPP(nat,$o,X12,zero_zero_nat)
=> ( ! [X21: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X21)
=> ( ~ vAPP(nat,$o,X12,X21)
=> ? [X28: nat] :
( ~ vAPP(nat,$o,X12,X28)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X28),X21) ) ) )
=> vAPP(nat,$o,X12,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_infinite__descent0) ).
thf(f4607,plain,
spl60_192,
inference(avatar_split_clause,[],[f1561,f4605]) ).
thf(f4605,plain,
( spl60_192
<=> ! [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)),vAPP(nat,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,vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK41,X0)))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK41,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_192])]) ).
thf(f1561,plain,
! [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)),vAPP(nat,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,vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK41,X0)))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK41,X0))) ) ),
inference(cnf_transformation,[],[f1245]) ).
thf(f1245,plain,
! [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)),vAPP(nat,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,vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK41,X0)))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK41,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f1076,f1244]) ).
thf(f1244,plain,
! [X0: nat > nat] :
( ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,nat,X0,X3)) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK41,X0)))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK41,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1076,plain,
! [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)),vAPP(nat,nat,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,nat,X0,X3)) ) ),
inference(flattening,[],[f1075]) ).
thf(f1075,plain,
! [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)),vAPP(nat,nat,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,nat,X0,X3)) ) ),
inference(ennf_transformation,[],[f711]) ).
thf(f711,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,nat,X0,X3)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X2)),vAPP(nat,nat,X0,X1)) ) ) ),
inference(fool_elimination,[],[f710]) ).
thf(f710,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,nat,X0,X3))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X2)),vAPP(nat,nat,X0,X1)) ) ),
inference(rectify,[],[f132]) ).
thf(f132,axiom,
! [X20: nat > nat,X4: nat,X22: nat] :
( ! [X21: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X20,vAPP(nat,nat,suc,X21))),vAPP(nat,nat,X20,X21))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X22)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X20,X22)),vAPP(nat,nat,X20,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_lift__Suc__antimono__le) ).
thf(f4603,plain,
spl60_191,
inference(avatar_split_clause,[],[f1558,f4601]) ).
thf(f4601,plain,
( spl60_191
<=> ! [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_eq_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK38,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK38,X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_191])]) ).
thf(f1558,plain,
! [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_eq_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK38,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK38,X0)))) ) ),
inference(cnf_transformation,[],[f1239]) ).
thf(f1239,plain,
! [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_eq_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK38,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK38,X0)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f1071,f1238]) ).
thf(f1238,plain,
! [X0: nat > nat] :
( ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK38,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK38,X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f1071,plain,
! [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] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(flattening,[],[f1070]) ).
thf(f1070,plain,
! [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] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(ennf_transformation,[],[f705]) ).
thf(f705,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3))) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ) ),
inference(fool_elimination,[],[f704]) ).
thf(f704,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,vAPP(nat,nat,suc,X3)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ),
inference(rectify,[],[f135]) ).
thf(f135,axiom,
! [X20: nat > nat,X4: nat,X22: nat] :
( ! [X21: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X20,X21)),vAPP(nat,nat,X20,vAPP(nat,nat,suc,X21)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X22)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X20,X4)),vAPP(nat,nat,X20,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_lift__Suc__mono__le) ).
thf(f4599,plain,
spl60_190,
inference(avatar_split_clause,[],[f1557,f4597]) ).
thf(f4597,plain,
( spl60_190
<=> ! [X2: nat,X0: nat > real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X2)),vAPP(nat,real,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK37,X0)))),vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK37,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_190])]) ).
thf(f1557,plain,
! [X2: nat,X0: nat > real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X2)),vAPP(nat,real,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK37,X0)))),vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK37,X0))) ) ),
inference(cnf_transformation,[],[f1237]) ).
thf(f1237,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X2)),vAPP(nat,real,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK37,X0)))),vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK37,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f1069,f1236]) ).
thf(f1236,plain,
! [X0: nat > real] :
( ? [X3: nat] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,real,X0,X3)) )
=> ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK37,X0)))),vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK37,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1069,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X2)),vAPP(nat,real,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,real,X0,X3)) ) ),
inference(flattening,[],[f1068]) ).
thf(f1068,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X2)),vAPP(nat,real,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,real,X0,X3)) ) ),
inference(ennf_transformation,[],[f703]) ).
thf(f703,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,real,X0,X3)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X2)),vAPP(nat,real,X0,X1)) ) ) ),
inference(fool_elimination,[],[f702]) ).
thf(f702,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,real,X0,X3))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X2)),vAPP(nat,real,X0,X1)) ) ),
inference(rectify,[],[f130]) ).
thf(f130,axiom,
! [X20: nat > real,X4: nat,X22: nat] :
( ! [X21: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X20,vAPP(nat,nat,suc,X21))),vAPP(nat,real,X20,X21))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X22)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X20,X22)),vAPP(nat,real,X20,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_lift__Suc__antimono__le) ).
thf(f4595,plain,
spl60_189,
inference(avatar_split_clause,[],[f1556,f4593]) ).
thf(f4593,plain,
( spl60_189
<=> ! [X2: nat,X0: nat > real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK36,X0))),vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK36,X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_189])]) ).
thf(f1556,plain,
! [X2: nat,X0: nat > real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK36,X0))),vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK36,X0)))) ) ),
inference(cnf_transformation,[],[f1235]) ).
thf(f1235,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK36,X0))),vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK36,X0)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f1067,f1234]) ).
thf(f1234,plain,
! [X0: nat > real] :
( ? [X3: nat] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))) )
=> ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,vAPP(sTfun(nat,real),nat,sK36,X0))),vAPP(nat,real,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,real),nat,sK36,X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f1067,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(flattening,[],[f1066]) ).
thf(f1066,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(ennf_transformation,[],[f701]) ).
thf(f701,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3))) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) ) ) ),
inference(fool_elimination,[],[f700]) ).
thf(f700,plain,
! [X0: nat > real,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X3)),vAPP(nat,real,X0,vAPP(nat,nat,suc,X3)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X0,X1)),vAPP(nat,real,X0,X2)) ) ),
inference(rectify,[],[f133]) ).
thf(f133,axiom,
! [X20: nat > real,X4: nat,X22: nat] :
( ! [X21: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X20,X21)),vAPP(nat,real,X20,vAPP(nat,nat,suc,X21)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X22)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,X20,X4)),vAPP(nat,real,X20,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_lift__Suc__mono__le) ).
thf(f4591,plain,
spl60_188,
inference(avatar_split_clause,[],[f1553,f4589]) ).
thf(f4589,plain,
( spl60_188
<=> ! [X2: nat,X0: nat > int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X2)),vAPP(nat,int,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK33,X0)))),vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK33,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_188])]) ).
thf(f1553,plain,
! [X2: nat,X0: nat > int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X2)),vAPP(nat,int,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK33,X0)))),vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK33,X0))) ) ),
inference(cnf_transformation,[],[f1229]) ).
thf(f1229,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X2)),vAPP(nat,int,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK33,X0)))),vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK33,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f1062,f1228]) ).
thf(f1228,plain,
! [X0: nat > int] :
( ? [X3: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,int,X0,X3)) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK33,X0)))),vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK33,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1062,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X2)),vAPP(nat,int,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,int,X0,X3)) ) ),
inference(flattening,[],[f1061]) ).
thf(f1061,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X2)),vAPP(nat,int,X0,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,int,X0,X3)) ) ),
inference(ennf_transformation,[],[f695]) ).
thf(f695,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,int,X0,X3)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X2)),vAPP(nat,int,X0,X1)) ) ) ),
inference(fool_elimination,[],[f694]) ).
thf(f694,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))),vAPP(nat,int,X0,X3))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X2)),vAPP(nat,int,X0,X1)) ) ),
inference(rectify,[],[f131]) ).
thf(f131,axiom,
! [X20: nat > int,X4: nat,X22: nat] :
( ! [X21: nat] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X20,vAPP(nat,nat,suc,X21))),vAPP(nat,int,X20,X21))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X22)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X20,X22)),vAPP(nat,int,X20,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_lift__Suc__antimono__le) ).
thf(f4587,plain,
spl60_187,
inference(avatar_split_clause,[],[f1552,f4585]) ).
thf(f4585,plain,
( spl60_187
<=> ! [X2: nat,X0: nat > int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK32,X0))),vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK32,X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_187])]) ).
thf(f1552,plain,
! [X2: nat,X0: nat > int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK32,X0))),vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK32,X0)))) ) ),
inference(cnf_transformation,[],[f1227]) ).
thf(f1227,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK32,X0))),vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK32,X0)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f1060,f1226]) ).
thf(f1226,plain,
! [X0: nat > int] :
( ? [X3: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,vAPP(sTfun(nat,int),nat,sK32,X0))),vAPP(nat,int,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,int),nat,sK32,X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f1060,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(flattening,[],[f1059]) ).
thf(f1059,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ? [X3: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))) ) ),
inference(ennf_transformation,[],[f693]) ).
thf(f693,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3))) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) ) ) ),
inference(fool_elimination,[],[f692]) ).
thf(f692,plain,
! [X0: nat > int,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X3)),vAPP(nat,int,X0,vAPP(nat,nat,suc,X3)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X0,X1)),vAPP(nat,int,X0,X2)) ) ),
inference(rectify,[],[f134]) ).
thf(f134,axiom,
! [X20: nat > int,X4: nat,X22: nat] :
( ! [X21: nat] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X20,X21)),vAPP(nat,int,X20,vAPP(nat,nat,suc,X21)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X22)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,X20,X4)),vAPP(nat,int,X20,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_lift__Suc__mono__le) ).
thf(f4575,plain,
spl60_186,
inference(avatar_split_clause,[],[f2289,f4573]) ).
thf(f4573,plain,
( spl60_186
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_186])]) ).
thf(f2289,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(trivial_inequality_removal,[],[f2288]) ).
thf(f2288,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(forward_demodulation,[],[f2287,f1374]) ).
thf(f2287,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(trivial_inequality_removal,[],[f2286]) ).
thf(f2286,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(forward_demodulation,[],[f1729,f1374]) ).
thf(f1729,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(definition_unfolding,[],[f1544,f1287]) ).
thf(f1544,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(cnf_transformation,[],[f1047]) ).
thf(f1047,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(flattening,[],[f1046]) ).
thf(f1046,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(ennf_transformation,[],[f679]) ).
thf(f679,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( X0 = X2 ) ) ) ) ),
inference(fool_elimination,[],[f678]) ).
thf(f678,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( X0 = X2 ) ) ) ) ),
inference(rectify,[],[f162]) ).
thf(f162,axiom,
! [X23: nat,X4: nat,X0: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X23),X4) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X4) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X23)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> ( X0 = X23 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_power__eq__imp__eq__base) ).
thf(f4560,plain,
spl60_185,
inference(avatar_split_clause,[],[f1713,f4558]) ).
thf(f1713,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) = X1 )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1506,f1287]) ).
thf(f1506,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK23,X1),X0)) = X1 )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1212]) ).
thf(f4523,plain,
spl60_184,
inference(avatar_split_clause,[],[f1704,f4521]) ).
thf(f4521,plain,
( spl60_184
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_184])]) ).
thf(f1704,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),X0),X1) ) ),
inference(definition_unfolding,[],[f1494,f1285]) ).
thf(f1285,plain,
nthRoo1352626670d_root = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),
inference(cnf_transformation,[],[f327]) ).
thf(f327,plain,
nthRoo1352626670d_root = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),
inference(fool_elimination,[],[f326]) ).
thf(f326,plain,
( nthRoo1352626670d_root
= ( ^ [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ) ),
inference(rectify,[],[f246]) ).
thf(f246,axiom,
( nthRoo1352626670d_root
= ( ^ [X43: nat,X44: nat] : ( vAPP(nat,nat,suc,X44) = X43 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_fixed__root__def) ).
thf(f1494,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) ) ),
inference(cnf_transformation,[],[f1009]) ).
thf(f1009,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) ) ),
inference(ennf_transformation,[],[f603]) ).
thf(f603,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) )
=> ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(fool_elimination,[],[f602]) ).
thf(f602,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1)
=> ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(rectify,[],[f247]) ).
thf(f247,axiom,
! [X37: nat,X42: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X37),X42)
=> ( vAPP(nat,nat,suc,X42) = X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_fixed__root_Op) ).
thf(f4519,plain,
spl60_183,
inference(avatar_split_clause,[],[f1624,f4517]) ).
thf(f4517,plain,
( spl60_183
<=> ! [X2: real,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_183])]) ).
thf(f1624,plain,
! [X2: real,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(cnf_transformation,[],[f1155]) ).
thf(f1155,plain,
! [X0: real,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(flattening,[],[f1154]) ).
thf(f1154,plain,
! [X0: real,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(ennf_transformation,[],[f791]) ).
thf(f791,plain,
! [X0: real,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1))) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X2) ) ) ),
inference(fool_elimination,[],[f790]) ).
thf(f790,plain,
! [X0: real,X1: nat,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X2) ) ),
inference(rectify,[],[f183]) ).
thf(f183,axiom,
! [X23: real,X4: nat,X0: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),vAPP(nat,nat,suc,X4))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X4)))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X23),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_power__le__imp__le__base) ).
thf(f4515,plain,
spl60_182,
inference(avatar_split_clause,[],[f1623,f4513]) ).
thf(f4513,plain,
( spl60_182
<=> ! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_182])]) ).
thf(f1623,plain,
! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(cnf_transformation,[],[f1153]) ).
thf(f1153,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(flattening,[],[f1152]) ).
thf(f1152,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(ennf_transformation,[],[f789]) ).
thf(f789,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1))) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X2) ) ) ),
inference(fool_elimination,[],[f788]) ).
thf(f788,plain,
! [X0: int,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1)))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X2) ) ),
inference(rectify,[],[f184]) ).
thf(f184,axiom,
! [X23: int,X4: nat,X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X23),vAPP(nat,nat,suc,X4))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X4)))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X23),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_power__le__imp__le__base) ).
thf(f4504,plain,
spl60_181,
inference(avatar_split_clause,[],[f1723,f4502]) ).
thf(f1723,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),vAPP(nat,nat,suc,X0)),X1) ) ),
inference(definition_unfolding,[],[f1520,f1287]) ).
thf(f1520,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(cnf_transformation,[],[f1216]) ).
thf(f4500,plain,
( spl60_180
| ~ spl60_113
| ~ spl60_149 ),
inference(avatar_split_clause,[],[f4026,f3992,f3419,f4497]) ).
thf(f4497,plain,
( spl60_180
<=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),pm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_180])]) ).
thf(f3992,plain,
( spl60_149
<=> ! [X0: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_149])]) ).
thf(f4026,plain,
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),pm) )
| ~ spl60_113
| ~ spl60_149 ),
inference(trivial_inequality_removal,[],[f4019]) ).
thf(f4019,plain,
( ( $true != $true )
| ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),pm) )
| ~ spl60_113
| ~ spl60_149 ),
inference(superposition,[],[f3993,f3421]) ).
thf(f3993,plain,
( ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) )
| ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) ) )
| ~ spl60_149 ),
inference(avatar_component_clause,[],[f3992]) ).
thf(f4447,plain,
spl60_179,
inference(avatar_split_clause,[],[f1772,f4445]) ).
thf(f1772,plain,
! [X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),vAPP(nat,nat,suc,X1)),X1) ),
inference(equality_resolution,[],[f1685]) ).
thf(f1685,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),X0),X1) )
| ( vAPP(nat,nat,suc,X1) != X0 ) ),
inference(definition_unfolding,[],[f1427,f1285]) ).
thf(f1427,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) )
| ( vAPP(nat,nat,suc,X1) != X0 ) ),
inference(cnf_transformation,[],[f930]) ).
thf(f930,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) )
| ( vAPP(nat,nat,suc,X1) != X0 ) ),
inference(ennf_transformation,[],[f505]) ).
thf(f505,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) ) ),
inference(fool_elimination,[],[f504]) ).
thf(f504,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) ),
inference(rectify,[],[f245]) ).
thf(f245,axiom,
! [X37: nat,X42: nat] :
( ( vAPP(nat,nat,suc,X42) = X37 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X37),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_fixed__root_Ointro) ).
thf(f4443,plain,
spl60_178,
inference(avatar_split_clause,[],[f1692,f4441]) ).
thf(f4441,plain,
( spl60_178
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_178])]) ).
thf(f1692,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(definition_unfolding,[],[f1443,f1287]) ).
thf(f1443,plain,
! [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,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1198]) ).
thf(f4439,plain,
spl60_177,
inference(avatar_split_clause,[],[f1690,f4437]) ).
thf(f4437,plain,
( spl60_177
<=> ! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X3),vAPP(sTfun(nat,$o),nat,sK12,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_177])]) ).
thf(f1690,plain,
! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X3),vAPP(sTfun(nat,$o),nat,sK12,X0)) ) ),
inference(definition_unfolding,[],[f1435,f1287]) ).
thf(f1435,plain,
! [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,sK12,X0)) ) ),
inference(cnf_transformation,[],[f1190]) ).
thf(f1190,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK12,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,sK12,X0)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f937,f1189]) ).
thf(f1189,plain,
! [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,sK12,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,sK12,X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f937,plain,
! [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) ) ) ) ),
inference(ennf_transformation,[],[f515]) ).
thf(f515,plain,
! [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) ) ),
inference(fool_elimination,[],[f514]) ).
thf(f514,plain,
! [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) ),
inference(rectify,[],[f124]) ).
thf(f124,axiom,
! [X12: nat > $o,X4: nat] :
( ! [X21: nat] :
( ! [X28: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X28),X21)
=> vAPP(nat,$o,X12,X28) )
=> vAPP(nat,$o,X12,X21) )
=> vAPP(nat,$o,X12,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_nat__less__induct) ).
thf(f4435,plain,
spl60_176,
inference(avatar_split_clause,[],[f1689,f4433]) ).
thf(f4433,plain,
( spl60_176
<=> ! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X3),vAPP(sTfun(nat,$o),nat,sK11,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_176])]) ).
thf(f1689,plain,
! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X3),vAPP(sTfun(nat,$o),nat,sK11,X0)) ) ),
inference(definition_unfolding,[],[f1434,f1287]) ).
thf(f1434,plain,
! [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,sK11,X0)) ) ),
inference(cnf_transformation,[],[f1188]) ).
thf(f1188,plain,
! [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,sK11,X0)) ) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f936,f1187]) ).
thf(f1187,plain,
! [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,sK11,X0)) ) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f936,plain,
! [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) ) ) ),
inference(ennf_transformation,[],[f891]) ).
thf(f891,plain,
! [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) ) ),
inference(flattening,[],[f513]) ).
thf(f513,plain,
! [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) ) ),
inference(fool_elimination,[],[f512]) ).
thf(f512,plain,
! [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) ),
inference(rectify,[],[f125]) ).
thf(f125,axiom,
! [X12: nat > $o,X4: nat] :
( ! [X21: nat] :
( ~ vAPP(nat,$o,X12,X21)
=> ? [X28: nat] :
( ~ vAPP(nat,$o,X12,X28)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X28),X21) ) )
=> vAPP(nat,$o,X12,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_infinite__descent) ).
thf(f4412,plain,
( spl60_175
| ~ spl60_113
| ~ spl60_148 ),
inference(avatar_split_clause,[],[f4018,f3988,f3419,f4409]) ).
thf(f4409,plain,
( spl60_175
<=> ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),pm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_175])]) ).
thf(f3988,plain,
( spl60_148
<=> ! [X0: nat] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_148])]) ).
thf(f4018,plain,
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),pm) )
| ~ spl60_113
| ~ spl60_148 ),
inference(trivial_inequality_removal,[],[f4011]) ).
thf(f4011,plain,
( ( $true != $true )
| ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),pm) )
| ~ spl60_113
| ~ spl60_148 ),
inference(superposition,[],[f3989,f3421]) ).
thf(f3989,plain,
( ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) )
| ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) ) )
| ~ spl60_148 ),
inference(avatar_component_clause,[],[f3988]) ).
thf(f4393,plain,
spl60_174,
inference(avatar_split_clause,[],[f1722,f4391]) ).
thf(f4391,plain,
( spl60_174
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_174])]) ).
thf(f1722,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(definition_unfolding,[],[f1518,f1287]) ).
thf(f1518,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(cnf_transformation,[],[f1038]) ).
thf(f1038,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(ennf_transformation,[],[f649]) ).
thf(f649,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(fool_elimination,[],[f648]) ).
thf(f648,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
inference(rectify,[],[f254]) ).
thf(f254,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X9)),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Suc__le__lessD) ).
thf(f4389,plain,
spl60_173,
inference(avatar_split_clause,[],[f1718,f4387]) ).
thf(f1718,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1510,f1287]) ).
thf(f1510,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1028]) ).
thf(f1028,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f633]) ).
thf(f633,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(fool_elimination,[],[f632]) ).
thf(f632,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ),
inference(rectify,[],[f250]) ).
thf(f250,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X9)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_Suc__leI) ).
thf(f4385,plain,
spl60_172,
inference(avatar_split_clause,[],[f1707,f4383]) ).
thf(f4383,plain,
( spl60_172
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_172])]) ).
thf(f1707,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(definition_unfolding,[],[f1499,f1287]) ).
thf(f1499,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1016]) ).
thf(f1016,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f613]) ).
thf(f613,plain,
! [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,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) ) ),
inference(fool_elimination,[],[f612]) ).
thf(f612,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f258]) ).
thf(f258,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),vAPP(nat,nat,suc,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_le__imp__less__Suc) ).
thf(f4319,plain,
( spl60_171
| ~ spl60_113
| ~ spl60_147 ),
inference(avatar_split_clause,[],[f4010,f3984,f3419,f4316]) ).
thf(f4316,plain,
( spl60_171
<=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),pm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_171])]) ).
thf(f3984,plain,
( spl60_147
<=> ! [X0: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_147])]) ).
thf(f4010,plain,
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),pm) )
| ~ spl60_113
| ~ spl60_147 ),
inference(trivial_inequality_removal,[],[f4003]) ).
thf(f4003,plain,
( ( $true != $true )
| ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),pm) )
| ~ spl60_113
| ~ spl60_147 ),
inference(superposition,[],[f3985,f3421]) ).
thf(f3985,plain,
( ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) )
| ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) ) )
| ~ spl60_147 ),
inference(avatar_component_clause,[],[f3984]) ).
thf(f4303,plain,
spl60_170,
inference(avatar_split_clause,[],[f1775,f4301]) ).
thf(f1775,plain,
! [X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),zero_zero_nat),X1) ),
inference(equality_resolution,[],[f1703]) ).
thf(f1703,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat)),suc)),X0),X1) ) ),
inference(definition_unfolding,[],[f1493,f1285]) ).
thf(f1493,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) ) ),
inference(cnf_transformation,[],[f1008]) ).
thf(f1008,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) ) ),
inference(ennf_transformation,[],[f601]) ).
thf(f601,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1) )
=> ( zero_zero_nat != X0 ) ),
inference(fool_elimination,[],[f600]) ).
thf(f600,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X0),X1)
=> ( zero_zero_nat != X0 ) ),
inference(rectify,[],[f244]) ).
thf(f244,axiom,
! [X37: nat,X42: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),nthRoo1352626670d_root,X37),X42)
=> ( zero_zero_nat != X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_fixed__root_Op0) ).
thf(f4299,plain,
spl60_169,
inference(avatar_split_clause,[],[f1706,f4297]) ).
thf(f4297,plain,
( spl60_169
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_169])]) ).
thf(f1706,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(definition_unfolding,[],[f1496,f1287]) ).
thf(f1496,plain,
! [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) ) ),
inference(cnf_transformation,[],[f1012]) ).
thf(f1012,plain,
! [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) ) ),
inference(flattening,[],[f1011]) ).
thf(f1011,plain,
! [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) ) ),
inference(ennf_transformation,[],[f607]) ).
thf(f607,plain,
! [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,$o),ord_less_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f606]) ).
thf(f606,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( ( X0 != X1 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f239]) ).
thf(f239,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4)
=> ( ( X4 != X9 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_le__neq__implies__less) ).
thf(f4295,plain,
spl60_168,
inference(avatar_split_clause,[],[f1600,f4293]) ).
thf(f4293,plain,
( spl60_168
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_168])]) ).
thf(f1600,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1262]) ).
thf(f4291,plain,
spl60_167,
inference(avatar_split_clause,[],[f1596,f4289]) ).
thf(f4289,plain,
( spl60_167
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_167])]) ).
thf(f1596,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1260]) ).
thf(f4287,plain,
spl60_166,
inference(avatar_split_clause,[],[f1567,f4285]) ).
thf(f4285,plain,
( spl60_166
<=> ! [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,sK44,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),sK45,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_166])]) ).
thf(f1567,plain,
! [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,sK44,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),sK45,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1251]) ).
thf(f1251,plain,
! [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,sK44,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) ) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK44,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),sK45,X2),X0)),X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK45,X2),X0)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45])],[f1248,f1250,f1249]) ).
thf(f1249,plain,
! [X0: nat > $o] :
( ? [X3: nat] :
( ! [X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
| ( $true != vAPP(nat,$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,sK44,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) ) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK44,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1250,plain,
! [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),sK45,X2),X0)),X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK45,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1248,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ? [X3: nat] :
( ! [X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
| ( $true != vAPP(nat,$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) ) ),
inference(rectify,[],[f1080]) ).
thf(f1080,plain,
! [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) ) ),
inference(flattening,[],[f1079]) ).
thf(f1079,plain,
! [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) ) ),
inference(ennf_transformation,[],[f715]) ).
thf(f715,plain,
! [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) ) ) ) ),
inference(fool_elimination,[],[f714]) ).
thf(f714,plain,
! [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) ) ) ),
inference(rectify,[],[f223]) ).
thf(f223,axiom,
! [X12: nat > $o,X16: nat,X0: nat] :
( vAPP(nat,$o,X12,X16)
=> ( ! [X31: nat] :
( vAPP(nat,$o,X12,X31)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X31),X0) )
=> ? [X30: nat] :
( ! [X36: nat] :
( vAPP(nat,$o,X12,X36)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X36),X30) )
& vAPP(nat,$o,X12,X30) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Nat_Oex__has__greatest__nat) ).
thf(f4283,plain,
spl60_165,
inference(avatar_split_clause,[],[f1546,f4281]) ).
thf(f4281,plain,
( spl60_165
<=> ! [X2: real,X0: real,X1: nat] :
( ( X0 = X2 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_165])]) ).
thf(f1546,plain,
! [X2: real,X0: real,X1: nat] :
( ( X0 = X2 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1)) ) ),
inference(cnf_transformation,[],[f1051]) ).
thf(f1051,plain,
! [X0: real,X1: nat,X2: real] :
( ( X0 = X2 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1)) ) ),
inference(flattening,[],[f1050]) ).
thf(f1050,plain,
! [X0: real,X1: nat,X2: real] :
( ( X0 = X2 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1)) ) ),
inference(ennf_transformation,[],[f683]) ).
thf(f683,plain,
! [X0: real,X1: nat,X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1)) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) = $true )
=> ( X0 = X2 ) ) ) ),
inference(fool_elimination,[],[f682]) ).
thf(f682,plain,
! [X0: real,X1: nat,X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X1)) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f180]) ).
thf(f180,axiom,
! [X23: real,X4: nat,X0: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),vAPP(nat,nat,suc,X4)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,X4)) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X23)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( X0 = X23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_power__inject__base) ).
thf(f4279,plain,
spl60_164,
inference(avatar_split_clause,[],[f1545,f4277]) ).
thf(f4277,plain,
( spl60_164
<=> ! [X2: int,X0: int,X1: nat] :
( ( X0 = X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_164])]) ).
thf(f1545,plain,
! [X2: int,X0: int,X1: nat] :
( ( X0 = X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(cnf_transformation,[],[f1049]) ).
thf(f1049,plain,
! [X0: int,X1: nat,X2: int] :
( ( X0 = X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(flattening,[],[f1048]) ).
thf(f1048,plain,
! [X0: int,X1: nat,X2: int] :
( ( X0 = X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(ennf_transformation,[],[f681]) ).
thf(f681,plain,
! [X0: int,X1: nat,X2: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1)) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( X0 = X2 ) ) ) ),
inference(fool_elimination,[],[f680]) ).
thf(f680,plain,
! [X0: int,X1: nat,X2: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X1)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(nat,nat,suc,X1)) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f181]) ).
thf(f181,axiom,
! [X23: int,X4: nat,X0: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X23),vAPP(nat,nat,suc,X4)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,X4)) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X23)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( X0 = X23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_power__inject__base) ).
thf(f4136,plain,
spl60_163,
inference(avatar_split_clause,[],[f1621,f4134]) ).
thf(f4134,plain,
( spl60_163
<=> ! [X2: real,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_163])]) ).
thf(f1621,plain,
! [X2: real,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(cnf_transformation,[],[f1149]) ).
thf(f1149,plain,
! [X0: real,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(flattening,[],[f1148]) ).
thf(f1148,plain,
! [X0: real,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(ennf_transformation,[],[f785]) ).
thf(f785,plain,
! [X0: real,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) ) ) ),
inference(fool_elimination,[],[f784]) ).
thf(f784,plain,
! [X0: real,X1: nat,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) ) ),
inference(rectify,[],[f174]) ).
thf(f174,axiom,
! [X23: real,X4: nat,X0: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),X4)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X4))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X23),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_power__less__imp__less__base) ).
thf(f4132,plain,
spl60_162,
inference(avatar_split_clause,[],[f1620,f4130]) ).
thf(f4130,plain,
( spl60_162
<=> ! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_162])]) ).
thf(f1620,plain,
! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(cnf_transformation,[],[f1147]) ).
thf(f1147,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(flattening,[],[f1146]) ).
thf(f1146,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(ennf_transformation,[],[f783]) ).
thf(f783,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) ) ) ),
inference(fool_elimination,[],[f782]) ).
thf(f782,plain,
! [X0: int,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) ) ),
inference(rectify,[],[f175]) ).
thf(f175,axiom,
! [X23: int,X4: nat,X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X23),X4)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X4))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X23),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_power__less__imp__less__base) ).
thf(f4128,plain,
spl60_161,
inference(avatar_split_clause,[],[f1589,f4126]) ).
thf(f4126,plain,
( spl60_161
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_161])]) ).
thf(f1589,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1124]) ).
thf(f1124,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(flattening,[],[f1123]) ).
thf(f1123,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(ennf_transformation,[],[f759]) ).
thf(f759,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) ) ) ),
inference(fool_elimination,[],[f758]) ).
thf(f758,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) ) ),
inference(rectify,[],[f262]) ).
thf(f262,axiom,
! [X23: real,X0: real,X38: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X23),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X38),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X38)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X23),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_divide__right__mono__neg) ).
thf(f4124,plain,
( ~ spl60_160
| ~ spl60_8
| ~ spl60_146 ),
inference(avatar_split_clause,[],[f4043,f3979,f2378,f4121]) ).
thf(f4121,plain,
( spl60_160
<=> ( pm = vAPP(nat,nat,sK5,pm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_160])]) ).
thf(f4043,plain,
( ( pm != vAPP(nat,nat,sK5,pm) )
| ~ spl60_8
| ~ spl60_146 ),
inference(superposition,[],[f2379,f3981]) ).
thf(f4119,plain,
spl60_159,
inference(avatar_split_clause,[],[f1588,f4117]) ).
thf(f4117,plain,
( spl60_159
<=> ! [X2: nat,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_159])]) ).
thf(f1588,plain,
! [X2: nat,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1122]) ).
thf(f1122,plain,
! [X0: real,X1: real,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(flattening,[],[f1121]) ).
thf(f1121,plain,
! [X0: real,X1: real,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(ennf_transformation,[],[f757]) ).
thf(f757,plain,
! [X0: real,X1: real,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) ) ) ),
inference(fool_elimination,[],[f756]) ).
thf(f756,plain,
! [X0: real,X1: real,X2: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) ) ),
inference(rectify,[],[f169]) ).
thf(f169,axiom,
! [X23: real,X0: real,X4: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X23),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X23)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),X4)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_power__mono) ).
thf(f4115,plain,
spl60_158,
inference(avatar_split_clause,[],[f1587,f4113]) ).
thf(f4113,plain,
( spl60_158
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_158])]) ).
thf(f1587,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1120]) ).
thf(f1120,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(flattening,[],[f1119]) ).
thf(f1119,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(ennf_transformation,[],[f755]) ).
thf(f755,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) ) ) ),
inference(fool_elimination,[],[f754]) ).
thf(f754,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) ) ),
inference(rectify,[],[f268]) ).
thf(f268,axiom,
! [X23: real,X0: real,X38: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X23),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X38)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X23),X38)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_divide__right__mono) ).
thf(f4111,plain,
spl60_157,
inference(avatar_split_clause,[],[f1586,f4109]) ).
thf(f4109,plain,
( spl60_157
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_157])]) ).
thf(f1586,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1118]) ).
thf(f1118,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(flattening,[],[f1117]) ).
thf(f1117,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f753]) ).
thf(f753,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) ) ) ),
inference(fool_elimination,[],[f752]) ).
thf(f752,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)) ) ),
inference(rectify,[],[f278]) ).
thf(f278,axiom,
! [X0: real,X23: real,X38: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X23)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X38),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X23),X38)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_divide__strict__right__mono__neg) ).
thf(f4107,plain,
spl60_156,
inference(avatar_split_clause,[],[f1584,f4105]) ).
thf(f4105,plain,
( spl60_156
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_156])]) ).
thf(f1584,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1114]) ).
thf(f1114,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(flattening,[],[f1113]) ).
thf(f1113,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f749]) ).
thf(f749,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) ) ) ),
inference(fool_elimination,[],[f748]) ).
thf(f748,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X1),X2)) ) ),
inference(rectify,[],[f277]) ).
thf(f277,axiom,
! [X23: real,X0: real,X38: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X23),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X38)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X23),X38)),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_divide__strict__right__mono) ).
thf(f4103,plain,
spl60_155,
inference(avatar_split_clause,[],[f1583,f4101]) ).
thf(f1583,plain,
! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(cnf_transformation,[],[f1112]) ).
thf(f1112,plain,
! [X0: int,X1: int,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(flattening,[],[f1111]) ).
thf(f1111,plain,
! [X0: int,X1: int,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(ennf_transformation,[],[f747]) ).
thf(f747,plain,
! [X0: int,X1: int,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) ) ),
inference(fool_elimination,[],[f746]) ).
thf(f746,plain,
! [X0: int,X1: int,X2: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) ),
inference(rectify,[],[f170]) ).
thf(f170,axiom,
! [X23: int,X0: int,X4: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X23),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X23)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X23),X4)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_power__mono) ).
thf(f4099,plain,
spl60_154,
inference(avatar_split_clause,[],[f1582,f4097]) ).
thf(f4097,plain,
( spl60_154
<=> ! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_154])]) ).
thf(f1582,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(cnf_transformation,[],[f1110]) ).
thf(f1110,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(flattening,[],[f1109]) ).
thf(f1109,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(ennf_transformation,[],[f745]) ).
thf(f745,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X2)) ) ) ),
inference(fool_elimination,[],[f744]) ).
thf(f744,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X2)) ) ),
inference(rectify,[],[f306]) ).
thf(f306,axiom,
! [X23: int,X49: int,X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X23),X49)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X23),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X49),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_zdiv__mono1) ).
thf(f4065,plain,
spl60_153,
inference(avatar_split_clause,[],[f1602,f4063]) ).
thf(f4063,plain,
( spl60_153
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0))) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_153])]) ).
thf(f1602,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0))) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1262]) ).
thf(f4061,plain,
spl60_152,
inference(avatar_split_clause,[],[f1599,f4059]) ).
thf(f4059,plain,
( spl60_152
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0))) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_152])]) ).
thf(f1599,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0))) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1260]) ).
thf(f4002,plain,
spl60_151,
inference(avatar_split_clause,[],[f2269,f4000]) ).
thf(f2269,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(trivial_inequality_removal,[],[f2268]) ).
thf(f2268,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(forward_demodulation,[],[f1695,f1374]) ).
thf(f1695,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true ) ),
inference(definition_unfolding,[],[f1484,f1287]) ).
thf(f1484,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f999]) ).
thf(f999,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f998]) ).
thf(f998,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f589]) ).
thf(f589,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f588]) ).
thf(f588,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) ) ) ),
inference(rectify,[],[f314]) ).
thf(f314,axiom,
! [X23: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X23)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X23),X0)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X23),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_unique__euclidean__semiring__numeral__class_Odiv__less) ).
thf(f3998,plain,
spl60_150,
inference(avatar_split_clause,[],[f1686,f3996]) ).
thf(f3996,plain,
( spl60_150
<=> ! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_150])]) ).
thf(f1686,plain,
! [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,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X1) ) ),
inference(definition_unfolding,[],[f1429,f1287]) ).
thf(f1429,plain,
! [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) ) ),
inference(cnf_transformation,[],[f932]) ).
thf(f932,plain,
! [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) ) ) ),
inference(ennf_transformation,[],[f507]) ).
thf(f507,plain,
! [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,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f506]) ).
thf(f506,plain,
! [X0: nat,X1: nat] :
( ( ( X0 = X1 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f240]) ).
thf(f240,axiom,
! [X9: nat,X4: nat] :
( ( ( X4 = X9 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X4) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_less__or__eq__imp__le) ).
thf(f3994,plain,
spl60_149,
inference(avatar_split_clause,[],[f1655,f3992]) ).
thf(f1655,plain,
! [X0: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1358,f1287]) ).
thf(f1358,plain,
! [X0: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f916]) ).
thf(f916,plain,
! [X0: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f395]) ).
thf(f395,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) ) ),
inference(fool_elimination,[],[f394]) ).
thf(f394,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) ) ),
inference(rectify,[],[f200]) ).
thf(f200,axiom,
! [X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_zero__power) ).
thf(f3990,plain,
spl60_148,
inference(avatar_split_clause,[],[f1654,f3988]) ).
thf(f1654,plain,
! [X0: nat] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1357,f1287]) ).
thf(f1357,plain,
! [X0: nat] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f915]) ).
thf(f915,plain,
! [X0: nat] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f393]) ).
thf(f393,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) ) ),
inference(fool_elimination,[],[f392]) ).
thf(f392,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) ) ),
inference(rectify,[],[f198]) ).
thf(f198,axiom,
! [X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_zero__power) ).
thf(f3986,plain,
spl60_147,
inference(avatar_split_clause,[],[f1653,f3984]) ).
thf(f1653,plain,
! [X0: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1356,f1287]) ).
thf(f1356,plain,
! [X0: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f914]) ).
thf(f914,plain,
! [X0: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f391]) ).
thf(f391,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) ) ),
inference(fool_elimination,[],[f390]) ).
thf(f390,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) ) ),
inference(rectify,[],[f199]) ).
thf(f199,axiom,
! [X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_zero__power) ).
thf(f3982,plain,
( spl60_146
| ~ spl60_113
| ~ spl60_145 ),
inference(avatar_split_clause,[],[f3977,f3967,f3419,f3979]) ).
thf(f3977,plain,
( ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,sK5,pm)) )
| ~ spl60_113
| ~ spl60_145 ),
inference(trivial_inequality_removal,[],[f3970]) ).
thf(f3970,plain,
( ( $true != $true )
| ( pm = vAPP(nat,nat,suc,vAPP(nat,nat,sK5,pm)) )
| ~ spl60_113
| ~ spl60_145 ),
inference(superposition,[],[f3968,f3421]) ).
thf(f3969,plain,
spl60_145,
inference(avatar_split_clause,[],[f1656,f3967]) ).
thf(f1656,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),X0) ) ),
inference(definition_unfolding,[],[f1359,f1287]) ).
thf(f1359,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f1176]) ).
thf(f1176,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f917,f1175]) ).
thf(f1175,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK5,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f917,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f397]) ).
thf(f397,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(fool_elimination,[],[f396]) ).
thf(f396,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(rectify,[],[f156]) ).
thf(f156,axiom,
! [X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X4)
=> ? [X33: nat] : ( vAPP(nat,nat,suc,X33) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_gr0__implies__Suc) ).
thf(f3891,plain,
spl60_144,
inference(avatar_split_clause,[],[f2313,f3889]) ).
thf(f3889,plain,
( spl60_144
<=> ! [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,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_144])]) ).
thf(f2313,plain,
! [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,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(trivial_inequality_removal,[],[f2312]) ).
thf(f2312,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$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,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(forward_demodulation,[],[f1625,f1374]) ).
thf(f1625,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(cnf_transformation,[],[f1157]) ).
thf(f1157,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(flattening,[],[f1156]) ).
thf(f1156,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1))) ) ),
inference(ennf_transformation,[],[f793]) ).
thf(f793,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1))) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f792]) ).
thf(f792,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
inference(rectify,[],[f185]) ).
thf(f185,axiom,
! [X23: nat,X4: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X23),vAPP(nat,nat,suc,X4))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X4)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X23),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_power__le__imp__le__base) ).
thf(f3887,plain,
spl60_143,
inference(avatar_split_clause,[],[f1603,f3885]) ).
thf(f3885,plain,
( spl60_143
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_143])]) ).
thf(f1603,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK53,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1262]) ).
thf(f3883,plain,
spl60_142,
inference(avatar_split_clause,[],[f1598,f3881]) ).
thf(f3881,plain,
( spl60_142
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_142])]) ).
thf(f1598,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK52,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1260]) ).
thf(f3879,plain,
spl60_141,
inference(avatar_split_clause,[],[f1566,f3877]) ).
thf(f3877,plain,
( spl60_141
<=> ! [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,sK44,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK45,X2),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_141])]) ).
thf(f1566,plain,
! [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,sK44,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK45,X2),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1251]) ).
thf(f3875,plain,
spl60_140,
inference(avatar_split_clause,[],[f2140,f3873]) ).
thf(f2140,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,suc,X1) != vAPP(nat,nat,suc,X0) ) ),
inference(equality_proxy_clausification,[],[f2139]) ).
thf(f2139,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)) ) ),
inference(equality_proxy_clausification,[],[f2135]) ).
thf(f2135,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)) ) ),
inference(binary_proxy_clausification,[],[f1394]) ).
thf(f1394,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)) ),
inference(cnf_transformation,[],[f447]) ).
thf(f447,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)) ),
inference(fool_elimination,[],[f446]) ).
thf(f446,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = vAPP(nat,nat,suc,X0) )
= ( X0 = X1 ) ),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
! [X5: nat,X6: nat] :
( ( vAPP(nat,nat,suc,X5) = vAPP(nat,nat,suc,X6) )
= ( X5 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nat_Oinject) ).
thf(f3859,plain,
spl60_139,
inference(avatar_split_clause,[],[f1533,f3857]) ).
thf(f3857,plain,
( spl60_139
<=> ! [X2: nat,X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_139])]) ).
thf(f1533,plain,
! [X2: nat,X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) ),
inference(cnf_transformation,[],[f901]) ).
thf(f901,plain,
! [X0: real,X1: real,X2: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) ),
inference(rectify,[],[f137]) ).
thf(f137,axiom,
! [X23: real,X0: real,X4: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X23),X0)),X4) = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),X4)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_power__divide) ).
thf(f3840,plain,
spl60_138,
inference(avatar_split_clause,[],[f1593,f3838]) ).
thf(f3838,plain,
( spl60_138
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0)) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_138])]) ).
thf(f1593,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0)) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1258]) ).
thf(f1258,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0))) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0)) ) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f1128,f1257]) ).
thf(f1257,plain,
! [X0: nat,X2: nat > $o] :
( ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
& ( $true = vAPP(nat,$o,X2,X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
=> ( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0))) )
& ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1128,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
& ( $true = vAPP(nat,$o,X2,X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1127]) ).
thf(f1127,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) )
& ( $true = vAPP(nat,$o,X2,X3) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f763]) ).
thf(f763,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,X2,X0) )
=> ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) )
=> ( ( $true = vAPP(nat,$o,X2,X3) )
=> ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) ) ) )
=> ( $true = vAPP(nat,$o,X2,X1) ) ) ) ),
inference(fool_elimination,[],[f762]) ).
thf(f762,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,X2,X0)
=> ( ! [X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3)
=> ( vAPP(nat,$o,X2,X3)
=> vAPP(nat,$o,X2,vAPP(nat,nat,suc,X3)) ) )
=> vAPP(nat,$o,X2,X1) ) ) ),
inference(rectify,[],[f229]) ).
thf(f229,axiom,
! [X9: nat,X4: nat,X12: nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4)
=> ( vAPP(nat,$o,X12,X9)
=> ( ! [X21: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X21)
=> ( vAPP(nat,$o,X12,X21)
=> vAPP(nat,$o,X12,vAPP(nat,nat,suc,X21)) ) )
=> vAPP(nat,$o,X12,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_nat__induct__at__least) ).
thf(f3821,plain,
spl60_137,
inference(avatar_split_clause,[],[f1595,f3819]) ).
thf(f3819,plain,
( spl60_137
<=> ! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0))) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_137])]) ).
thf(f1595,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true != vAPP(nat,$o,X2,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0))) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1258]) ).
thf(f3790,plain,
spl60_136,
inference(avatar_split_clause,[],[f2138,f3788]) ).
thf(f3788,plain,
( spl60_136
<=> ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,nat,suc,X1) = vAPP(nat,nat,suc,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_136])]) ).
thf(f2138,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,nat,suc,X1) = vAPP(nat,nat,suc,X0) ) ),
inference(equality_proxy_clausification,[],[f2137]) ).
thf(f2137,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)) ) ),
inference(equality_proxy_clausification,[],[f2136]) ).
thf(f2136,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)) ) ),
inference(binary_proxy_clausification,[],[f1394]) ).
thf(f3677,plain,
spl60_135,
inference(avatar_split_clause,[],[f1483,f3675]) ).
thf(f3675,plain,
( spl60_135
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_135])]) ).
thf(f1483,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(cnf_transformation,[],[f997]) ).
thf(f997,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(flattening,[],[f996]) ).
thf(f996,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(ennf_transformation,[],[f587]) ).
thf(f587,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ) ),
inference(fool_elimination,[],[f586]) ).
thf(f586,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ),
inference(rectify,[],[f263]) ).
thf(f263,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X19),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_divide__nonpos__nonpos) ).
thf(f3673,plain,
spl60_134,
inference(avatar_split_clause,[],[f1482,f3671]) ).
thf(f3671,plain,
( spl60_134
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_134])]) ).
thf(f1482,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(cnf_transformation,[],[f995]) ).
thf(f995,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(flattening,[],[f994]) ).
thf(f994,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(ennf_transformation,[],[f585]) ).
thf(f585,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ) ),
inference(fool_elimination,[],[f584]) ).
thf(f584,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ),
inference(rectify,[],[f285]) ).
thf(f285,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X19),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_divide__nonpos__neg) ).
thf(f3669,plain,
spl60_133,
inference(avatar_split_clause,[],[f1481,f3667]) ).
thf(f3667,plain,
( spl60_133
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_133])]) ).
thf(f1481,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(cnf_transformation,[],[f993]) ).
thf(f993,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(flattening,[],[f992]) ).
thf(f992,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(ennf_transformation,[],[f583]) ).
thf(f583,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ) ),
inference(fool_elimination,[],[f582]) ).
thf(f582,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ),
inference(rectify,[],[f264]) ).
thf(f264,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X19)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)),zero_zero_real) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_divide__nonpos__nonneg) ).
thf(f3665,plain,
spl60_132,
inference(avatar_split_clause,[],[f1480,f3663]) ).
thf(f3663,plain,
( spl60_132
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_132])]) ).
thf(f1480,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(cnf_transformation,[],[f991]) ).
thf(f991,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(flattening,[],[f990]) ).
thf(f990,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) != $true ) ),
inference(ennf_transformation,[],[f581]) ).
thf(f581,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) = $true )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ) ),
inference(fool_elimination,[],[f580]) ).
thf(f580,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ),
inference(rectify,[],[f286]) ).
thf(f286,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X19)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)),zero_zero_real) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_divide__nonpos__pos) ).
thf(f3661,plain,
spl60_131,
inference(avatar_split_clause,[],[f1479,f3659]) ).
thf(f3659,plain,
( spl60_131
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_131])]) ).
thf(f1479,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) != $true ) ),
inference(cnf_transformation,[],[f989]) ).
thf(f989,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) != $true ) ),
inference(flattening,[],[f988]) ).
thf(f988,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) != $true ) ),
inference(ennf_transformation,[],[f579]) ).
thf(f579,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ) ),
inference(fool_elimination,[],[f578]) ).
thf(f578,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ),
inference(rectify,[],[f270]) ).
thf(f270,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X19),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_divide__neg__neg) ).
thf(f3657,plain,
spl60_130,
inference(avatar_split_clause,[],[f1478,f3655]) ).
thf(f3655,plain,
( spl60_130
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_130])]) ).
thf(f1478,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) != $true ) ),
inference(cnf_transformation,[],[f987]) ).
thf(f987,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) != $true ) ),
inference(flattening,[],[f986]) ).
thf(f986,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) != $true ) ),
inference(ennf_transformation,[],[f577]) ).
thf(f577,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = $true )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ) ),
inference(fool_elimination,[],[f576]) ).
thf(f576,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ),
inference(rectify,[],[f271]) ).
thf(f271,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X19)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)),zero_zero_real) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_divide__neg__pos) ).
thf(f3653,plain,
spl60_129,
inference(avatar_split_clause,[],[f1476,f3651]) ).
thf(f3651,plain,
( spl60_129
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_129])]) ).
thf(f1476,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f984]) ).
thf(f984,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(flattening,[],[f983]) ).
thf(f983,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f573]) ).
thf(f573,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ) ),
inference(fool_elimination,[],[f572]) ).
thf(f572,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ),
inference(rectify,[],[f265]) ).
thf(f265,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X19),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)),zero_zero_real) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_divide__nonneg__nonpos) ).
thf(f3649,plain,
spl60_128,
inference(avatar_split_clause,[],[f1475,f3647]) ).
thf(f3647,plain,
( spl60_128
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_128])]) ).
thf(f1475,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f982]) ).
thf(f982,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(flattening,[],[f981]) ).
thf(f981,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f571]) ).
thf(f571,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ) ),
inference(fool_elimination,[],[f570]) ).
thf(f570,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ),
inference(rectify,[],[f283]) ).
thf(f283,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X19),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)),zero_zero_real) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_divide__nonneg__neg) ).
thf(f3645,plain,
spl60_127,
inference(avatar_split_clause,[],[f1474,f3643]) ).
thf(f3643,plain,
( spl60_127
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_127])]) ).
thf(f1474,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f980]) ).
thf(f980,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(flattening,[],[f979]) ).
thf(f979,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f569]) ).
thf(f569,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ) ),
inference(fool_elimination,[],[f568]) ).
thf(f568,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ),
inference(rectify,[],[f266]) ).
thf(f266,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X19)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_divide__nonneg__nonneg) ).
thf(f3630,plain,
spl60_126,
inference(avatar_split_clause,[],[f1473,f3628]) ).
thf(f3628,plain,
( spl60_126
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_126])]) ).
thf(f1473,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f978]) ).
thf(f978,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(flattening,[],[f977]) ).
thf(f977,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f567]) ).
thf(f567,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ) ),
inference(fool_elimination,[],[f566]) ).
thf(f566,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ),
inference(rectify,[],[f284]) ).
thf(f284,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X19)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_divide__nonneg__pos) ).
thf(f3626,plain,
spl60_125,
inference(avatar_split_clause,[],[f1469,f3624]) ).
thf(f3624,plain,
( spl60_125
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_125])]) ).
thf(f1469,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f974]) ).
thf(f974,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(flattening,[],[f973]) ).
thf(f973,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f561]) ).
thf(f561,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ) ),
inference(fool_elimination,[],[f560]) ).
thf(f560,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)),zero_zero_real) ) ),
inference(rectify,[],[f272]) ).
thf(f272,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X19),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)),zero_zero_real) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_divide__pos__neg) ).
thf(f3622,plain,
spl60_124,
inference(avatar_split_clause,[],[f1468,f3620]) ).
thf(f3620,plain,
( spl60_124
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_124])]) ).
thf(f1468,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f972]) ).
thf(f972,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(flattening,[],[f971]) ).
thf(f971,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f559]) ).
thf(f559,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ) ),
inference(fool_elimination,[],[f558]) ).
thf(f558,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),X1)) ) ),
inference(rectify,[],[f273]) ).
thf(f273,axiom,
! [X2: real,X19: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X19)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X2),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_divide__pos__pos) ).
thf(f3618,plain,
spl60_123,
inference(avatar_split_clause,[],[f1466,f3616]) ).
thf(f3616,plain,
( spl60_123
<=> ! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_123])]) ).
thf(f1466,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(cnf_transformation,[],[f968]) ).
thf(f968,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(flattening,[],[f967]) ).
thf(f967,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(ennf_transformation,[],[f555]) ).
thf(f555,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) ) ) ),
inference(fool_elimination,[],[f554]) ).
thf(f554,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) ) ),
inference(rectify,[],[f319]) ).
thf(f319,axiom,
! [X23: int,X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X23),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X23),X0)),zero_zero_int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_div__nonpos__pos__le0) ).
thf(f3614,plain,
spl60_122,
inference(avatar_split_clause,[],[f1465,f3612]) ).
thf(f3612,plain,
( spl60_122
<=> ! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_122])]) ).
thf(f1465,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) != $true ) ),
inference(cnf_transformation,[],[f966]) ).
thf(f966,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) != $true ) ),
inference(flattening,[],[f965]) ).
thf(f965,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) != $true ) ),
inference(ennf_transformation,[],[f553]) ).
thf(f553,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) ) ) ),
inference(fool_elimination,[],[f552]) ).
thf(f552,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1)),zero_zero_int) ) ),
inference(rectify,[],[f310]) ).
thf(f310,axiom,
! [X23: int,X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X23),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X23),X0)),zero_zero_int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_div__neg__pos__less0) ).
thf(f3610,plain,
spl60_121,
inference(avatar_split_clause,[],[f1457,f3608]) ).
thf(f3608,plain,
( spl60_121
<=> ! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_121])]) ).
thf(f1457,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f955]) ).
thf(f955,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ),
inference(flattening,[],[f954]) ).
thf(f954,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f537]) ).
thf(f537,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f536]) ).
thf(f536,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X1),X0)) ) ),
inference(rectify,[],[f311]) ).
thf(f311,axiom,
! [X0: int,X23: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X23)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X23),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_div__positive) ).
thf(f3546,plain,
spl60_120,
inference(avatar_split_clause,[],[f1665,f3544]) ).
thf(f1665,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),vAPP(nat,nat,suc,X0)) ),
inference(definition_unfolding,[],[f1380,f1287]) ).
thf(f1380,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X0)) ),
inference(cnf_transformation,[],[f439]) ).
thf(f439,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X0)) ),
inference(fool_elimination,[],[f438]) ).
thf(f438,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X0)),
inference(rectify,[],[f24]) ).
thf(f24,axiom,
! [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),vAPP(nat,nat,suc,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_lessI) ).
thf(f3534,plain,
spl60_119,
inference(avatar_split_clause,[],[f1664,f3532]) ).
thf(f1664,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),vAPP(nat,nat,suc,X0)) ),
inference(definition_unfolding,[],[f1379,f1287]) ).
thf(f1379,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) ),
inference(cnf_transformation,[],[f437]) ).
thf(f437,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) ),
inference(fool_elimination,[],[f436]) ).
thf(f436,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)),
inference(rectify,[],[f99]) ).
thf(f99,axiom,
! [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_zero__less__Suc) ).
thf(f3530,plain,
spl60_118,
inference(avatar_split_clause,[],[f1450,f3528]) ).
thf(f1450,plain,
! [X3: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0)) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1202]) ).
thf(f3519,plain,
spl60_117,
inference(avatar_split_clause,[],[f1565,f3517]) ).
thf(f3517,plain,
( spl60_117
<=> ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK44,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),sK45,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_117])]) ).
thf(f1565,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK44,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),sK45,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1251]) ).
thf(f3471,plain,
spl60_116,
inference(avatar_split_clause,[],[f2307,f3469]) ).
thf(f2307,plain,
! [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),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f2306]) ).
thf(f2306,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(forward_demodulation,[],[f1604,f1374]) ).
thf(f1604,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1134]) ).
thf(f1134,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1133]) ).
thf(f1133,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f769]) ).
thf(f769,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ) ) ),
inference(fool_elimination,[],[f768]) ).
thf(f768,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ) ),
inference(rectify,[],[f171]) ).
thf(f171,axiom,
! [X23: nat,X0: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X23),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X23)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X23),X4)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_power__mono) ).
thf(f3467,plain,
spl60_115,
inference(avatar_split_clause,[],[f1606,f3465]) ).
thf(f3465,plain,
( spl60_115
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_115])]) ).
thf(f1606,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1137]) ).
thf(f1137,plain,
! [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),divide_divide_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f773]) ).
thf(f773,plain,
! [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,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2)) ) ),
inference(fool_elimination,[],[f772]) ).
thf(f772,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2)) ),
inference(rectify,[],[f292]) ).
thf(f292,axiom,
! [X9: nat,X4: nat,X16: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X9),X16)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X4),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_div__le__mono) ).
thf(f3463,plain,
spl60_114,
inference(avatar_split_clause,[],[f1594,f3461]) ).
thf(f1594,plain,
! [X2: nat > $o,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,X2,X1) )
| ( $true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK51,X2),X0)) )
| ( $true != vAPP(nat,$o,X2,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1258]) ).
thf(f3422,plain,
spl60_113,
inference(avatar_split_clause,[],[f1766,f3419]) ).
thf(f1766,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),zero_zero_nat),pm),
inference(definition_unfolding,[],[f1635,f1287]) ).
thf(f1635,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),pm) = $true,
inference(cnf_transformation,[],[f813]) ).
thf(f813,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),pm) = $true,
inference(fool_elimination,[],[f812]) ).
thf(f812,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),pm),
inference(rectify,[],[f85]) ).
thf(f85,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),pm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_pm0) ).
thf(f3417,plain,
spl60_112,
inference(avatar_split_clause,[],[f1662,f3415]) ).
thf(f3415,plain,
( spl60_112
<=> ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_112])]) ).
thf(f1662,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),X0) ),
inference(definition_unfolding,[],[f1366,f1287]) ).
thf(f1366,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
inference(cnf_transformation,[],[f868]) ).
thf(f868,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
inference(flattening,[],[f411]) ).
thf(f411,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
inference(fool_elimination,[],[f410]) ).
thf(f410,plain,
! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0),
inference(rectify,[],[f119]) ).
thf(f119,axiom,
! [X4: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_less__not__refl) ).
thf(f3413,plain,
spl60_111,
inference(avatar_split_clause,[],[f1657,f3411]) ).
thf(f1657,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),suc),X0),zero_zero_nat) ),
inference(definition_unfolding,[],[f1361,f1287]) ).
thf(f1361,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f863]) ).
thf(f863,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) ),
inference(flattening,[],[f401]) ).
thf(f401,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) ),
inference(fool_elimination,[],[f400]) ).
thf(f400,plain,
! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat),
inference(rectify,[],[f128]) ).
thf(f128,axiom,
! [X23: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X23),zero_zero_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_bot__nat__0_Oextremum__strict) ).
thf(f3409,plain,
spl60_110,
inference(avatar_split_clause,[],[f1512,f3407]) ).
thf(f3407,plain,
( spl60_110
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_110])]) ).
thf(f1512,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ),
inference(cnf_transformation,[],[f1030]) ).
thf(f1030,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ),
inference(ennf_transformation,[],[f637]) ).
thf(f637,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ),
inference(fool_elimination,[],[f636]) ).
thf(f636,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ),
inference(rectify,[],[f248]) ).
thf(f248,axiom,
! [X10: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),X10)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X10),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_nat__one__le__power) ).
thf(f3403,plain,
spl60_109,
inference(avatar_split_clause,[],[f1608,f3401]) ).
thf(f3401,plain,
( spl60_109
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0))) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_109])]) ).
thf(f1608,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0))) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f1266]) ).
thf(f3399,plain,
( spl60_108
| ~ spl60_7
| ~ spl60_26
| ~ spl60_74 ),
inference(avatar_split_clause,[],[f2909,f2860,f2464,f2373,f3396]) ).
thf(f3396,plain,
( spl60_108
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_108])]) ).
thf(f2909,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),zero_zero_real) )
| ~ spl60_7
| ~ spl60_26
| ~ spl60_74 ),
inference(forward_demodulation,[],[f2908,f2375]) ).
thf(f2908,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,zero_zero_int)) )
| ~ spl60_26
| ~ spl60_74 ),
inference(trivial_inequality_removal,[],[f2899]) ).
thf(f2899,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,zero_zero_int)) )
| ~ spl60_26
| ~ spl60_74 ),
inference(superposition,[],[f2861,f2466]) ).
thf(f3345,plain,
spl60_107,
inference(avatar_split_clause,[],[f2314,f3342]) ).
thf(f3342,plain,
( spl60_107
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),pm)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_107])]) ).
thf(f2314,plain,
$true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),pm)))),
inference(forward_demodulation,[],[f1764,f1386]) ).
thf(f1386,plain,
! [X0: int,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X0)),X1) = vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ),
inference(cnf_transformation,[],[f876]) ).
thf(f876,plain,
! [X0: int,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X0)),X1) = vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X3: int,X4: nat] : ( vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X4)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,X3)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_of__int__power) ).
thf(f1764,plain,
$true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),pm))),
inference(definition_unfolding,[],[f1633,f1284]) ).
thf(f1284,plain,
ny = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),pm)),
inference(cnf_transformation,[],[f79]) ).
thf(f79,axiom,
ny = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),pm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_NY__def) ).
thf(f1633,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),ny) = $true,
inference(cnf_transformation,[],[f809]) ).
thf(f809,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),ny) = $true,
inference(fool_elimination,[],[f808]) ).
thf(f808,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),ny),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),ny),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_NY0) ).
thf(f3340,plain,
spl60_106,
inference(avatar_split_clause,[],[f1564,f3338]) ).
thf(f3338,plain,
( spl60_106
<=> ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK44,X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK45,X2),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_106])]) ).
thf(f1564,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK44,X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK45,X2),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1251]) ).
thf(f3336,plain,
spl60_105,
inference(avatar_split_clause,[],[f1446,f3334]) ).
thf(f3334,plain,
( spl60_105
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)),X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_105])]) ).
thf(f1446,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)),X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1200]) ).
thf(f3308,plain,
( spl60_104
| ~ spl60_5
| spl60_15 ),
inference(avatar_split_clause,[],[f2478,f2414,f2336,f3305]) ).
thf(f2414,plain,
( spl60_15
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_15])]) ).
thf(f2478,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) = $false )
| ~ spl60_5
| spl60_15 ),
inference(trivial_inequality_removal,[],[f2477]) ).
thf(f2477,plain,
( ( $true != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) = $false )
| ~ spl60_5
| spl60_15 ),
inference(superposition,[],[f2416,f2337]) ).
thf(f2416,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) != $true )
| spl60_15 ),
inference(avatar_component_clause,[],[f2414]) ).
thf(f3303,plain,
spl60_103,
inference(avatar_split_clause,[],[f1616,f3301]) ).
thf(f1616,plain,
! [X0: nat > nat > $o] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1272]) ).
thf(f3299,plain,
spl60_102,
inference(avatar_split_clause,[],[f1615,f3297]) ).
thf(f3297,plain,
( spl60_102
<=> ! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_102])]) ).
thf(f1615,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK58,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1272]) ).
thf(f3295,plain,
spl60_101,
inference(avatar_split_clause,[],[f1614,f3293]) ).
thf(f3293,plain,
( spl60_101
<=> ! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_101])]) ).
thf(f1614,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK56,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK57,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1272]) ).
thf(f3291,plain,
spl60_100,
inference(avatar_split_clause,[],[f1471,f3289]) ).
thf(f1471,plain,
! [X0: real,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)),vAPP(nat,nat,suc,X1)) = X0 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f1206]) ).
thf(f1206,plain,
! [X0: real,X1: nat] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)),vAPP(nat,nat,suc,X1)) = X0 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)) ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f975,f1205]) ).
thf(f1205,plain,
! [X0: real,X1: nat] :
( ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
=> ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)),vAPP(nat,nat,suc,X1)) = X0 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f975,plain,
! [X0: real,X1: nat] :
( ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f563]) ).
thf(f563,plain,
! [X0: real,X1: nat] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) ) ),
inference(fool_elimination,[],[f562]) ).
thf(f562,plain,
! [X0: real,X1: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),vAPP(nat,nat,suc,X1)) = X0 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) ) ),
inference(rectify,[],[f75]) ).
thf(f75,axiom,
! [X23: real,X4: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X23)
=> ? [X24: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X24),vAPP(nat,nat,suc,X4)) = X23 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_realpow__pos__nth2) ).
thf(f3231,plain,
spl60_99,
inference(avatar_split_clause,[],[f1605,f3229]) ).
thf(f1605,plain,
! [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) ) ),
inference(cnf_transformation,[],[f1136]) ).
thf(f1136,plain,
! [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) ) ),
inference(flattening,[],[f1135]) ).
thf(f1135,plain,
! [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) ) ),
inference(ennf_transformation,[],[f771]) ).
thf(f771,plain,
! [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,$o),ord_less_eq_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f770]) ).
thf(f770,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$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,$o),ord_less_eq_nat,X0),X2) ) ),
inference(rectify,[],[f219]) ).
thf(f219,axiom,
! [X10: nat,X11: nat,X16: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X10),X11)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X11),X16)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X10),X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_le__trans) ).
thf(f3227,plain,
spl60_98,
inference(avatar_split_clause,[],[f1467,f3225]) ).
thf(f3225,plain,
( spl60_98
<=> ! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_98])]) ).
thf(f1467,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(cnf_transformation,[],[f970]) ).
thf(f970,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(flattening,[],[f969]) ).
thf(f969,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(ennf_transformation,[],[f557]) ).
thf(f557,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f556]) ).
thf(f556,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) ) ) ),
inference(rectify,[],[f287]) ).
thf(f287,axiom,
! [X16: int,X48: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X16),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X48),X16)
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X16),X48) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_div__neg__neg__trivial) ).
thf(f3223,plain,
( spl60_97
| ~ spl60_5
| spl60_13 ),
inference(avatar_split_clause,[],[f2476,f2404,f2336,f3220]) ).
thf(f3220,plain,
( spl60_97
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_97])]) ).
thf(f2404,plain,
( spl60_13
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_13])]) ).
thf(f2476,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int) = $false )
| ~ spl60_5
| spl60_13 ),
inference(trivial_inequality_removal,[],[f2475]) ).
thf(f2475,plain,
( ( $true != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int) = $false )
| ~ spl60_5
| spl60_13 ),
inference(superposition,[],[f2406,f2337]) ).
thf(f2406,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int) != $true )
| spl60_13 ),
inference(avatar_component_clause,[],[f2404]) ).
thf(f3218,plain,
spl60_96,
inference(avatar_split_clause,[],[f1460,f3216]) ).
thf(f1460,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f959]) ).
thf(f959,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(flattening,[],[f958]) ).
thf(f958,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f543]) ).
thf(f543,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f542]) ).
thf(f542,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),X1) ) ) ),
inference(rectify,[],[f288]) ).
thf(f288,axiom,
! [X16: int,X48: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X16)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X16),X48)
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X16),X48) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_div__pos__pos__trivial) ).
thf(f3214,plain,
spl60_95,
inference(avatar_split_clause,[],[f1451,f3212]) ).
thf(f1451,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK18,X1),X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1202]) ).
thf(f3200,plain,
spl60_94,
inference(avatar_split_clause,[],[f1609,f3198]) ).
thf(f1609,plain,
! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK54,X1),X0)) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f1266]) ).
thf(f3156,plain,
spl60_93,
inference(avatar_split_clause,[],[f1524,f3154]) ).
thf(f3154,plain,
( spl60_93
<=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_93])]) ).
thf(f1524,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,suc,X0)),X1)) ),
inference(cnf_transformation,[],[f659]) ).
thf(f659,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,suc,X0)),X1)) ),
inference(fool_elimination,[],[f658]) ).
thf(f658,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,suc,X0)),X1)),
inference(rectify,[],[f295]) ).
thf(f295,axiom,
! [X9: nat,X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X9),X4)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,suc,X9)),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_Suc__div__le__mono) ).
thf(f3152,plain,
spl60_92,
inference(avatar_split_clause,[],[f1514,f3150]) ).
thf(f3150,plain,
( spl60_92
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
| ( $true = vAPP(nat,$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,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_92])]) ).
thf(f1514,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
| ( $true = vAPP(nat,$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,suc,X1)) ) ),
inference(cnf_transformation,[],[f1033]) ).
thf(f1033,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
| ( $true = vAPP(nat,$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,suc,X1)) ) ),
inference(flattening,[],[f1032]) ).
thf(f1032,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) = X0 )
| ( $true = vAPP(nat,$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,suc,X1)) ) ),
inference(ennf_transformation,[],[f895]) ).
thf(f895,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( vAPP(nat,nat,suc,X1) = X0 ) ) ),
inference(flattening,[],[f641]) ).
thf(f641,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( vAPP(nat,nat,suc,X1) = X0 ) ) ),
inference(fool_elimination,[],[f640]) ).
thf(f640,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1))
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,nat,suc,X1) = X0 ) ) ),
inference(rectify,[],[f236]) ).
thf(f236,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),vAPP(nat,nat,suc,X4))
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4)
=> ( vAPP(nat,nat,suc,X4) = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_le__SucE) ).
thf(f3148,plain,
spl60_91,
inference(avatar_split_clause,[],[f1437,f3146]) ).
thf(f3146,plain,
( spl60_91
<=> ! [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,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X3)),vAPP(sTfun(nat,$o),nat,sK13,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_91])]) ).
thf(f1437,plain,
! [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,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X3)),vAPP(sTfun(nat,$o),nat,sK13,X0)) ) ),
inference(cnf_transformation,[],[f1192]) ).
thf(f1192,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) )
& ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X3)),vAPP(sTfun(nat,$o),nat,sK13,X0)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f938,f1191]) ).
thf(f1191,plain,
! [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_eq_nat,vAPP(nat,nat,suc,X3)),X2) ) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) )
& ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X3)),vAPP(sTfun(nat,$o),nat,sK13,X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f938,plain,
! [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_eq_nat,vAPP(nat,nat,suc,X3)),X2) ) ) ) ),
inference(ennf_transformation,[],[f517]) ).
thf(f517,plain,
! [X0: nat > $o,X1: nat] :
( ! [X2: nat] :
( ! [X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X3)),X2) )
=> ( $true = vAPP(nat,$o,X0,X3) ) )
=> ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( $true = vAPP(nat,$o,X0,X1) ) ),
inference(fool_elimination,[],[f516]) ).
thf(f516,plain,
! [X0: nat > $o,X1: nat] :
( ! [X2: nat] :
( ! [X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X3)),X2)
=> vAPP(nat,$o,X0,X3) )
=> vAPP(nat,$o,X0,X2) )
=> vAPP(nat,$o,X0,X1) ),
inference(rectify,[],[f230]) ).
thf(f230,axiom,
! [X12: nat > $o,X4: nat] :
( ! [X21: nat] :
( ! [X28: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X28)),X21)
=> vAPP(nat,$o,X12,X28) )
=> vAPP(nat,$o,X12,X21) )
=> vAPP(nat,$o,X12,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_full__nat__induct) ).
thf(f3144,plain,
( spl60_90
| ~ spl60_5
| spl60_12 ),
inference(avatar_split_clause,[],[f2474,f2399,f2336,f3141]) ).
thf(f3141,plain,
( spl60_90
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_90])]) ).
thf(f2399,plain,
( spl60_12
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_12])]) ).
thf(f2474,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) = $false )
| ~ spl60_5
| spl60_12 ),
inference(trivial_inequality_removal,[],[f2473]) ).
thf(f2473,plain,
( ( $true != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) = $false )
| ~ spl60_5
| spl60_12 ),
inference(superposition,[],[f2401,f2337]) ).
thf(f2401,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) != $true )
| spl60_12 ),
inference(avatar_component_clause,[],[f2399]) ).
thf(f3085,plain,
spl60_89,
inference(avatar_split_clause,[],[f1477,f3083]) ).
thf(f1477,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f985]) ).
thf(f985,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f575]) ).
thf(f575,plain,
! [X0: real,X1: nat] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ) ),
inference(fool_elimination,[],[f574]) ).
thf(f574,plain,
! [X0: real,X1: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ),
inference(rectify,[],[f166]) ).
thf(f166,axiom,
! [X23: real,X4: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X23)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_zero__le__power) ).
thf(f3081,plain,
spl60_88,
inference(avatar_split_clause,[],[f1472,f3079]) ).
thf(f1472,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f976]) ).
thf(f976,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(ennf_transformation,[],[f565]) ).
thf(f565,plain,
! [X0: real,X1: nat] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ) ),
inference(fool_elimination,[],[f564]) ).
thf(f564,plain,
! [X0: real,X1: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ),
inference(rectify,[],[f76]) ).
thf(f76,axiom,
! [X23: real,X4: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X23)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_zero__less__power) ).
thf(f3077,plain,
spl60_87,
inference(avatar_split_clause,[],[f1470,f3075]) ).
thf(f1470,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK20,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ),
inference(cnf_transformation,[],[f1206]) ).
thf(f3073,plain,
spl60_86,
inference(avatar_split_clause,[],[f1462,f3071]) ).
thf(f1462,plain,
! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f962]) ).
thf(f962,plain,
! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f547]) ).
thf(f547,plain,
! [X0: int,X1: nat] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) ),
inference(fool_elimination,[],[f546]) ).
thf(f546,plain,
! [X0: int,X1: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ),
inference(rectify,[],[f167]) ).
thf(f167,axiom,
! [X23: int,X4: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X23)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X23),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_zero__le__power) ).
thf(f3069,plain,
spl60_85,
inference(avatar_split_clause,[],[f1458,f3067]) ).
thf(f1458,plain,
! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f956]) ).
thf(f956,plain,
! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f539]) ).
thf(f539,plain,
! [X0: int,X1: nat] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) ),
inference(fool_elimination,[],[f538]) ).
thf(f538,plain,
! [X0: int,X1: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ),
inference(rectify,[],[f77]) ).
thf(f77,axiom,
! [X23: int,X4: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X23)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X23),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_zero__less__power) ).
thf(f3044,plain,
spl60_84,
inference(avatar_split_clause,[],[f1448,f3042]) ).
thf(f1448,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK17,X1),X0)) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1200]) ).
thf(f3031,plain,
spl60_83,
inference(avatar_split_clause,[],[f2293,f3029]) ).
thf(f2293,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(trivial_inequality_removal,[],[f2292]) ).
thf(f2292,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(forward_demodulation,[],[f2291,f1374]) ).
thf(f2291,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(trivial_inequality_removal,[],[f2290]) ).
thf(f2290,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( X0 = X2 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(forward_demodulation,[],[f1547,f1374]) ).
thf(f1547,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(cnf_transformation,[],[f1053]) ).
thf(f1053,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X2 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(flattening,[],[f1052]) ).
thf(f1052,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X2 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) ) ),
inference(ennf_transformation,[],[f685]) ).
thf(f685,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) = $true )
=> ( X0 = X2 ) ) ) ),
inference(fool_elimination,[],[f684]) ).
thf(f684,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),vAPP(nat,nat,suc,X1)) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2)
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f182]) ).
thf(f182,axiom,
! [X23: nat,X4: nat,X0: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X23),vAPP(nat,nat,suc,X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,X4)) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X23)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( X0 = X23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_power__inject__base) ).
thf(f2955,plain,
spl60_82,
inference(avatar_split_clause,[],[f1452,f2953]) ).
thf(f1452,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1204]) ).
thf(f1204,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f950,f1203]) ).
thf(f1203,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK19,X0))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f950,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(flattening,[],[f949]) ).
thf(f949,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f529]) ).
thf(f529,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
=> ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
inference(fool_elimination,[],[f528]) ).
thf(f528,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,X1)
=> ( ! [X2: nat] :
( vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))
=> vAPP(nat,$o,X0,X2) )
=> vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(rectify,[],[f148]) ).
thf(f148,axiom,
! [X12: nat > $o,X16: nat] :
( vAPP(nat,$o,X12,X16)
=> ( ! [X21: nat] :
( vAPP(nat,$o,X12,vAPP(nat,nat,suc,X21))
=> vAPP(nat,$o,X12,X21) )
=> vAPP(nat,$o,X12,zero_zero_nat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_zero__induct) ).
thf(f2951,plain,
spl60_81,
inference(avatar_split_clause,[],[f1442,f2949]) ).
thf(f1442,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1196]) ).
thf(f1196,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f942,f1195]) ).
thf(f1195,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK15,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f942,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(flattening,[],[f941]) ).
thf(f941,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(ennf_transformation,[],[f521]) ).
thf(f521,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,X2) )
=> ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
=> ( $true = vAPP(nat,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f520]) ).
thf(f520,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,zero_zero_nat)
=> ( ! [X2: nat] :
( vAPP(nat,$o,X0,X2)
=> vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
=> vAPP(nat,$o,X0,X1) ) ),
inference(rectify,[],[f146]) ).
thf(f146,axiom,
! [X12: nat > $o,X4: nat] :
( vAPP(nat,$o,X12,zero_zero_nat)
=> ( ! [X21: nat] :
( vAPP(nat,$o,X12,X21)
=> vAPP(nat,$o,X12,vAPP(nat,nat,suc,X21)) )
=> vAPP(nat,$o,X12,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_nat__induct) ).
thf(f2947,plain,
spl60_80,
inference(avatar_split_clause,[],[f1440,f2945]) ).
thf(f1440,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1194]) ).
thf(f1194,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f940,f1193]) ).
thf(f1193,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK14,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f940,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(flattening,[],[f939]) ).
thf(f939,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(ennf_transformation,[],[f519]) ).
thf(f519,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,X2) )
=> ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
=> ( $true = vAPP(nat,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f518]) ).
thf(f518,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,zero_zero_nat)
=> ( ! [X2: nat] :
( vAPP(nat,$o,X0,X2)
=> vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
=> vAPP(nat,$o,X0,X1) ) ),
inference(rectify,[],[f153]) ).
thf(f153,axiom,
! [X12: nat > $o,X7: nat] :
( vAPP(nat,$o,X12,zero_zero_nat)
=> ( ! [X32: nat] :
( vAPP(nat,$o,X12,X32)
=> vAPP(nat,$o,X12,vAPP(nat,nat,suc,X32)) )
=> vAPP(nat,$o,X12,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_old_Onat_Oinducts) ).
thf(f2943,plain,
spl60_79,
inference(avatar_split_clause,[],[f1386,f2941]) ).
thf(f2939,plain,
spl60_78,
inference(avatar_split_clause,[],[f1385,f2937]) ).
thf(f1385,plain,
! [X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X0)),X1) = vAPP(int,int,ring_1_of_int_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ),
inference(cnf_transformation,[],[f875]) ).
thf(f875,plain,
! [X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X0)),X1) = vAPP(int,int,ring_1_of_int_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X3: int,X4: nat] : ( vAPP(int,int,ring_1_of_int_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X4)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,ring_1_of_int_int,X3)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_of__int__power) ).
thf(f2935,plain,
spl60_77,
inference(avatar_split_clause,[],[f1351,f2933]) ).
thf(f1351,plain,
! [X2: nat,X0: nat > $o] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,X0))) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1174]) ).
thf(f1174,plain,
! [X0: nat > $o] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,X0))) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK4,X0)) ) )
| ! [X2: nat] : ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f1172,f1173]) ).
thf(f1173,plain,
! [X0: nat > $o] :
( ? [X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X1)) )
& ( $true != vAPP(nat,$o,X0,X1) ) )
=> ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK4,X0))) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK4,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1172,plain,
! [X0: nat > $o] :
( ? [X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X1)) )
& ( $true != vAPP(nat,$o,X0,X1) ) )
| ! [X2: nat] : ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(rectify,[],[f909]) ).
thf(f909,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true != vAPP(nat,$o,X0,X2) ) )
| ! [X1: nat] : ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(flattening,[],[f908]) ).
thf(f908,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true != vAPP(nat,$o,X0,X2) ) )
| ! [X1: nat] : ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(ennf_transformation,[],[f862]) ).
thf(f862,plain,
! [X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
=> ( ? [X1: nat] : ( $true = vAPP(nat,$o,X0,X1) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true != vAPP(nat,$o,X0,X2) ) ) ) ),
inference(flattening,[],[f381]) ).
thf(f381,plain,
! [X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
=> ( ? [X1: nat] : ( $true = vAPP(nat,$o,X0,X1) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true != vAPP(nat,$o,X0,X2) ) ) ) ),
inference(fool_elimination,[],[f380]) ).
thf(f380,plain,
! [X0: nat > $o] :
( ~ vAPP(nat,$o,X0,zero_zero_nat)
=> ( ? [X1: nat] : vAPP(nat,$o,X0,X1)
=> ? [X2: nat] :
( vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))
& ~ vAPP(nat,$o,X0,X2) ) ) ),
inference(rectify,[],[f139]) ).
thf(f139,axiom,
! [X12: nat > $o] :
( ~ vAPP(nat,$o,X12,zero_zero_nat)
=> ( ? [X29: nat] : vAPP(nat,$o,X12,X29)
=> ? [X21: nat] :
( vAPP(nat,$o,X12,vAPP(nat,nat,suc,X21))
& ~ vAPP(nat,$o,X12,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_exists__least__lemma) ).
thf(f2870,plain,
spl60_76,
inference(avatar_split_clause,[],[f1517,f2868]) ).
thf(f1517,plain,
! [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,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(cnf_transformation,[],[f1037]) ).
thf(f1037,plain,
! [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,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(ennf_transformation,[],[f647]) ).
thf(f647,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f646]) ).
thf(f646,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f237]) ).
thf(f237,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X9)),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Suc__leD) ).
thf(f2866,plain,
spl60_75,
inference(avatar_split_clause,[],[f1498,f2864]) ).
thf(f1498,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1015]) ).
thf(f1015,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f611]) ).
thf(f611,plain,
! [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,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) ) ),
inference(fool_elimination,[],[f610]) ).
thf(f610,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f235]) ).
thf(f235,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),vAPP(nat,nat,suc,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_le__SucI) ).
thf(f2862,plain,
spl60_74,
inference(avatar_split_clause,[],[f1355,f2860]) ).
thf(f1355,plain,
! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f913]) ).
thf(f913,plain,
! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f389]) ).
thf(f389,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ),
inference(fool_elimination,[],[f388]) ).
thf(f388,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ),
inference(rectify,[],[f172]) ).
thf(f172,axiom,
! [X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_of__int__nonneg) ).
thf(f2858,plain,
spl60_73,
inference(avatar_split_clause,[],[f1354,f2856]) ).
thf(f1354,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f912]) ).
thf(f912,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f387]) ).
thf(f387,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(fool_elimination,[],[f386]) ).
thf(f386,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ),
inference(rectify,[],[f173]) ).
thf(f173,axiom,
! [X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_of__int__nonneg) ).
thf(f2854,plain,
spl60_72,
inference(avatar_split_clause,[],[f1353,f2852]) ).
thf(f1353,plain,
! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f911]) ).
thf(f911,plain,
! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f385]) ).
thf(f385,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ) ),
inference(fool_elimination,[],[f384]) ).
thf(f384,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X0)) ),
inference(rectify,[],[f57]) ).
thf(f57,axiom,
! [X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_of__int__pos) ).
thf(f2850,plain,
spl60_71,
inference(avatar_split_clause,[],[f1352,f2848]) ).
thf(f1352,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f910]) ).
thf(f910,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f383]) ).
thf(f383,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(fool_elimination,[],[f382]) ).
thf(f382,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,ring_1_of_int_int,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_of__int__pos) ).
thf(f2820,plain,
spl60_70,
inference(avatar_split_clause,[],[f1497,f2818]) ).
thf(f1497,plain,
! [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) ) ),
inference(cnf_transformation,[],[f1014]) ).
thf(f1014,plain,
! [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) ) ),
inference(flattening,[],[f1013]) ).
thf(f1013,plain,
! [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) ) ),
inference(ennf_transformation,[],[f609]) ).
thf(f609,plain,
! [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,$o),ord_less_eq_nat,X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f608]) ).
thf(f608,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f221]) ).
thf(f221,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X9)
=> ( X4 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_le__antisym) ).
thf(f2816,plain,
spl60_69,
inference(avatar_split_clause,[],[f1420,f2814]) ).
thf(f2814,plain,
( spl60_69
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_69])]) ).
thf(f1420,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f922]) ).
thf(f922,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 ) ),
inference(flattening,[],[f921]) ).
thf(f921,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f882]) ).
thf(f882,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
=> ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ) ),
inference(flattening,[],[f499]) ).
thf(f499,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
=> ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ) ),
inference(fool_elimination,[],[f498]) ).
thf(f498,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
=> ( ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ),
inference(rectify,[],[f304]) ).
thf(f304,axiom,
! [X2: real,X19: real] :
( ( X2 != X19 )
=> ( ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X19)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X19),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_linorder__neqE__linordered__idom) ).
thf(f2812,plain,
spl60_68,
inference(avatar_split_clause,[],[f1419,f2810]) ).
thf(f1419,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f920]) ).
thf(f920,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 ) ),
inference(flattening,[],[f919]) ).
thf(f919,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f881]) ).
thf(f881,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) ) ) ),
inference(flattening,[],[f497]) ).
thf(f497,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) ) ) ),
inference(fool_elimination,[],[f496]) ).
thf(f496,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) ) ),
inference(rectify,[],[f305]) ).
thf(f305,axiom,
! [X2: int,X19: int] :
( ( X2 != X19 )
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X19)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X19),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_linorder__neqE__linordered__idom) ).
thf(f2798,plain,
spl60_67,
inference(avatar_split_clause,[],[f1516,f2796]) ).
thf(f1516,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(cnf_transformation,[],[f1214]) ).
thf(f1214,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f1036,f1213]) ).
thf(f1213,plain,
! [X1: nat] :
( ? [X2: nat] : ( vAPP(nat,nat,suc,X2) = X1 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK24,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
thf(f1036,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] : ( vAPP(nat,nat,suc,X2) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(ennf_transformation,[],[f645]) ).
thf(f645,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
=> ? [X2: nat] : ( vAPP(nat,nat,suc,X2) = X1 ) ),
inference(fool_elimination,[],[f644]) ).
thf(f644,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1)
=> ? [X2: nat] : ( vAPP(nat,nat,suc,X2) = X1 ) ),
inference(rectify,[],[f234]) ).
thf(f234,axiom,
! [X4: nat,X40: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X4)),X40)
=> ? [X33: nat] : ( vAPP(nat,nat,suc,X33) = X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_Suc__le__D) ).
thf(f2781,plain,
( spl60_66
| ~ spl60_8
| ~ spl60_30 ),
inference(avatar_split_clause,[],[f2498,f2488,f2378,f2779]) ).
thf(f2779,plain,
( spl60_66
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK3,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_66])]) ).
thf(f2498,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK3,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_8
| ~ spl60_30 ),
inference(superposition,[],[f2379,f2489]) ).
thf(f2709,plain,
spl60_65,
inference(avatar_split_clause,[],[f1769,f2706]) ).
thf(f1769,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,x),vAPP(nat,nat,suc,pm))),na),
inference(definition_unfolding,[],[f1640,f1280,f1281]) ).
thf(f1281,plain,
p = vAPP(nat,nat,suc,pm),
inference(cnf_transformation,[],[f87]) ).
thf(f87,axiom,
p = vAPP(nat,nat,suc,pm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_p) ).
thf(f1280,plain,
y = x,
inference(cnf_transformation,[],[f289]) ).
thf(f289,axiom,
y = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_x) ).
thf(f1640,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,y),p)),na) = $true,
inference(cnf_transformation,[],[f823]) ).
thf(f823,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,y),p)),na) = $true,
inference(fool_elimination,[],[f822]) ).
thf(f822,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,y),p)),na),
inference(rectify,[],[f201]) ).
thf(f201,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,y),p)),na),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_yyn_H) ).
thf(f2704,plain,
spl60_64,
inference(avatar_split_clause,[],[f1768,f2701]) ).
thf(f2701,plain,
( spl60_64
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_64])]) ).
thf(f1768,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))),
inference(definition_unfolding,[],[f1639,f1281]) ).
thf(f1639,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),p)) = $true,
inference(cnf_transformation,[],[f821]) ).
thf(f821,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),p)) = $true,
inference(fool_elimination,[],[f820]) ).
thf(f820,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),p)),
inference(rectify,[],[f86]) ).
thf(f86,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),p)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85__C1_Oprems_C_I1_J) ).
thf(f2699,plain,
spl60_63,
inference(avatar_split_clause,[],[f1767,f2696]) ).
thf(f1767,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm))),
inference(definition_unfolding,[],[f1638,f1281]) ).
thf(f1638,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),p)) = $true,
inference(cnf_transformation,[],[f819]) ).
thf(f819,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),p)) = $true,
inference(fool_elimination,[],[f818]) ).
thf(f818,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),p)),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),p)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_yyn) ).
thf(f2694,plain,
spl60_62,
inference(avatar_split_clause,[],[f1453,f2692]) ).
thf(f1453,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK19,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1204]) ).
thf(f2690,plain,
spl60_61,
inference(avatar_split_clause,[],[f1444,f2688]) ).
thf(f1444,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1198]) ).
thf(f2686,plain,
spl60_60,
inference(avatar_split_clause,[],[f1441,f2684]) ).
thf(f1441,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1196]) ).
thf(f2682,plain,
( spl60_59
| ~ spl60_8
| ~ spl60_29 ),
inference(avatar_split_clause,[],[f2496,f2484,f2378,f2680]) ).
thf(f2680,plain,
( spl60_59
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK2,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_59])]) ).
thf(f2496,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK2,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl60_8
| ~ spl60_29 ),
inference(superposition,[],[f2379,f2485]) ).
thf(f2678,plain,
spl60_58,
inference(avatar_split_clause,[],[f1439,f2676]) ).
thf(f1439,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK14,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1194]) ).
thf(f2674,plain,
spl60_57,
inference(avatar_split_clause,[],[f1350,f2672]) ).
thf(f1350,plain,
! [X2: nat,X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK4,X0)) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f1174]) ).
thf(f2652,plain,
spl60_56,
inference(avatar_split_clause,[],[f1418,f2650]) ).
thf(f1418,plain,
! [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) ) ),
inference(cnf_transformation,[],[f495]) ).
thf(f495,plain,
! [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,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f494]) ).
thf(f494,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f222]) ).
thf(f222,axiom,
! [X9: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X9)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_nat__le__linear) ).
thf(f2643,plain,
spl60_55,
inference(avatar_split_clause,[],[f1523,f2641]) ).
thf(f1523,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X0) ),
inference(cnf_transformation,[],[f657]) ).
thf(f657,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X0) ),
inference(fool_elimination,[],[f656]) ).
thf(f656,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X0),
inference(rectify,[],[f293]) ).
thf(f293,axiom,
! [X9: nat,X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X9),X4)),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_div__le__dividend) ).
thf(f2638,plain,
spl60_54,
inference(avatar_split_clause,[],[f1373,f2636]) ).
thf(f2636,plain,
( spl60_54
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK10,X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_54])]) ).
thf(f1373,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK10,X0))),X0) ),
inference(cnf_transformation,[],[f1186]) ).
thf(f1186,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK10,X0))),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f425,f1185]) ).
thf(f1185,plain,
! [X0: real] :
( ? [X1: int] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X1)),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK10,X0))),X0) ) ),
introduced(choice_axiom,[]) ).
thf(f425,plain,
! [X0: real] :
? [X1: int] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X1)),X0) ),
inference(fool_elimination,[],[f424]) ).
thf(f424,plain,
! [X0: real] :
? [X1: int] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X1)),X0),
inference(rectify,[],[f80]) ).
thf(f80,axiom,
! [X2: real] :
? [X25: int] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,X25)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ex__of__int__less) ).
thf(f2634,plain,
spl60_53,
inference(avatar_split_clause,[],[f1372,f2632]) ).
thf(f1372,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK9,X0))) ),
inference(cnf_transformation,[],[f1184]) ).
thf(f1184,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK9,X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f423,f1183]) ).
thf(f1183,plain,
! [X0: real] :
( ? [X1: int] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,ring_1_of_int_real,X1)) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK9,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f423,plain,
! [X0: real] :
? [X1: int] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,ring_1_of_int_real,X1)) ),
inference(fool_elimination,[],[f422]) ).
thf(f422,plain,
! [X0: real] :
? [X1: int] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,ring_1_of_int_real,X1)),
inference(rectify,[],[f138]) ).
thf(f138,axiom,
! [X2: real] :
? [X25: int] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),vAPP(int,real,ring_1_of_int_real,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_ex__le__of__int) ).
thf(f2630,plain,
spl60_52,
inference(avatar_split_clause,[],[f1371,f2628]) ).
thf(f1371,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,X0))) ),
inference(cnf_transformation,[],[f1182]) ).
thf(f1182,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f421,f1181]) ).
thf(f1181,plain,
! [X0: real] :
( ? [X1: int] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,ring_1_of_int_real,X1)) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,ring_1_of_int_real,vAPP(real,int,sK8,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f421,plain,
! [X0: real] :
? [X1: int] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,ring_1_of_int_real,X1)) ),
inference(fool_elimination,[],[f420]) ).
thf(f420,plain,
! [X0: real] :
? [X1: int] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,ring_1_of_int_real,X1)),
inference(rectify,[],[f81]) ).
thf(f81,axiom,
! [X2: real] :
? [X25: int] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),vAPP(int,real,ring_1_of_int_real,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ex__less__of__int) ).
thf(f2626,plain,
spl60_51,
inference(avatar_split_clause,[],[f1320,f2624]) ).
thf(f1320,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) ),
inference(cnf_transformation,[],[f851]) ).
thf(f851,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) ),
inference(rectify,[],[f91]) ).
thf(f91,axiom,
! [X4: nat] : ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,suc,zero_zero_nat)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_power__Suc__0) ).
thf(f2592,plain,
spl60_50,
inference(avatar_split_clause,[],[f1438,f2590]) ).
thf(f1438,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) ) ),
inference(cnf_transformation,[],[f1192]) ).
thf(f2588,plain,
spl60_49,
inference(avatar_split_clause,[],[f1436,f2586]) ).
thf(f1436,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK12,X0)) ) ),
inference(cnf_transformation,[],[f1190]) ).
thf(f2584,plain,
spl60_48,
inference(avatar_split_clause,[],[f1433,f2582]) ).
thf(f1433,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) ),
inference(cnf_transformation,[],[f1188]) ).
thf(f2573,plain,
spl60_47,
inference(avatar_split_clause,[],[f2239,f2571]) ).
thf(f2571,plain,
( spl60_47
<=> ! [X0: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,ring_1_of_int_int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_47])]) ).
thf(f2239,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,ring_1_of_int_int,X0) ) ),
inference(equality_proxy_clausification,[],[f2238]) ).
thf(f2238,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(equality_proxy_clausification,[],[f2234]) ).
thf(f2234,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(binary_proxy_clausification,[],[f1334]) ).
thf(f1334,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ),
inference(cnf_transformation,[],[f353]) ).
thf(f353,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ),
inference(fool_elimination,[],[f352]) ).
thf(f352,plain,
! [X0: int] :
( ( zero_zero_int = vAPP(int,int,ring_1_of_int_int,X0) )
= ( zero_zero_int = X0 ) ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X3: int] :
( ( zero_zero_int = vAPP(int,int,ring_1_of_int_int,X3) )
= ( zero_zero_int = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_of__int__0__eq__iff) ).
thf(f2565,plain,
spl60_46,
inference(avatar_split_clause,[],[f1637,f2562]) ).
thf(f1637,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,ya)) = $true,
inference(cnf_transformation,[],[f817]) ).
thf(f817,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,ya)) = $true,
inference(fool_elimination,[],[f816]) ).
thf(f816,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,ya)),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,ya)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_y0) ).
thf(f2560,plain,
spl60_45,
inference(avatar_split_clause,[],[f1636,f2557]) ).
thf(f1636,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,na)) = $true,
inference(cnf_transformation,[],[f815]) ).
thf(f815,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,na)) = $true,
inference(fool_elimination,[],[f814]) ).
thf(f814,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,na)),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,ring_1_of_int_real,na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_n0) ).
thf(f2555,plain,
spl60_44,
inference(avatar_split_clause,[],[f1370,f2553]) ).
thf(f2553,plain,
( spl60_44
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,sK7,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_44])]) ).
thf(f1370,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,sK7,X0)),X0) ),
inference(cnf_transformation,[],[f1180]) ).
thf(f1180,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,sK7,X0)),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f419,f1179]) ).
thf(f1179,plain,
! [X0: real] :
( ? [X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,sK7,X0)),X0) ) ),
introduced(choice_axiom,[]) ).
thf(f419,plain,
! [X0: real] :
? [X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ),
inference(fool_elimination,[],[f418]) ).
thf(f418,plain,
! [X0: real] :
? [X1: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0),
inference(rectify,[],[f260]) ).
thf(f260,axiom,
! [X46: real] :
? [X31: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X31),X46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_linordered__field__no__lb) ).
thf(f2551,plain,
spl60_43,
inference(avatar_split_clause,[],[f1369,f2549]) ).
thf(f1369,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,sK6,X0)) ),
inference(cnf_transformation,[],[f1178]) ).
thf(f1178,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,sK6,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f417,f1177]) ).
thf(f1177,plain,
! [X0: real] :
( ? [X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,sK6,X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f417,plain,
! [X0: real] :
? [X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ),
inference(fool_elimination,[],[f416]) ).
thf(f416,plain,
! [X0: real] :
? [X1: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1),
inference(rectify,[],[f259]) ).
thf(f259,axiom,
! [X46: real] :
? [X47: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X46),X47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_linordered__field__no__ub) ).
thf(f2547,plain,
spl60_42,
inference(avatar_split_clause,[],[f1368,f2545]) ).
thf(f1368,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X0) ),
inference(cnf_transformation,[],[f870]) ).
thf(f870,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X0) ),
inference(flattening,[],[f415]) ).
thf(f415,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X0) ),
inference(fool_elimination,[],[f414]) ).
thf(f414,plain,
! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X0),
inference(rectify,[],[f232]) ).
thf(f232,axiom,
! [X4: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X4)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_Suc__n__not__le__n) ).
thf(f2543,plain,
spl60_41,
inference(avatar_split_clause,[],[f1319,f2541]) ).
thf(f1319,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ),
inference(cnf_transformation,[],[f850]) ).
thf(f850,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ),
inference(rectify,[],[f98]) ).
thf(f98,axiom,
! [X23: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X23),vAPP(nat,nat,suc,zero_zero_nat)) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_power__Suc0__right) ).
thf(f2539,plain,
spl60_40,
inference(avatar_split_clause,[],[f1318,f2537]) ).
thf(f2537,plain,
( spl60_40
<=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_40])]) ).
thf(f1318,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ),
inference(cnf_transformation,[],[f849]) ).
thf(f849,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ),
inference(rectify,[],[f290]) ).
thf(f290,axiom,
! [X9: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X9),vAPP(nat,nat,suc,zero_zero_nat)) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_div__by__Suc__0) ).
thf(f2535,plain,
spl60_39,
inference(avatar_split_clause,[],[f1317,f2533]) ).
thf(f2533,plain,
( spl60_39
<=> ! [X0: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_39])]) ).
thf(f1317,plain,
! [X0: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ),
inference(cnf_transformation,[],[f848]) ).
thf(f848,plain,
! [X0: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ),
inference(rectify,[],[f96]) ).
thf(f96,axiom,
! [X23: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X23),vAPP(nat,nat,suc,zero_zero_nat)) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_power__Suc0__right) ).
thf(f2531,plain,
spl60_38,
inference(avatar_split_clause,[],[f2237,f2529]) ).
thf(f2529,plain,
( spl60_38
<=> ! [X0: int] :
( ( zero_zero_int != X0 )
| ( zero_zero_int = vAPP(int,int,ring_1_of_int_int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_38])]) ).
thf(f2237,plain,
! [X0: int] :
( ( zero_zero_int != X0 )
| ( zero_zero_int = vAPP(int,int,ring_1_of_int_int,X0) ) ),
inference(equality_proxy_clausification,[],[f2236]) ).
thf(f2236,plain,
! [X0: int] :
( ( zero_zero_int != X0 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(equality_proxy_clausification,[],[f2235]) ).
thf(f2235,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),vAPP(int,int,ring_1_of_int_int,X0)) ) ),
inference(binary_proxy_clausification,[],[f1334]) ).
thf(f2527,plain,
spl60_37,
inference(avatar_split_clause,[],[f1316,f2525]) ).
thf(f2525,plain,
( spl60_37
<=> ! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_37])]) ).
thf(f1316,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ),
inference(cnf_transformation,[],[f847]) ).
thf(f847,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ),
inference(rectify,[],[f97]) ).
thf(f97,axiom,
! [X23: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X23),vAPP(nat,nat,suc,zero_zero_nat)) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_power__Suc0__right) ).
thf(f2523,plain,
spl60_36,
inference(avatar_split_clause,[],[f1315,f2521]) ).
thf(f1315,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) ),
inference(cnf_transformation,[],[f846]) ).
thf(f846,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) ),
inference(rectify,[],[f69]) ).
thf(f69,axiom,
! [X4: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(nat,nat,suc,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_power__0__Suc) ).
thf(f2519,plain,
spl60_35,
inference(avatar_split_clause,[],[f1314,f2517]) ).
thf(f1314,plain,
! [X0: nat] : ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(nat,nat,suc,X0)) ),
inference(cnf_transformation,[],[f845]) ).
thf(f845,plain,
! [X0: nat] : ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(nat,nat,suc,X0)) ),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
! [X4: nat] : ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(nat,nat,suc,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_power__0__Suc) ).
thf(f2515,plain,
spl60_34,
inference(avatar_split_clause,[],[f1313,f2513]) ).
thf(f1313,plain,
! [X0: nat] : ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(nat,nat,suc,X0)) ),
inference(cnf_transformation,[],[f844]) ).
thf(f844,plain,
! [X0: nat] : ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(nat,nat,suc,X0)) ),
inference(rectify,[],[f68]) ).
thf(f68,axiom,
! [X4: nat] : ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(nat,nat,suc,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_power__0__Suc) ).
thf(f2507,plain,
spl60_33,
inference(avatar_split_clause,[],[f1360,f2505]) ).
thf(f2505,plain,
( spl60_33
<=> ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_33])]) ).
thf(f1360,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ),
inference(cnf_transformation,[],[f918]) ).
thf(f918,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ),
inference(ennf_transformation,[],[f399]) ).
thf(f399,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) )
=> ( zero_zero_nat = X0 ) ),
inference(fool_elimination,[],[f398]) ).
thf(f398,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat)
=> ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f224]) ).
thf(f224,axiom,
! [X23: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X23),zero_zero_nat)
=> ( zero_zero_nat = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_bot__nat__0_Oextremum__uniqueI) ).
thf(f2503,plain,
( spl60_32
| spl60_3 ),
inference(avatar_split_clause,[],[f1289,f2326,f2500]) ).
thf(f2326,plain,
( spl60_3
<=> ( zero_zero_int = ya ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_3])]) ).
thf(f1289,plain,
( ( zero_zero_int = ya )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),ya) = $true ) ),
inference(cnf_transformation,[],[f335]) ).
thf(f335,plain,
( ( zero_zero_int = ya )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),ya) = $true ) ),
inference(fool_elimination,[],[f334]) ).
thf(f334,plain,
( ( zero_zero_int = ya )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),ya) ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
( ( zero_zero_int = ya )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),ya) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062) ).
thf(f2494,plain,
spl60_31,
inference(avatar_split_clause,[],[f2227,f2492]) ).
thf(f2492,plain,
( spl60_31
<=> ! [X0: int] :
( ( zero_zero_int = X0 )
| ( vAPP(int,real,ring_1_of_int_real,X0) != zero_zero_real ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_31])]) ).
thf(f2227,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( vAPP(int,real,ring_1_of_int_real,X0) != zero_zero_real ) ),
inference(equality_proxy_clausification,[],[f2226]) ).
thf(f2226,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ),
inference(equality_proxy_clausification,[],[f2222]) ).
thf(f2222,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1336]) ).
thf(f1336,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ),
inference(cnf_transformation,[],[f357]) ).
thf(f357,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ),
inference(fool_elimination,[],[f356]) ).
thf(f356,plain,
! [X0: int] :
( ( vAPP(int,real,ring_1_of_int_real,X0) = zero_zero_real )
= ( zero_zero_int = X0 ) ),
inference(rectify,[],[f33]) ).
thf(f33,axiom,
! [X3: int] :
( ( vAPP(int,real,ring_1_of_int_real,X3) = zero_zero_real )
= ( zero_zero_int = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_of__int__eq__0__iff) ).
thf(f2490,plain,
spl60_30,
inference(avatar_split_clause,[],[f1347,f2488]) ).
thf(f1347,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f1171]) ).
thf(f1171,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f905,f1170]) ).
thf(f1170,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f905,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f861]) ).
thf(f861,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(rectify,[],[f154]) ).
thf(f154,axiom,
! [X4: nat] :
( ( zero_zero_nat != X4 )
=> ? [X33: nat] : ( vAPP(nat,nat,suc,X33) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_not0__implies__Suc) ).
thf(f2486,plain,
spl60_29,
inference(avatar_split_clause,[],[f1346,f2484]) ).
thf(f1346,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK2,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f1169]) ).
thf(f1169,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK2,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f904,f1168]) ).
thf(f1168,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK2,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f904,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f860]) ).
thf(f860,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ~ ! [X1: nat] : ( vAPP(nat,nat,suc,X1) != X0 ) ),
inference(rectify,[],[f152]) ).
thf(f152,axiom,
! [X19: nat] :
( ( zero_zero_nat != X19 )
=> ~ ! [X32: nat] : ( vAPP(nat,nat,suc,X32) != X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_old_Onat_Oexhaust) ).
thf(f2482,plain,
spl60_28,
inference(avatar_split_clause,[],[f2225,f2480]) ).
thf(f2480,plain,
( spl60_28
<=> ! [X0: int] :
( ( zero_zero_int != X0 )
| ( vAPP(int,real,ring_1_of_int_real,X0) = zero_zero_real ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_28])]) ).
thf(f2225,plain,
! [X0: int] :
( ( zero_zero_int != X0 )
| ( vAPP(int,real,ring_1_of_int_real,X0) = zero_zero_real ) ),
inference(equality_proxy_clausification,[],[f2224]) ).
thf(f2224,plain,
! [X0: int] :
( ( zero_zero_int != X0 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ),
inference(equality_proxy_clausification,[],[f2223]) ).
thf(f2223,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),zero_zero_int),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(int,real,ring_1_of_int_real,X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1336]) ).
thf(f2472,plain,
spl60_27,
inference(avatar_split_clause,[],[f1763,f2469]) ).
thf(f1763,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),x),
inference(definition_unfolding,[],[f1629,f1280]) ).
thf(f1629,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),y) = $true,
inference(cnf_transformation,[],[f801]) ).
thf(f801,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),y) = $true,
inference(fool_elimination,[],[f800]) ).
thf(f800,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),y),
inference(rectify,[],[f202]) ).
thf(f202,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_y_H0) ).
thf(f2467,plain,
spl60_26,
inference(avatar_split_clause,[],[f1632,f2464]) ).
thf(f1632,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) = $true,
inference(cnf_transformation,[],[f807]) ).
thf(f807,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int) = $true,
inference(fool_elimination,[],[f806]) ).
thf(f806,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int),
inference(rectify,[],[f141]) ).
thf(f141,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_less__eq__int__code_I1_J) ).
thf(f2462,plain,
spl60_25,
inference(avatar_split_clause,[],[f1631,f2459]) ).
thf(f1631,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),ya) = $true,
inference(cnf_transformation,[],[f805]) ).
thf(f805,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),ya) = $true,
inference(fool_elimination,[],[f804]) ).
thf(f804,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),ya),
inference(rectify,[],[f27]) ).
thf(f27,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),ya),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__C1_Oprems_C_I2_J) ).
thf(f2454,plain,
spl60_24,
inference(avatar_split_clause,[],[f1630,f2451]) ).
thf(f1630,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),na) = $true,
inference(cnf_transformation,[],[f803]) ).
thf(f803,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),na) = $true,
inference(fool_elimination,[],[f802]) ).
thf(f802,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),na),
inference(rectify,[],[f28]) ).
thf(f28,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),na),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__C1_Oprems_C_I3_J) ).
thf(f2449,plain,
spl60_23,
inference(avatar_split_clause,[],[f1378,f2447]) ).
thf(f1378,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
inference(cnf_transformation,[],[f435]) ).
thf(f435,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
inference(fool_elimination,[],[f434]) ).
thf(f434,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0),
inference(rectify,[],[f218]) ).
thf(f218,axiom,
! [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_le__refl) ).
thf(f2445,plain,
spl60_22,
inference(avatar_split_clause,[],[f1374,f2443]) ).
thf(f2441,plain,
spl60_21,
inference(avatar_split_clause,[],[f1311,f2439]) ).
thf(f2439,plain,
( spl60_21
<=> ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_21])]) ).
thf(f1311,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f842]) ).
thf(f842,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),zero_zero_nat) ),
inference(rectify,[],[f300]) ).
thf(f300,axiom,
! [X23: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X23),zero_zero_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_div__by__0) ).
thf(f2437,plain,
spl60_20,
inference(avatar_split_clause,[],[f1309,f2435]) ).
thf(f2435,plain,
( spl60_20
<=> ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,zero_zero_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_20])]) ).
thf(f1309,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,zero_zero_nat),X0) ),
inference(cnf_transformation,[],[f840]) ).
thf(f840,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,zero_zero_nat),X0) ),
inference(rectify,[],[f214]) ).
thf(f214,axiom,
! [X23: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,zero_zero_nat),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_bits__div__0) ).
thf(f2433,plain,
spl60_19,
inference(avatar_split_clause,[],[f1307,f2431]) ).
thf(f2431,plain,
( spl60_19
<=> ! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_19])]) ).
thf(f1307,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),zero_zero_real) ),
inference(cnf_transformation,[],[f838]) ).
thf(f838,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X0),zero_zero_real) ),
inference(rectify,[],[f298]) ).
thf(f298,axiom,
! [X23: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,X23),zero_zero_real) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_div__by__0) ).
thf(f2429,plain,
spl60_18,
inference(avatar_split_clause,[],[f1306,f2427]) ).
thf(f2427,plain,
( spl60_18
<=> ! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,zero_zero_real),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_18])]) ).
thf(f1306,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,zero_zero_real),X0) ),
inference(cnf_transformation,[],[f837]) ).
thf(f837,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,zero_zero_real),X0) ),
inference(rectify,[],[f301]) ).
thf(f301,axiom,
! [X23: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),divide_divide_real,zero_zero_real),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_div__0) ).
thf(f2425,plain,
spl60_17,
inference(avatar_split_clause,[],[f1304,f2423]) ).
thf(f2423,plain,
( spl60_17
<=> ! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_17])]) ).
thf(f1304,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),zero_zero_int) ),
inference(cnf_transformation,[],[f835]) ).
thf(f835,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X0),zero_zero_int) ),
inference(rectify,[],[f208]) ).
thf(f208,axiom,
! [X23: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,X23),zero_zero_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_bits__div__by__0) ).
thf(f2421,plain,
spl60_16,
inference(avatar_split_clause,[],[f1302,f2419]) ).
thf(f2419,plain,
( spl60_16
<=> ! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,zero_zero_int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_16])]) ).
thf(f1302,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,zero_zero_int),X0) ),
inference(cnf_transformation,[],[f833]) ).
thf(f833,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,zero_zero_int),X0) ),
inference(rectify,[],[f302]) ).
thf(f302,axiom,
! [X23: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),divide_divide_int,zero_zero_int),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_div__0) ).
thf(f2417,plain,
~ spl60_15,
inference(avatar_split_clause,[],[f1294,f2414]) ).
thf(f1294,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) != $true,
inference(cnf_transformation,[],[f825]) ).
thf(f825,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) != $true,
inference(flattening,[],[f341]) ).
thf(f341,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) != $true,
inference(fool_elimination,[],[f340]) ).
thf(f340,plain,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__int__code_I1_J) ).
thf(f2412,plain,
( spl60_14
| ~ spl60_5
| spl60_11 ),
inference(avatar_split_clause,[],[f2397,f2392,f2336,f2409]) ).
thf(f2392,plain,
( spl60_11
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_11])]) ).
thf(f2397,plain,
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm)))) )
| ~ spl60_5
| spl60_11 ),
inference(trivial_inequality_removal,[],[f2396]) ).
thf(f2396,plain,
( ( $true != $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm)))) )
| ~ spl60_5
| spl60_11 ),
inference(superposition,[],[f2394,f2337]) ).
thf(f2394,plain,
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm)))) )
| spl60_11 ),
inference(avatar_component_clause,[],[f2392]) ).
thf(f2407,plain,
~ spl60_13,
inference(avatar_split_clause,[],[f1291,f2404]) ).
thf(f1291,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int) != $true,
inference(cnf_transformation,[],[f902]) ).
thf(f902,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int) != $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) != $true ) ),
inference(ennf_transformation,[],[f337]) ).
thf(f337,plain,
~ ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int) = $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) = $true ) ),
inference(fool_elimination,[],[f336]) ).
thf(f336,plain,
~ ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) ),
inference(rectify,[],[f25]) ).
thf(f25,axiom,
~ ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,na),zero_zero_int)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_not_I1_J) ).
thf(f2402,plain,
~ spl60_12,
inference(avatar_split_clause,[],[f1290,f2399]) ).
thf(f1290,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,ya),zero_zero_int) != $true,
inference(cnf_transformation,[],[f902]) ).
thf(f2395,plain,
( ~ spl60_11
| spl60_10 ),
inference(avatar_split_clause,[],[f2390,f2386,f2392]) ).
thf(f2386,plain,
( spl60_10
<=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),vAPP(nat,nat,suc,pm))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_10])]) ).
thf(f2390,plain,
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(int,real,ring_1_of_int_real,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,ya),vAPP(nat,nat,suc,pm)))) )
| spl60_10 ),
inference(forward_demodulation,[],[f2388,f1386]) ).
thf(f2388,plain,
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),vAPP(nat,nat,suc,pm))) != $true )
| spl60_10 ),
inference(avatar_component_clause,[],[f2386]) ).
thf(f2389,plain,
~ spl60_10,
inference(avatar_split_clause,[],[f1275,f2386]) ).
thf(f1275,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),vAPP(nat,nat,suc,pm))) != $true,
inference(cnf_transformation,[],[f824]) ).
thf(f824,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),vAPP(nat,nat,suc,pm))) != $true,
inference(flattening,[],[f325]) ).
thf(f325,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),vAPP(nat,nat,suc,pm))) != $true,
inference(fool_elimination,[],[f324]) ).
thf(f324,plain,
~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),vAPP(nat,nat,suc,pm))),
inference(rectify,[],[f321]) ).
thf(f321,negated_conjecture,
~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),vAPP(nat,nat,suc,pm))),
inference(negated_conjecture,[],[f320]) ).
thf(f320,conjecture,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,ring_1_of_int_real,na)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,ring_1_of_int_real,ya)),vAPP(nat,nat,suc,pm))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f2384,plain,
spl60_9,
inference(avatar_split_clause,[],[f1296,f2382]) ).
thf(f1296,plain,
! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) ),
inference(cnf_transformation,[],[f827]) ).
thf(f827,plain,
! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) ),
inference(rectify,[],[f142]) ).
thf(f142,axiom,
! [X5: nat] : ( vAPP(nat,nat,suc,X5) != zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_nat_Odistinct_I1_J) ).
thf(f2380,plain,
spl60_8,
inference(avatar_split_clause,[],[f1295,f2378]) ).
thf(f1295,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(cnf_transformation,[],[f826]) ).
thf(f826,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(rectify,[],[f59]) ).
thf(f59,axiom,
! [X4: nat] : ( vAPP(nat,nat,suc,X4) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_n__not__Suc__n) ).
thf(f2376,plain,
spl60_7,
inference(avatar_split_clause,[],[f1283,f2373]) ).
thf(f1283,plain,
zero_zero_real = vAPP(int,real,ring_1_of_int_real,zero_zero_int),
inference(cnf_transformation,[],[f29]) ).
thf(f29,axiom,
zero_zero_real = vAPP(int,real,ring_1_of_int_real,zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_of__int__0) ).
thf(f2371,plain,
spl60_6,
inference(avatar_split_clause,[],[f1282,f2368]) ).
thf(f1282,plain,
zero_zero_int = vAPP(int,int,ring_1_of_int_int,zero_zero_int),
inference(cnf_transformation,[],[f30]) ).
thf(f30,axiom,
zero_zero_int = vAPP(int,int,ring_1_of_int_int,zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_of__int__0) ).
thf(f2338,plain,
spl60_5,
inference(avatar_split_clause,[],[f323,f2336]) ).
thf(f323,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f2334,plain,
~ spl60_4,
inference(avatar_split_clause,[],[f1278,f2331]) ).
thf(f2331,plain,
( spl60_4
<=> ( zero_zero_nat = pm ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_4])]) ).
thf(f1278,plain,
zero_zero_nat != pm,
inference(cnf_transformation,[],[f83]) ).
thf(f83,axiom,
zero_zero_nat != pm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82__092_060open_062pm_A_061_A0_A_092_060Longrightarrow_062_AFalse_092_060close_062) ).
thf(f2329,plain,
~ spl60_3,
inference(avatar_split_clause,[],[f1277,f2326]) ).
thf(f1277,plain,
zero_zero_int != ya,
inference(cnf_transformation,[],[f20]) ).
thf(f20,axiom,
zero_zero_int != ya,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_y00) ).
thf(f2324,plain,
~ spl60_2,
inference(avatar_split_clause,[],[f1276,f2321]) ).
thf(f2321,plain,
( spl60_2
<=> ( na = zero_zero_int ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_2])]) ).
thf(f1276,plain,
na != zero_zero_int,
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
na != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n00) ).
thf(f2319,plain,
~ spl60_1,
inference(avatar_split_clause,[],[f322,f2316]) ).
thf(f2316,plain,
( spl60_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl60_1])]) ).
thf(f322,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP130^1 : TPTP v8.2.0. Released v7.5.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 15:51:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (3895)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38 % (3896)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38 % (3898)WARNING: value z3 for option sas not known
% 0.20/0.39 % (3897)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.39 % (3899)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.39 % (3901)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)
% 0.20/0.39 % (3900)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)
% 0.20/0.39 % (3898)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)
% 0.20/0.39 % (3902)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)
% 0.20/0.40 % Exception at run slice level
% 0.20/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.41 % (3902)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.41 % (3903)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.42 % Exception at run slice level
% 0.20/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.42 % Exception at run slice level
% 0.20/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.43 % (3904)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 % (3903)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.44 % (3905)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)
% 0.20/0.44 % Exception at run slice level
% 0.20/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.45 % (3912)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)
% 0.20/0.46 % (3904)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.62/0.88 % (3900)First to succeed.
% 3.62/0.91 % (3900)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3895"
% 3.62/0.92 % (3900)Refutation found. Thanks to Tanya!
% 3.62/0.92 % SZS status Theorem for theBenchmark
% 3.62/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/0.93 % (3900)------------------------------
% 3.62/0.93 % (3900)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.62/0.93 % (3900)Termination reason: Refutation
% 3.62/0.93
% 3.62/0.93 % (3900)Memory used [KB]: 6416
% 3.62/0.93 % (3900)Time elapsed: 0.530 s
% 3.62/0.93 % (3900)Instructions burned: 1582 (million)
% 3.62/0.93 % (3895)Success in time 0.551 s
%------------------------------------------------------------------------------