TSTP Solution File: ITP103^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP103^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 : Sun May 5 07:03:49 EDT 2024
% Result : Theorem 2.11s 0.66s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 446
% Syntax : Number of formulae : 1474 ( 284 unt; 85 typ; 0 def)
% Number of atoms : 13484 (2454 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 3990 (1515 ~;1755 |; 142 &; 0 @)
% ( 234 <=>; 344 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 435 ( 434 >; 1 *; 0 +; 0 <<)
% Number of symbols : 313 ( 310 usr; 240 con; 0-6 aty)
% Number of variables : 2249 ( 20 ^2100 !; 115 ?;2249 :)
% ( 14 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
list_P1467822637od_a_a: $tType ).
thf(type_def_8,type,
list_P1891567085od_a_a: $tType ).
thf(type_def_9,type,
list_a: $tType ).
thf(type_def_10,type,
list_P319927492_a_a_a: $tType ).
thf(type_def_11,type,
list_P1458844246od_a_a: $tType ).
thf(func_def_0,type,
list_P1891567085od_a_a: $tType ).
thf(func_def_1,type,
list_P1458844246od_a_a: $tType ).
thf(func_def_2,type,
list_P319927492_a_a_a: $tType ).
thf(func_def_3,type,
list_P1467822637od_a_a: $tType ).
thf(func_def_4,type,
list_a: $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
times_times_nat: nat > nat > nat ).
thf(func_def_7,type,
zero_zero_nat: nat ).
thf(func_def_8,type,
produc1055075589od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1891567085od_a_a ).
thf(func_def_9,type,
produc778776796_a_a_a: list_P1467822637od_a_a > list_a > list_P319927492_a_a_a ).
thf(func_def_10,type,
produc16441326od_a_a: list_a > list_P1467822637od_a_a > list_P1458844246od_a_a ).
thf(func_def_11,type,
product_a_a: list_a > list_a > list_P1467822637od_a_a ).
thf(func_def_12,type,
suc: nat > nat ).
thf(func_def_13,type,
size_s1052379225od_a_a: list_P1891567085od_a_a > nat ).
thf(func_def_14,type,
size_s736232240_a_a_a: list_P319927492_a_a_a > nat ).
thf(func_def_15,type,
size_s1875148994od_a_a: list_P1458844246od_a_a > nat ).
thf(func_def_16,type,
size_s642698393od_a_a: list_P1467822637od_a_a > nat ).
thf(func_def_17,type,
size_size_list_a: list_a > nat ).
thf(func_def_18,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_19,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_20,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_21,type,
k: nat ).
thf(func_def_22,type,
n: nat ).
thf(func_def_23,type,
xs: list_a ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_29,type,
vNOT: $o > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_32,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_33,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_34,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_35,type,
vOR: $o > $o > $o ).
thf(func_def_36,type,
vAND: $o > $o > $o ).
thf(func_def_37,type,
sP0: nat > ( nat > $o ) > $o ).
thf(func_def_38,type,
sP1: ( nat > nat > $o ) > $o ).
thf(func_def_39,type,
sK2: nat > nat ).
thf(func_def_40,type,
sK3: nat > nat ).
thf(func_def_41,type,
sK4: nat > nat ).
thf(func_def_42,type,
sK5: ( nat > $o ) > nat ).
thf(func_def_43,type,
sK6: nat > nat ).
thf(func_def_44,type,
sK7: nat > list_a ).
thf(func_def_45,type,
sK8: nat > list_P1467822637od_a_a ).
thf(func_def_46,type,
sK9: ( nat > $o ) > nat ).
thf(func_def_47,type,
sK10: ( nat > $o ) > nat ).
thf(func_def_48,type,
sK11: ( list_a > $o ) > list_a ).
thf(func_def_49,type,
sK12: ( list_P1467822637od_a_a > $o ) > list_P1467822637od_a_a ).
thf(func_def_50,type,
sK13: ( nat > $o ) > nat ).
thf(func_def_51,type,
sK14: ( nat > $o ) > nat ).
thf(func_def_52,type,
sK15: ( nat > $o ) > nat ).
thf(func_def_53,type,
sK16: ( nat > $o ) > nat ).
thf(func_def_54,type,
sK17: nat > nat > nat ).
thf(func_def_55,type,
sK18: nat > nat > nat ).
thf(func_def_56,type,
sK19: ( nat > nat > $o ) > nat ).
thf(func_def_57,type,
sK20: ( nat > nat > $o ) > nat ).
thf(func_def_58,type,
sK21: ( nat > nat > $o ) > nat ).
thf(func_def_59,type,
sK22: ( nat > nat > $o ) > nat ).
thf(func_def_60,type,
sK23: ( nat > nat ) > nat ).
thf(func_def_61,type,
sK24: ( nat > nat ) > nat ).
thf(func_def_62,type,
sK25: nat > ( nat > $o ) > nat ).
thf(func_def_63,type,
sK26: ( nat > $o ) > nat > nat ).
thf(func_def_64,type,
sK27: ( nat > nat > $o ) > nat ).
thf(func_def_65,type,
sK28: ( nat > nat > $o ) > nat ).
thf(func_def_66,type,
sK29: ( nat > nat > $o ) > nat ).
thf(func_def_67,type,
sK30: ( nat > nat > $o ) > nat ).
thf(func_def_69,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_70,type,
sK32: nat > ( nat > $o ) > nat > nat ).
thf(func_def_71,type,
sK33: nat > nat > nat ).
thf(func_def_72,type,
sK34: nat > nat > nat ).
thf(func_def_73,type,
sK35: ( nat > $o ) > nat > nat ).
thf(func_def_74,type,
sK36: ( nat > $o ) > nat > nat ).
thf(func_def_75,type,
sK37: ( nat > $o ) > nat > nat ).
thf(func_def_76,type,
sK38: ( nat > $o ) > nat > nat ).
thf(func_def_77,type,
sK39: ( nat > $o ) > nat > nat ).
thf(func_def_78,type,
sK40: ( nat > $o ) > nat > nat ).
thf(func_def_79,type,
sK41: ( nat > $o ) > nat > nat ).
thf(func_def_80,type,
sK42: ( nat > $o ) > nat > nat ).
thf(func_def_81,type,
sK43: nat > nat ).
thf(f9692,plain,
$false,
inference(avatar_sat_refutation,[],[f1336,f1341,f1345,f1378,f1384,f1388,f1393,f1397,f1401,f1405,f1409,f1413,f1417,f1421,f1425,f1432,f1440,f1444,f1448,f1452,f1462,f1466,f1470,f1480,f1484,f1488,f1492,f1496,f1537,f1541,f1546,f1550,f1560,f1564,f1568,f1572,f1588,f1605,f1609,f1613,f1617,f1621,f1682,f1686,f1704,f1708,f1712,f1716,f1784,f1788,f1792,f1796,f1823,f1827,f1831,f1859,f1863,f1867,f1871,f1875,f1895,f1899,f1903,f1907,f1951,f1955,f1973,f2009,f2013,f2017,f2021,f2025,f2029,f2033,f2054,f2068,f2072,f2084,f2090,f2094,f2098,f2102,f2106,f2110,f2213,f2219,f2223,f2227,f2231,f2235,f2322,f2326,f2330,f2366,f2378,f2382,f2386,f2402,f2406,f2410,f2441,f2445,f2449,f2453,f2457,f2499,f2509,f2513,f2523,f2553,f2568,f2580,f2585,f2606,f2611,f2706,f2720,f2724,f2728,f2732,f2736,f2740,f2744,f2752,f2865,f2868,f2873,f2876,f3727,f3745,f3767,f3771,f3775,f3779,f3783,f3787,f3791,f3795,f4350,f4415,f4419,f4423,f4427,f4431,f4435,f4441,f4450,f4454,f4494,f4502,f4526,f4550,f4552,f4555,f4558,f4562,f4653,f4702,f4706,f4710,f4921,f4925,f4929,f4933,f4937,f4941,f4945,f4949,f5118,f5628,f5632,f5636,f5640,f5644,f5648,f5652,f5657,f5707,f6218,f6222,f6226,f6230,f6545,f6549,f6553,f6557,f6561,f6565,f6569,f6573,f6577,f6581,f7002,f7455,f7459,f7463,f7593,f7597,f7601,f7605,f7609,f7613,f7617,f7621,f7630,f7639,f8771,f8775,f8779,f8783,f8787,f8791,f9207,f9211,f9215,f9219,f9223,f9227,f9231,f9236,f9240,f9282,f9291,f9295,f9448,f9452,f9456,f9460,f9464,f9469,f9473,f9477,f9481,f9485,f9489,f9493,f9497,f9501,f9685,f9688]) ).
thf(f9688,plain,
( ~ spl31_23
| ~ spl31_58
| ~ spl31_226 ),
inference(avatar_contradiction_clause,[],[f9687]) ).
thf(f9687,plain,
( $false
| ~ spl31_23
| ~ spl31_58
| ~ spl31_226 ),
inference(trivial_inequality_removal,[],[f9686]) ).
thf(f9686,plain,
( ( $true = $false )
| ~ spl31_23
| ~ spl31_58
| ~ spl31_226 ),
inference(forward_demodulation,[],[f9651,f1866]) ).
thf(f1866,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) = $false )
| ~ spl31_58 ),
inference(avatar_component_clause,[],[f1865]) ).
thf(f1865,plain,
( spl31_58
<=> ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_58])]) ).
thf(f9651,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n),n) )
| ~ spl31_23
| ~ spl31_226 ),
inference(superposition,[],[f1469,f9468]) ).
thf(f9468,plain,
( ( n = vAPP(nat,nat,suc,n) )
| ~ spl31_226 ),
inference(avatar_component_clause,[],[f9466]) ).
thf(f9466,plain,
( spl31_226
<=> ( n = vAPP(nat,nat,suc,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_226])]) ).
thf(f1469,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X0)) = $true )
| ~ spl31_23 ),
inference(avatar_component_clause,[],[f1468]) ).
thf(f1468,plain,
( spl31_23
<=> ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X0)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_23])]) ).
thf(f9685,plain,
( ~ spl31_6
| ~ spl31_226 ),
inference(avatar_contradiction_clause,[],[f9684]) ).
thf(f9684,plain,
( $false
| ~ spl31_6
| ~ spl31_226 ),
inference(trivial_inequality_removal,[],[f9649]) ).
thf(f9649,plain,
( ( n != n )
| ~ spl31_6
| ~ spl31_226 ),
inference(superposition,[],[f1387,f9468]) ).
thf(f1387,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 )
| ~ spl31_6 ),
inference(avatar_component_clause,[],[f1386]) ).
thf(f1386,plain,
( spl31_6
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_6])]) ).
thf(f9501,plain,
( spl31_234
| ~ spl31_21
| ~ spl31_81 ),
inference(avatar_split_clause,[],[f2127,f2096,f1460,f9499]) ).
thf(f9499,plain,
( spl31_234
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,suc,zero_zero_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_234])]) ).
thf(f1460,plain,
( spl31_21
<=> ! [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,[spl31_21])]) ).
thf(f2096,plain,
( spl31_81
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_81])]) ).
thf(f2127,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,suc,zero_zero_nat))) )
| ~ spl31_21
| ~ spl31_81 ),
inference(superposition,[],[f2097,f1461]) ).
thf(f1461,plain,
( ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 )
| ~ spl31_21 ),
inference(avatar_component_clause,[],[f1460]) ).
thf(f2097,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X2) )
| ~ spl31_81 ),
inference(avatar_component_clause,[],[f2096]) ).
thf(f9497,plain,
( spl31_233
| ~ spl31_21
| ~ spl31_81 ),
inference(avatar_split_clause,[],[f2125,f2096,f1460,f9495]) ).
thf(f9495,plain,
( spl31_233
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_233])]) ).
thf(f2125,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1)) )
| ~ spl31_21
| ~ spl31_81 ),
inference(superposition,[],[f2097,f1461]) ).
thf(f9493,plain,
( spl31_232
| ~ spl31_3
| ~ spl31_66 ),
inference(avatar_split_clause,[],[f1968,f1953,f1343,f9491]) ).
thf(f9491,plain,
( spl31_232
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = X1 )
| ( 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) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_232])]) ).
thf(f1343,plain,
( spl31_3
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_3])]) ).
thf(f1953,plain,
( spl31_66
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $true )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_66])]) ).
thf(f1968,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$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) = $false ) )
| ~ spl31_3
| ~ spl31_66 ),
inference(trivial_inequality_removal,[],[f1967]) ).
thf(f1967,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$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) = $false ) )
| ~ spl31_3
| ~ spl31_66 ),
inference(superposition,[],[f1954,f1344]) ).
thf(f1344,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl31_3 ),
inference(avatar_component_clause,[],[f1343]) ).
thf(f1954,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $true ) )
| ~ spl31_66 ),
inference(avatar_component_clause,[],[f1953]) ).
thf(f9489,plain,
( spl31_231
| ~ spl31_3
| ~ spl31_65 ),
inference(avatar_split_clause,[],[f1961,f1949,f1343,f9487]) ).
thf(f9487,plain,
( spl31_231
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_231])]) ).
thf(f1949,plain,
( spl31_65
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) = X1 )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_65])]) ).
thf(f1961,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
| ~ spl31_3
| ~ spl31_65 ),
inference(trivial_inequality_removal,[],[f1960]) ).
thf(f1960,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
| ~ spl31_3
| ~ spl31_65 ),
inference(superposition,[],[f1950,f1344]) ).
thf(f1950,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) = X1 ) )
| ~ spl31_65 ),
inference(avatar_component_clause,[],[f1949]) ).
thf(f9485,plain,
( spl31_230
| ~ spl31_20
| ~ spl31_55 ),
inference(avatar_split_clause,[],[f1851,f1829,f1450,f9483]) ).
thf(f9483,plain,
( spl31_230
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),X0) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,sK4,X0)) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_230])]) ).
thf(f1450,plain,
( spl31_20
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_20])]) ).
thf(f1829,plain,
( spl31_55
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_55])]) ).
thf(f1851,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),X0) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,sK4,X0)) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_20
| ~ spl31_55 ),
inference(superposition,[],[f1830,f1451]) ).
thf(f1451,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_20 ),
inference(avatar_component_clause,[],[f1450]) ).
thf(f1830,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) )
| ~ spl31_55 ),
inference(avatar_component_clause,[],[f1829]) ).
thf(f9481,plain,
( spl31_229
| ~ spl31_18
| ~ spl31_55 ),
inference(avatar_split_clause,[],[f1850,f1829,f1442,f9479]) ).
thf(f9479,plain,
( spl31_229
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),X0) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,sK3,X0)) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_229])]) ).
thf(f1442,plain,
( spl31_18
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_18])]) ).
thf(f1850,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),X0) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,sK3,X0)) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_18
| ~ spl31_55 ),
inference(superposition,[],[f1830,f1443]) ).
thf(f1443,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_18 ),
inference(avatar_component_clause,[],[f1442]) ).
thf(f9477,plain,
( spl31_228
| ~ spl31_17
| ~ spl31_55 ),
inference(avatar_split_clause,[],[f1849,f1829,f1438,f9475]) ).
thf(f9475,plain,
( spl31_228
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),X0) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,sK2,X0)) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_228])]) ).
thf(f1438,plain,
( spl31_17
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK2,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_17])]) ).
thf(f1849,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),X0) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,sK2,X0)) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_17
| ~ spl31_55 ),
inference(superposition,[],[f1830,f1439]) ).
thf(f1439,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK2,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_17 ),
inference(avatar_component_clause,[],[f1438]) ).
thf(f9473,plain,
( spl31_227
| ~ spl31_20
| ~ spl31_55 ),
inference(avatar_split_clause,[],[f1848,f1829,f1450,f9471]) ).
thf(f9471,plain,
( spl31_227
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK4,X0)),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_227])]) ).
thf(f1848,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK4,X0)),X1) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_20
| ~ spl31_55 ),
inference(superposition,[],[f1830,f1451]) ).
thf(f9469,plain,
( spl31_226
| ~ spl31_29
| ~ spl31_216 ),
inference(avatar_split_clause,[],[f9283,f9233,f1534,f9466]) ).
thf(f1534,plain,
( spl31_29
<=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(list_a,nat,size_size_list_a,xs)),k) = vAPP(nat,nat,suc,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_29])]) ).
thf(f9233,plain,
( spl31_216
<=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(list_a,nat,size_size_list_a,xs)),k) = n ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_216])]) ).
thf(f9283,plain,
( ( n = vAPP(nat,nat,suc,n) )
| ~ spl31_29
| ~ spl31_216 ),
inference(superposition,[],[f9235,f1536]) ).
thf(f1536,plain,
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(list_a,nat,size_size_list_a,xs)),k) = vAPP(nat,nat,suc,n) )
| ~ spl31_29 ),
inference(avatar_component_clause,[],[f1534]) ).
thf(f9235,plain,
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(list_a,nat,size_size_list_a,xs)),k) = n )
| ~ spl31_216 ),
inference(avatar_component_clause,[],[f9233]) ).
thf(f9464,plain,
( spl31_225
| ~ spl31_18
| ~ spl31_55 ),
inference(avatar_split_clause,[],[f1847,f1829,f1442,f9462]) ).
thf(f9462,plain,
( spl31_225
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK3,X0)),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_225])]) ).
thf(f1847,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK3,X0)),X1) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_18
| ~ spl31_55 ),
inference(superposition,[],[f1830,f1443]) ).
thf(f9460,plain,
( spl31_224
| ~ spl31_17
| ~ spl31_55 ),
inference(avatar_split_clause,[],[f1846,f1829,f1438,f9458]) ).
thf(f9458,plain,
( spl31_224
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK2,X0)),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_224])]) ).
thf(f1846,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK2,X0)),X1) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_17
| ~ spl31_55 ),
inference(superposition,[],[f1830,f1439]) ).
thf(f9456,plain,
( spl31_223
| ~ spl31_20
| ~ spl31_54 ),
inference(avatar_split_clause,[],[f1841,f1825,f1450,f9454]) ).
thf(f9454,plain,
( spl31_223
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),vAPP(nat,nat,sK4,X0))) = X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_223])]) ).
thf(f1825,plain,
( spl31_54
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_54])]) ).
thf(f1841,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),vAPP(nat,nat,sK4,X0))) = X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_20
| ~ spl31_54 ),
inference(superposition,[],[f1826,f1451]) ).
thf(f1826,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) = X1 ) )
| ~ spl31_54 ),
inference(avatar_component_clause,[],[f1825]) ).
thf(f9452,plain,
( spl31_222
| ~ spl31_18
| ~ spl31_54 ),
inference(avatar_split_clause,[],[f1840,f1825,f1442,f9450]) ).
thf(f9450,plain,
( spl31_222
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),vAPP(nat,nat,sK3,X0))) = X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_222])]) ).
thf(f1840,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),vAPP(nat,nat,sK3,X0))) = X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_18
| ~ spl31_54 ),
inference(superposition,[],[f1826,f1443]) ).
thf(f9448,plain,
( spl31_221
| ~ spl31_17
| ~ spl31_54 ),
inference(avatar_split_clause,[],[f1839,f1825,f1438,f9446]) ).
thf(f9446,plain,
( spl31_221
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),vAPP(nat,nat,sK2,X0))) = X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_221])]) ).
thf(f1839,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),vAPP(nat,nat,sK2,X0))) = X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_17
| ~ spl31_54 ),
inference(superposition,[],[f1826,f1439]) ).
thf(f9295,plain,
( spl31_220
| ~ spl31_22
| ~ spl31_65 ),
inference(avatar_split_clause,[],[f1962,f1949,f1464,f9293]) ).
thf(f9293,plain,
( spl31_220
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,suc,X0) )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,vAPP(nat,nat,suc,X0)),zero_zero_nat)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_220])]) ).
thf(f1464,plain,
( spl31_22
<=> ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_22])]) ).
thf(f1962,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,suc,X0) )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,vAPP(nat,nat,suc,X0)),zero_zero_nat)) ) )
| ~ spl31_22
| ~ spl31_65 ),
inference(trivial_inequality_removal,[],[f1957]) ).
thf(f1957,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,suc,X0) )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,vAPP(nat,nat,suc,X0)),zero_zero_nat)) ) )
| ~ spl31_22
| ~ spl31_65 ),
inference(superposition,[],[f1950,f1465]) ).
thf(f1465,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) = $true )
| ~ spl31_22 ),
inference(avatar_component_clause,[],[f1464]) ).
thf(f9291,plain,
( spl31_219
| ~ spl31_3
| ~ spl31_64 ),
inference(avatar_split_clause,[],[f1945,f1905,f1343,f9289]) ).
thf(f9289,plain,
( spl31_219
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_219])]) ).
thf(f1905,plain,
( spl31_64
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_64])]) ).
thf(f1945,plain,
( ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $false ) )
| ~ spl31_3
| ~ spl31_64 ),
inference(trivial_inequality_removal,[],[f1944]) ).
thf(f1944,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $false ) )
| ~ spl31_3
| ~ spl31_64 ),
inference(superposition,[],[f1906,f1344]) ).
thf(f1906,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) ) )
| ~ spl31_64 ),
inference(avatar_component_clause,[],[f1905]) ).
thf(f9282,plain,
( spl31_218
| ~ spl31_3
| ~ spl31_63 ),
inference(avatar_split_clause,[],[f1940,f1901,f1343,f9280]) ).
thf(f9280,plain,
( spl31_218
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_218])]) ).
thf(f1901,plain,
( spl31_63
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_63])]) ).
thf(f1940,plain,
( ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $false ) )
| ~ spl31_3
| ~ spl31_63 ),
inference(trivial_inequality_removal,[],[f1939]) ).
thf(f1939,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $false ) )
| ~ spl31_3
| ~ spl31_63 ),
inference(superposition,[],[f1902,f1344]) ).
thf(f1902,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) ) )
| ~ spl31_63 ),
inference(avatar_component_clause,[],[f1901]) ).
thf(f9240,plain,
( spl31_217
| ~ spl31_8
| ~ spl31_60 ),
inference(avatar_split_clause,[],[f1889,f1873,f1395,f9238]) ).
thf(f9238,plain,
( spl31_217
<=> ! [X0: nat,X1: list_a] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X1)),X0) = vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(list_a,list_P1467822637od_a_a,vAPP(list_a,sTfun(list_a,list_P1467822637od_a_a),product_a_a,X1),vAPP(nat,list_a,sK7,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_217])]) ).
thf(f1395,plain,
( spl31_8
<=> ! [X0: nat] : ( vAPP(list_a,nat,size_size_list_a,vAPP(nat,list_a,sK7,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_8])]) ).
thf(f1873,plain,
( spl31_60
<=> ! [X0: list_a,X1: list_a] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(list_a,list_P1467822637od_a_a,vAPP(list_a,sTfun(list_a,list_P1467822637od_a_a),product_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X0)),vAPP(list_a,nat,size_size_list_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_60])]) ).
thf(f1889,plain,
( ! [X0: nat,X1: list_a] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X1)),X0) = vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(list_a,list_P1467822637od_a_a,vAPP(list_a,sTfun(list_a,list_P1467822637od_a_a),product_a_a,X1),vAPP(nat,list_a,sK7,X0))) )
| ~ spl31_8
| ~ spl31_60 ),
inference(superposition,[],[f1874,f1396]) ).
thf(f1396,plain,
( ! [X0: nat] : ( vAPP(list_a,nat,size_size_list_a,vAPP(nat,list_a,sK7,X0)) = X0 )
| ~ spl31_8 ),
inference(avatar_component_clause,[],[f1395]) ).
thf(f1874,plain,
( ! [X0: list_a,X1: list_a] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(list_a,list_P1467822637od_a_a,vAPP(list_a,sTfun(list_a,list_P1467822637od_a_a),product_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X0)),vAPP(list_a,nat,size_size_list_a,X1)) )
| ~ spl31_60 ),
inference(avatar_component_clause,[],[f1873]) ).
thf(f9236,plain,
( spl31_1
| spl31_216
| ~ spl31_33
| ~ spl31_173 ),
inference(avatar_split_clause,[],[f7491,f6211,f1558,f9233,f1333]) ).
thf(f1333,plain,
( spl31_1
<=> ( zero_zero_nat = k ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_1])]) ).
thf(f1558,plain,
( spl31_33
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_33])]) ).
thf(f6211,plain,
( spl31_173
<=> ( vAPP(list_a,nat,size_size_list_a,xs) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_173])]) ).
thf(f7491,plain,
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(list_a,nat,size_size_list_a,xs)),k) = n )
| ( zero_zero_nat = k )
| ~ spl31_33
| ~ spl31_173 ),
inference(superposition,[],[f1559,f6213]) ).
thf(f6213,plain,
( ( vAPP(list_a,nat,size_size_list_a,xs) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k) )
| ~ spl31_173 ),
inference(avatar_component_clause,[],[f6211]) ).
thf(f1559,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_33 ),
inference(avatar_component_clause,[],[f1558]) ).
thf(f9231,plain,
( spl31_215
| ~ spl31_8
| ~ spl31_60 ),
inference(avatar_split_clause,[],[f1888,f1873,f1395,f9229]) ).
thf(f9229,plain,
( spl31_215
<=> ! [X0: nat,X1: list_a] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(list_a,nat,size_size_list_a,X1)) = vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(list_a,list_P1467822637od_a_a,vAPP(list_a,sTfun(list_a,list_P1467822637od_a_a),product_a_a,vAPP(nat,list_a,sK7,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_215])]) ).
thf(f1888,plain,
( ! [X0: nat,X1: list_a] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(list_a,nat,size_size_list_a,X1)) = vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(list_a,list_P1467822637od_a_a,vAPP(list_a,sTfun(list_a,list_P1467822637od_a_a),product_a_a,vAPP(nat,list_a,sK7,X0)),X1)) )
| ~ spl31_8
| ~ spl31_60 ),
inference(superposition,[],[f1874,f1396]) ).
thf(f9227,plain,
( spl31_214
| ~ spl31_9
| ~ spl31_59 ),
inference(avatar_split_clause,[],[f1885,f1869,f1399,f9225]) ).
thf(f9225,plain,
( spl31_214
<=> ! [X0: nat,X1: list_P1467822637od_a_a] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)),X0) = vAPP(list_P1891567085od_a_a,nat,size_s1052379225od_a_a,vAPP(list_P1467822637od_a_a,list_P1891567085od_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,list_P1891567085od_a_a),produc1055075589od_a_a,X1),vAPP(nat,list_P1467822637od_a_a,sK8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_214])]) ).
thf(f1399,plain,
( spl31_9
<=> ! [X0: nat] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(nat,list_P1467822637od_a_a,sK8,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_9])]) ).
thf(f1869,plain,
( spl31_59
<=> ! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a] : ( vAPP(list_P1891567085od_a_a,nat,size_s1052379225od_a_a,vAPP(list_P1467822637od_a_a,list_P1891567085od_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,list_P1891567085od_a_a),produc1055075589od_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X0)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_59])]) ).
thf(f1885,plain,
( ! [X0: nat,X1: list_P1467822637od_a_a] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)),X0) = vAPP(list_P1891567085od_a_a,nat,size_s1052379225od_a_a,vAPP(list_P1467822637od_a_a,list_P1891567085od_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,list_P1891567085od_a_a),produc1055075589od_a_a,X1),vAPP(nat,list_P1467822637od_a_a,sK8,X0))) )
| ~ spl31_9
| ~ spl31_59 ),
inference(superposition,[],[f1870,f1400]) ).
thf(f1400,plain,
( ! [X0: nat] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(nat,list_P1467822637od_a_a,sK8,X0)) = X0 )
| ~ spl31_9 ),
inference(avatar_component_clause,[],[f1399]) ).
thf(f1870,plain,
( ! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a] : ( vAPP(list_P1891567085od_a_a,nat,size_s1052379225od_a_a,vAPP(list_P1467822637od_a_a,list_P1891567085od_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,list_P1891567085od_a_a),produc1055075589od_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X0)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) )
| ~ spl31_59 ),
inference(avatar_component_clause,[],[f1869]) ).
thf(f9223,plain,
( spl31_213
| ~ spl31_9
| ~ spl31_59 ),
inference(avatar_split_clause,[],[f1884,f1869,f1399,f9221]) ).
thf(f9221,plain,
( spl31_213
<=> ! [X0: nat,X1: list_P1467822637od_a_a] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) = vAPP(list_P1891567085od_a_a,nat,size_s1052379225od_a_a,vAPP(list_P1467822637od_a_a,list_P1891567085od_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,list_P1891567085od_a_a),produc1055075589od_a_a,vAPP(nat,list_P1467822637od_a_a,sK8,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_213])]) ).
thf(f1884,plain,
( ! [X0: nat,X1: list_P1467822637od_a_a] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) = vAPP(list_P1891567085od_a_a,nat,size_s1052379225od_a_a,vAPP(list_P1467822637od_a_a,list_P1891567085od_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,list_P1891567085od_a_a),produc1055075589od_a_a,vAPP(nat,list_P1467822637od_a_a,sK8,X0)),X1)) )
| ~ spl31_9
| ~ spl31_59 ),
inference(superposition,[],[f1870,f1400]) ).
thf(f9219,plain,
( spl31_212
| ~ spl31_9
| ~ spl31_57 ),
inference(avatar_split_clause,[],[f1881,f1861,f1399,f9217]) ).
thf(f9217,plain,
( spl31_212
<=> ! [X0: nat,X1: list_a] : ( vAPP(list_P1458844246od_a_a,nat,size_s1875148994od_a_a,vAPP(list_P1467822637od_a_a,list_P1458844246od_a_a,vAPP(list_a,sTfun(list_P1467822637od_a_a,list_P1458844246od_a_a),produc16441326od_a_a,X1),vAPP(nat,list_P1467822637od_a_a,sK8,X0))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_212])]) ).
thf(f1861,plain,
( spl31_57
<=> ! [X0: list_a,X1: list_P1467822637od_a_a] : ( vAPP(list_P1458844246od_a_a,nat,size_s1875148994od_a_a,vAPP(list_P1467822637od_a_a,list_P1458844246od_a_a,vAPP(list_a,sTfun(list_P1467822637od_a_a,list_P1458844246od_a_a),produc16441326od_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X0)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_57])]) ).
thf(f1881,plain,
( ! [X0: nat,X1: list_a] : ( vAPP(list_P1458844246od_a_a,nat,size_s1875148994od_a_a,vAPP(list_P1467822637od_a_a,list_P1458844246od_a_a,vAPP(list_a,sTfun(list_P1467822637od_a_a,list_P1458844246od_a_a),produc16441326od_a_a,X1),vAPP(nat,list_P1467822637od_a_a,sK8,X0))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X1)),X0) )
| ~ spl31_9
| ~ spl31_57 ),
inference(superposition,[],[f1862,f1400]) ).
thf(f1862,plain,
( ! [X0: list_a,X1: list_P1467822637od_a_a] : ( vAPP(list_P1458844246od_a_a,nat,size_s1875148994od_a_a,vAPP(list_P1467822637od_a_a,list_P1458844246od_a_a,vAPP(list_a,sTfun(list_P1467822637od_a_a,list_P1458844246od_a_a),produc16441326od_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X0)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) )
| ~ spl31_57 ),
inference(avatar_component_clause,[],[f1861]) ).
thf(f9215,plain,
( spl31_211
| ~ spl31_8
| ~ spl31_57 ),
inference(avatar_split_clause,[],[f1880,f1861,f1395,f9213]) ).
thf(f9213,plain,
( spl31_211
<=> ! [X0: nat,X1: list_P1467822637od_a_a] : ( vAPP(list_P1458844246od_a_a,nat,size_s1875148994od_a_a,vAPP(list_P1467822637od_a_a,list_P1458844246od_a_a,vAPP(list_a,sTfun(list_P1467822637od_a_a,list_P1458844246od_a_a),produc16441326od_a_a,vAPP(nat,list_a,sK7,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_211])]) ).
thf(f1880,plain,
( ! [X0: nat,X1: list_P1467822637od_a_a] : ( vAPP(list_P1458844246od_a_a,nat,size_s1875148994od_a_a,vAPP(list_P1467822637od_a_a,list_P1458844246od_a_a,vAPP(list_a,sTfun(list_P1467822637od_a_a,list_P1458844246od_a_a),produc16441326od_a_a,vAPP(nat,list_a,sK7,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) )
| ~ spl31_8
| ~ spl31_57 ),
inference(superposition,[],[f1862,f1396]) ).
thf(f9211,plain,
( spl31_210
| ~ spl31_8
| ~ spl31_56 ),
inference(avatar_split_clause,[],[f1877,f1857,f1395,f9209]) ).
thf(f9209,plain,
( spl31_210
<=> ! [X0: nat,X1: list_P1467822637od_a_a] : ( vAPP(list_P319927492_a_a_a,nat,size_s736232240_a_a_a,vAPP(list_a,list_P319927492_a_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_a,list_P319927492_a_a_a),produc778776796_a_a_a,X1),vAPP(nat,list_a,sK7,X0))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_210])]) ).
thf(f1857,plain,
( spl31_56
<=> ! [X0: list_P1467822637od_a_a,X1: list_a] : ( vAPP(list_P319927492_a_a_a,nat,size_s736232240_a_a_a,vAPP(list_a,list_P319927492_a_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_a,list_P319927492_a_a_a),produc778776796_a_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X0)),vAPP(list_a,nat,size_size_list_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_56])]) ).
thf(f1877,plain,
( ! [X0: nat,X1: list_P1467822637od_a_a] : ( vAPP(list_P319927492_a_a_a,nat,size_s736232240_a_a_a,vAPP(list_a,list_P319927492_a_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_a,list_P319927492_a_a_a),produc778776796_a_a_a,X1),vAPP(nat,list_a,sK7,X0))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)),X0) )
| ~ spl31_8
| ~ spl31_56 ),
inference(superposition,[],[f1858,f1396]) ).
thf(f1858,plain,
( ! [X0: list_P1467822637od_a_a,X1: list_a] : ( vAPP(list_P319927492_a_a_a,nat,size_s736232240_a_a_a,vAPP(list_a,list_P319927492_a_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_a,list_P319927492_a_a_a),produc778776796_a_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X0)),vAPP(list_a,nat,size_size_list_a,X1)) )
| ~ spl31_56 ),
inference(avatar_component_clause,[],[f1857]) ).
thf(f9207,plain,
( spl31_209
| ~ spl31_9
| ~ spl31_56 ),
inference(avatar_split_clause,[],[f1876,f1857,f1399,f9205]) ).
thf(f9205,plain,
( spl31_209
<=> ! [X0: nat,X1: list_a] : ( vAPP(list_P319927492_a_a_a,nat,size_s736232240_a_a_a,vAPP(list_a,list_P319927492_a_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_a,list_P319927492_a_a_a),produc778776796_a_a_a,vAPP(nat,list_P1467822637od_a_a,sK8,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(list_a,nat,size_size_list_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_209])]) ).
thf(f1876,plain,
( ! [X0: nat,X1: list_a] : ( vAPP(list_P319927492_a_a_a,nat,size_s736232240_a_a_a,vAPP(list_a,list_P319927492_a_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_a,list_P319927492_a_a_a),produc778776796_a_a_a,vAPP(nat,list_P1467822637od_a_a,sK8,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(list_a,nat,size_size_list_a,X1)) )
| ~ spl31_9
| ~ spl31_56 ),
inference(superposition,[],[f1858,f1400]) ).
thf(f8791,plain,
( spl31_208
| ~ spl31_3
| ~ spl31_54 ),
inference(avatar_split_clause,[],[f1844,f1825,f1343,f8789]) ).
thf(f8789,plain,
( spl31_208
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_208])]) ).
thf(f1844,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $false ) )
| ~ spl31_3
| ~ spl31_54 ),
inference(trivial_inequality_removal,[],[f1843]) ).
thf(f1843,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $false ) )
| ~ spl31_3
| ~ spl31_54 ),
inference(superposition,[],[f1826,f1344]) ).
thf(f8787,plain,
spl31_207,
inference(avatar_split_clause,[],[f1231,f8785]) ).
thf(f8785,plain,
( spl31_207
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_207])]) ).
thf(f1231,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(binary_proxy_clausification,[],[f769]) ).
thf(f769,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(cnf_transformation,[],[f485]) ).
thf(f485,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
! [X1: nat,X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Suc__less__eq) ).
thf(f8783,plain,
spl31_206,
inference(avatar_split_clause,[],[f1230,f8781]) ).
thf(f8781,plain,
( spl31_206
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_206])]) ).
thf(f1230,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(binary_proxy_clausification,[],[f769]) ).
thf(f8779,plain,
spl31_205,
inference(avatar_split_clause,[],[f1229,f8777]) ).
thf(f8777,plain,
( spl31_205
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_205])]) ).
thf(f1229,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ),
inference(binary_proxy_clausification,[],[f770]) ).
thf(f770,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(cnf_transformation,[],[f162]) ).
thf(f162,axiom,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Suc__le__mono) ).
thf(f8775,plain,
spl31_204,
inference(avatar_split_clause,[],[f1228,f8773]) ).
thf(f8773,plain,
( spl31_204
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_204])]) ).
thf(f1228,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ),
inference(binary_proxy_clausification,[],[f770]) ).
thf(f8771,plain,
spl31_203,
inference(avatar_split_clause,[],[f1009,f8769]) ).
thf(f8769,plain,
( spl31_203
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X1 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_203])]) ).
thf(f1009,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X1 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X2) ) ),
inference(equality_proxy_clausification,[],[f1008]) ).
thf(f1008,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X1 = X2 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X2)) ) ),
inference(equality_proxy_clausification,[],[f1004]) ).
thf(f1004,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X2)) ) ),
inference(binary_proxy_clausification,[],[f871]) ).
thf(f871,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X2)) ),
inference(cnf_transformation,[],[f389]) ).
thf(f389,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X2)) ),
inference(fool_elimination,[],[f388]) ).
thf(f388,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X2) )
= ( X1 = X2 ) ),
inference(rectify,[],[f79]) ).
thf(f79,axiom,
! [X2: nat,X1: nat,X0: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X2)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X2)),X0) )
= ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Suc__mult__cancel1) ).
thf(f7639,plain,
( ~ spl31_201
| ~ spl31_202
| ~ spl31_74 ),
inference(avatar_split_clause,[],[f2064,f2031,f7636,f7632]) ).
thf(f7632,plain,
( spl31_201
<=> ( $true = vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_201])]) ).
thf(f7636,plain,
( spl31_202
<=> ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,vEQ(nat)) = vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,vEQ(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_202])]) ).
thf(f2031,plain,
( spl31_74
<=> ! [X0: nat > nat > $o] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_74])]) ).
thf(f2064,plain,
( ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,vEQ(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,vEQ(nat)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) )
| ~ spl31_74 ),
inference(equality_proxy_clausification,[],[f2061]) ).
thf(f2061,plain,
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,vEQ(nat))) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,vEQ(nat)) )
| ~ spl31_74 ),
inference(primitive_instantiation,[],[f2032]) ).
thf(f2032,plain,
( ! [X0: nat > nat > $o] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) )
| ~ spl31_74 ),
inference(avatar_component_clause,[],[f2031]) ).
thf(f7630,plain,
( spl31_199
| spl31_1
| ~ spl31_200
| ~ spl31_118
| ~ spl31_173 ),
inference(avatar_split_clause,[],[f7503,f6211,f2722,f7627,f1333,f7623]) ).
thf(f7623,plain,
( spl31_199
<=> ( zero_zero_nat = n ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_199])]) ).
thf(f7627,plain,
( spl31_200
<=> ( zero_zero_nat = vAPP(list_a,nat,size_size_list_a,xs) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_200])]) ).
thf(f2722,plain,
( spl31_118
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( zero_zero_nat = X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_118])]) ).
thf(f7503,plain,
( ( zero_zero_nat != vAPP(list_a,nat,size_size_list_a,xs) )
| ( zero_zero_nat = k )
| ( zero_zero_nat = n )
| ~ spl31_118
| ~ spl31_173 ),
inference(superposition,[],[f2723,f6213]) ).
thf(f2723,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( zero_zero_nat = X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_118 ),
inference(avatar_component_clause,[],[f2722]) ).
thf(f7621,plain,
( spl31_198
| ~ spl31_23
| ~ spl31_54 ),
inference(avatar_split_clause,[],[f1845,f1825,f1468,f7619]) ).
thf(f7619,plain,
( spl31_198
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_198])]) ).
thf(f1845,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)) )
| ~ spl31_23
| ~ spl31_54 ),
inference(trivial_inequality_removal,[],[f1842]) ).
thf(f1842,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),sK18,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)) ) )
| ~ spl31_23
| ~ spl31_54 ),
inference(superposition,[],[f1826,f1469]) ).
thf(f7617,plain,
( spl31_197
| ~ spl31_3
| ~ spl31_52 ),
inference(avatar_split_clause,[],[f1816,f1794,f1343,f7615]) ).
thf(f7615,plain,
( spl31_197
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_197])]) ).
thf(f1794,plain,
( spl31_52
<=> ! [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,sK15,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_52])]) ).
thf(f1816,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_3
| ~ spl31_52 ),
inference(trivial_inequality_removal,[],[f1815]) ).
thf(f1815,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_3
| ~ spl31_52 ),
inference(superposition,[],[f1795,f1344]) ).
thf(f1795,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_52 ),
inference(avatar_component_clause,[],[f1794]) ).
thf(f7613,plain,
( spl31_196
| ~ spl31_3
| ~ spl31_51 ),
inference(avatar_split_clause,[],[f1808,f1790,f1343,f7611]) ).
thf(f7611,plain,
( spl31_196
<=> ! [X2: nat,X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK10,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_196])]) ).
thf(f1790,plain,
( spl31_51
<=> ! [X0: nat > $o,X1: nat,X3: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK10,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_51])]) ).
thf(f1808,plain,
( ! [X2: nat,X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK10,X1)) ) )
| ~ spl31_3
| ~ spl31_51 ),
inference(trivial_inequality_removal,[],[f1807]) ).
thf(f1807,plain,
( ! [X2: nat,X0: nat,X1: nat > $o] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK10,X1)) ) )
| ~ spl31_3
| ~ spl31_51 ),
inference(superposition,[],[f1791,f1344]) ).
thf(f1791,plain,
( ! [X3: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK10,X0)) )
| ( $true = vAPP(nat,$o,X0,X3) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_51 ),
inference(avatar_component_clause,[],[f1790]) ).
thf(f7609,plain,
( spl31_195
| ~ spl31_3
| ~ spl31_50 ),
inference(avatar_split_clause,[],[f1806,f1786,f1343,f7607]) ).
thf(f7607,plain,
( spl31_195
<=> ! [X2: nat,X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK9,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_195])]) ).
thf(f1786,plain,
( spl31_50
<=> ! [X0: nat > $o,X1: nat,X3: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK9,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_50])]) ).
thf(f1806,plain,
( ! [X2: nat,X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK9,X1)) ) )
| ~ spl31_3
| ~ spl31_50 ),
inference(trivial_inequality_removal,[],[f1805]) ).
thf(f1805,plain,
( ! [X2: nat,X0: nat,X1: nat > $o] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK9,X1)) ) )
| ~ spl31_3
| ~ spl31_50 ),
inference(superposition,[],[f1787,f1344]) ).
thf(f1787,plain,
( ! [X3: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK9,X0)) )
| ( $true = vAPP(nat,$o,X0,X3) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_50 ),
inference(avatar_component_clause,[],[f1786]) ).
thf(f7605,plain,
( spl31_194
| ~ spl31_20
| ~ spl31_44 ),
inference(avatar_split_clause,[],[f1696,f1684,f1450,f7603]) ).
thf(f7603,plain,
( spl31_194
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK4,X0)),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_194])]) ).
thf(f1684,plain,
( spl31_44
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$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) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_44])]) ).
thf(f1696,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK4,X0)),X1) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_20
| ~ spl31_44 ),
inference(superposition,[],[f1685,f1451]) ).
thf(f1685,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$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) = $true ) )
| ~ spl31_44 ),
inference(avatar_component_clause,[],[f1684]) ).
thf(f7601,plain,
( spl31_193
| ~ spl31_18
| ~ spl31_44 ),
inference(avatar_split_clause,[],[f1695,f1684,f1442,f7599]) ).
thf(f7599,plain,
( spl31_193
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK3,X0)),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_193])]) ).
thf(f1695,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK3,X0)),X1) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_18
| ~ spl31_44 ),
inference(superposition,[],[f1685,f1443]) ).
thf(f7597,plain,
( spl31_192
| ~ spl31_17
| ~ spl31_44 ),
inference(avatar_split_clause,[],[f1694,f1684,f1438,f7595]) ).
thf(f7595,plain,
( spl31_192
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK2,X0)),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_192])]) ).
thf(f1694,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK2,X0)),X1) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_17
| ~ spl31_44 ),
inference(superposition,[],[f1685,f1439]) ).
thf(f7593,plain,
spl31_191,
inference(avatar_split_clause,[],[f1092,f7591]) ).
thf(f7591,plain,
( spl31_191
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) = $false )
| ( X0 = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_191])]) ).
thf(f1092,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) = $false )
| ( X0 = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ),
inference(equality_proxy_clausification,[],[f1091]) ).
thf(f1091,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ),
inference(binary_proxy_clausification,[],[f1090]) ).
thf(f1090,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) = $false )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f790]) ).
thf(f790,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) ),
inference(cnf_transformation,[],[f285]) ).
thf(f285,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) ),
inference(fool_elimination,[],[f284]) ).
thf(f284,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1))
= ( X0 = X1 ) )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
inference(rectify,[],[f69]) ).
thf(f69,axiom,
! [X1: nat,X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0))
= ( X0 = X1 ) )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__Suc__eq) ).
thf(f7463,plain,
( spl31_125
| spl31_190
| ~ spl31_68 ),
inference(avatar_split_clause,[],[f2039,f2007,f7461,f2750]) ).
thf(f2750,plain,
( spl31_125
<=> ! [X0: nat] : ( zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_125])]) ).
thf(f7461,plain,
( spl31_190
<=> ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat))) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_190])]) ).
thf(f2007,plain,
( spl31_68
<=> ! [X0: nat > $o,X1: nat,X3: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_68])]) ).
thf(f2039,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat))) )
| ( zero_zero_nat = X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_68 ),
inference(equality_proxy_clausification,[],[f2034]) ).
thf(f2034,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_68 ),
inference(leibniz_equality_elimination,[],[f2008]) ).
thf(f2008,plain,
( ! [X3: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X3) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_68 ),
inference(avatar_component_clause,[],[f2007]) ).
thf(f7459,plain,
( spl31_189
| ~ spl31_22
| ~ spl31_66 ),
inference(avatar_split_clause,[],[f1969,f1953,f1464,f7457]) ).
thf(f7457,plain,
( spl31_189
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,suc,X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,suc,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_189])]) ).
thf(f1969,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,suc,X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,suc,X0)) ) )
| ~ spl31_22
| ~ spl31_66 ),
inference(trivial_inequality_removal,[],[f1964]) ).
thf(f1964,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = vAPP(nat,nat,suc,X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,suc,X0)) ) )
| ~ spl31_22
| ~ spl31_66 ),
inference(superposition,[],[f1954,f1465]) ).
thf(f7455,plain,
( spl31_188
| ~ spl31_52 ),
inference(avatar_split_clause,[],[f1819,f1794,f7453]) ).
thf(f7453,plain,
( spl31_188
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_188])]) ).
thf(f1819,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( X0 = X1 ) )
| ~ spl31_52 ),
inference(equality_proxy_clausification,[],[f1818]) ).
thf(f1818,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_52 ),
inference(equality_proxy_clausification,[],[f1813]) ).
thf(f1813,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,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_52 ),
inference(primitive_instantiation,[],[f1795]) ).
thf(f7002,plain,
( ~ spl31_29
| ~ spl31_88
| ~ spl31_136
| ~ spl31_174
| ~ spl31_175 ),
inference(avatar_contradiction_clause,[],[f7001]) ).
thf(f7001,plain,
( $false
| ~ spl31_29
| ~ spl31_88
| ~ spl31_136
| ~ spl31_174
| ~ spl31_175 ),
inference(trivial_inequality_removal,[],[f7000]) ).
thf(f7000,plain,
( ( $true = $false )
| ~ spl31_29
| ~ spl31_88
| ~ spl31_136
| ~ spl31_174
| ~ spl31_175 ),
inference(forward_demodulation,[],[f6999,f6338]) ).
thf(f6338,plain,
( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X0) )
| ~ spl31_136
| ~ spl31_175 ),
inference(trivial_inequality_removal,[],[f6239]) ).
thf(f6239,plain,
( ! [X0: nat] :
( ( $true = $false )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X0) ) )
| ~ spl31_136
| ~ spl31_175 ),
inference(superposition,[],[f6221,f4349]) ).
thf(f4349,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))) )
| ~ spl31_136 ),
inference(avatar_component_clause,[],[f4348]) ).
thf(f4348,plain,
( spl31_136
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_136])]) ).
thf(f6221,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
| ~ spl31_175 ),
inference(avatar_component_clause,[],[f6220]) ).
thf(f6220,plain,
( spl31_175
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_175])]) ).
thf(f6999,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,n)),n) )
| ~ spl31_29
| ~ spl31_88
| ~ spl31_174 ),
inference(forward_demodulation,[],[f6997,f1536]) ).
thf(f6997,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(list_a,nat,size_size_list_a,xs)),k)),n) )
| ~ spl31_88
| ~ spl31_174 ),
inference(trivial_inequality_removal,[],[f6967]) ).
thf(f6967,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(list_a,nat,size_size_list_a,xs)),k)),n) )
| ~ spl31_88
| ~ spl31_174 ),
inference(superposition,[],[f2226,f6217]) ).
thf(f6217,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)) )
| ~ spl31_174 ),
inference(avatar_component_clause,[],[f6215]) ).
thf(f6215,plain,
( spl31_174
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_174])]) ).
thf(f2226,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X2)),X1) ) )
| ~ spl31_88 ),
inference(avatar_component_clause,[],[f2225]) ).
thf(f2225,plain,
( spl31_88
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_88])]) ).
thf(f6581,plain,
( spl31_187
| ~ spl31_23
| ~ spl31_69 ),
inference(avatar_split_clause,[],[f2048,f2011,f1468,f6579]) ).
thf(f6579,plain,
( spl31_187
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_187])]) ).
thf(f2011,plain,
( spl31_69
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_69])]) ).
thf(f2048,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)) )
| ~ spl31_23
| ~ spl31_69 ),
inference(trivial_inequality_removal,[],[f2043]) ).
thf(f2043,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))),X0)) ) )
| ~ spl31_23
| ~ spl31_69 ),
inference(superposition,[],[f2012,f1469]) ).
thf(f2012,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) ) )
| ~ spl31_69 ),
inference(avatar_component_clause,[],[f2011]) ).
thf(f6577,plain,
( spl31_186
| ~ spl31_22
| ~ spl31_62 ),
inference(avatar_split_clause,[],[f1937,f1897,f1464,f6575]) ).
thf(f6575,plain,
( spl31_186
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_186])]) ).
thf(f1897,plain,
( spl31_62
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_62])]) ).
thf(f1937,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X0)) = X1 )
| ~ spl31_22
| ~ spl31_62 ),
inference(trivial_inequality_removal,[],[f1931]) ).
thf(f1931,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X0)) = X1 ) )
| ~ spl31_22
| ~ spl31_62 ),
inference(superposition,[],[f1898,f1465]) ).
thf(f1898,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 ) )
| ~ spl31_62 ),
inference(avatar_component_clause,[],[f1897]) ).
thf(f6573,plain,
( spl31_185
| ~ spl31_22
| ~ spl31_61 ),
inference(avatar_split_clause,[],[f1930,f1893,f1464,f6571]) ).
thf(f6571,plain,
( spl31_185
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,suc,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_185])]) ).
thf(f1893,plain,
( spl31_61
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_61])]) ).
thf(f1930,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,suc,X0)) = X1 )
| ~ spl31_22
| ~ spl31_61 ),
inference(trivial_inequality_removal,[],[f1924]) ).
thf(f1924,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,suc,X0))),vAPP(nat,nat,suc,X0)) = X1 ) )
| ~ spl31_22
| ~ spl31_61 ),
inference(superposition,[],[f1894,f1465]) ).
thf(f1894,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 ) )
| ~ spl31_61 ),
inference(avatar_component_clause,[],[f1893]) ).
thf(f6569,plain,
( spl31_184
| ~ spl31_3
| ~ spl31_48 ),
inference(avatar_split_clause,[],[f1771,f1714,f1343,f6567]) ).
thf(f6567,plain,
( spl31_184
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_184])]) ).
thf(f1714,plain,
( spl31_48
<=> ! [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,sK16,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_48])]) ).
thf(f1771,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_3
| ~ spl31_48 ),
inference(trivial_inequality_removal,[],[f1770]) ).
thf(f1770,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_3
| ~ spl31_48 ),
inference(superposition,[],[f1715,f1344]) ).
thf(f1715,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,sK16,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_48 ),
inference(avatar_component_clause,[],[f1714]) ).
thf(f6565,plain,
( spl31_183
| ~ spl31_3
| ~ spl31_47 ),
inference(avatar_split_clause,[],[f1756,f1710,f1343,f6563]) ).
thf(f6563,plain,
( spl31_183
<=> ! [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,[spl31_183])]) ).
thf(f1710,plain,
( spl31_47
<=> ! [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,[spl31_47])]) ).
thf(f1756,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))) ) )
| ~ spl31_3
| ~ spl31_47 ),
inference(trivial_inequality_removal,[],[f1755]) ).
thf(f1755,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))) ) )
| ~ spl31_3
| ~ spl31_47 ),
inference(superposition,[],[f1711,f1344]) ).
thf(f1711,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) ) )
| ~ spl31_47 ),
inference(avatar_component_clause,[],[f1710]) ).
thf(f6561,plain,
( spl31_182
| ~ spl31_3
| ~ spl31_46 ),
inference(avatar_split_clause,[],[f1743,f1706,f1343,f6559]) ).
thf(f6559,plain,
( spl31_182
<=> ! [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,sK13,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_182])]) ).
thf(f1706,plain,
( spl31_46
<=> ! [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,sK13,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_46])]) ).
thf(f1743,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,sK13,X0))) ) )
| ~ spl31_3
| ~ spl31_46 ),
inference(trivial_inequality_removal,[],[f1742]) ).
thf(f1742,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,sK13,X0))) ) )
| ~ spl31_3
| ~ spl31_46 ),
inference(superposition,[],[f1707,f1344]) ).
thf(f1707,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK13,X0))) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_46 ),
inference(avatar_component_clause,[],[f1706]) ).
thf(f6557,plain,
( spl31_181
| ~ spl31_3
| ~ spl31_45 ),
inference(avatar_split_clause,[],[f1726,f1702,f1343,f6555]) ).
thf(f6555,plain,
( spl31_181
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_181])]) ).
thf(f1702,plain,
( spl31_45
<=> ! [X2: nat,X0: nat > $o] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,X0))) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_45])]) ).
thf(f1726,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_3
| ~ spl31_45 ),
inference(trivial_inequality_removal,[],[f1725]) ).
thf(f1725,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_3
| ~ spl31_45 ),
inference(superposition,[],[f1703,f1344]) ).
thf(f1703,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,sK5,X0))) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_45 ),
inference(avatar_component_clause,[],[f1702]) ).
thf(f6553,plain,
spl31_180,
inference(avatar_split_clause,[],[f1249,f6551]) ).
thf(f6551,plain,
( spl31_180
<=> ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))) = $false )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_180])]) ).
thf(f1249,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))) = $false )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f1248]) ).
thf(f1248,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))) = $false )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(equality_proxy_clausification,[],[f1247]) ).
thf(f1247,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))) = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(binary_proxy_clausification,[],[f1246]) ).
thf(f1246,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))) = $false )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ) ),
inference(binary_proxy_clausification,[],[f745]) ).
thf(f745,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ),
inference(cnf_transformation,[],[f220]) ).
thf(f220,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ),
inference(fool_elimination,[],[f142]) ).
thf(f142,axiom,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat)))
= ( vAPP(nat,nat,suc,zero_zero_nat) = X0 ) )
| ( zero_zero_nat = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_nat__lessSucSuc0__conv) ).
thf(f6549,plain,
spl31_179,
inference(avatar_split_clause,[],[f1244,f6547]) ).
thf(f6547,plain,
( spl31_179
<=> ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0) = $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_179])]) ).
thf(f1244,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0) = $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f1243]) ).
thf(f1243,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0) = $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(not_proxy_clausification,[],[f1242]) ).
thf(f1242,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0) = $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ) ),
inference(equality_proxy_clausification,[],[f1241]) ).
thf(f1241,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0) = $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0) )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ) ),
inference(not_proxy_clausification,[],[f1240]) ).
thf(f1240,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0) = $true )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ) ),
inference(binary_proxy_clausification,[],[f1232]) ).
thf(f1232,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0) = $true )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0))) ) ),
inference(binary_proxy_clausification,[],[f746]) ).
thf(f746,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0))) ),
inference(cnf_transformation,[],[f221]) ).
thf(f221,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0))) ),
inference(fool_elimination,[],[f172]) ).
thf(f172,axiom,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,vAPP(nat,nat,suc,zero_zero_nat))),X0)
= ( vAPP(nat,nat,suc,zero_zero_nat) != X0 ) )
& ( zero_zero_nat != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_nat__geSucSuc0__conv) ).
thf(f6545,plain,
spl31_178,
inference(avatar_split_clause,[],[f1166,f6543]) ).
thf(f6543,plain,
( spl31_178
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,suc,zero_zero_nat) )
| ( vAPP(nat,nat,suc,zero_zero_nat) != X1 )
| ( vAPP(nat,nat,suc,zero_zero_nat) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_178])]) ).
thf(f1166,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,suc,zero_zero_nat) )
| ( vAPP(nat,nat,suc,zero_zero_nat) != X1 )
| ( vAPP(nat,nat,suc,zero_zero_nat) != X0 ) ),
inference(equality_proxy_clausification,[],[f1165]) ).
thf(f1165,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,suc,zero_zero_nat) )
| ( vAPP(nat,nat,suc,zero_zero_nat) != X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ),
inference(equality_proxy_clausification,[],[f1164]) ).
thf(f1164,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,suc,zero_zero_nat) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0) ) ),
inference(binary_proxy_clausification,[],[f1163]) ).
thf(f1163,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,suc,zero_zero_nat) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X1)) ) ),
inference(equality_proxy_clausification,[],[f1156]) ).
thf(f1156,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,suc,zero_zero_nat)) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X1)) ) ),
inference(binary_proxy_clausification,[],[f782]) ).
thf(f782,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,suc,zero_zero_nat)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X1)) ),
inference(cnf_transformation,[],[f269]) ).
thf(f269,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,suc,zero_zero_nat)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X1)) ),
inference(fool_elimination,[],[f268]) ).
thf(f268,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,suc,zero_zero_nat) )
= ( vAPP(nat,nat,suc,zero_zero_nat) = X1 ) )
& ( vAPP(nat,nat,suc,zero_zero_nat) = X0 ) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X1: nat,X0: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) = vAPP(nat,nat,suc,zero_zero_nat) )
= ( vAPP(nat,nat,suc,zero_zero_nat) = X0 ) )
& ( vAPP(nat,nat,suc,zero_zero_nat) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_one__eq__mult__iff) ).
thf(f6230,plain,
( spl31_177
| ~ spl31_3
| ~ spl31_44 ),
inference(avatar_split_clause,[],[f1699,f1684,f1343,f6228]) ).
thf(f6228,plain,
( spl31_177
<=> ! [X0: nat,X1: nat] :
( ( 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) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_177])]) ).
thf(f1699,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$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) = $false ) )
| ~ spl31_3
| ~ spl31_44 ),
inference(trivial_inequality_removal,[],[f1698]) ).
thf(f1698,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $false ) )
| ~ spl31_3
| ~ spl31_44 ),
inference(superposition,[],[f1685,f1344]) ).
thf(f6226,plain,
spl31_176,
inference(avatar_split_clause,[],[f1144,f6224]) ).
thf(f6224,plain,
( spl31_176
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_176])]) ).
thf(f1144,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ),
inference(not_proxy_clausification,[],[f1141]) ).
thf(f1141,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) = $true )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f784]) ).
thf(f784,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f273]) ).
thf(f273,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ),
inference(fool_elimination,[],[f272]) ).
thf(f272,plain,
! [X0: nat,X1: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) ),
inference(rectify,[],[f68]) ).
thf(f68,axiom,
! [X1: nat,X0: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_not__less__eq) ).
thf(f6222,plain,
spl31_175,
inference(avatar_split_clause,[],[f1143,f6220]) ).
thf(f1143,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ),
inference(not_proxy_clausification,[],[f1142]) ).
thf(f1142,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) = $false )
| ( $true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f784]) ).
thf(f6218,plain,
( spl31_173
| spl31_174
| ~ spl31_7
| ~ spl31_167 ),
inference(avatar_split_clause,[],[f6002,f5638,f1390,f6215,f6211]) ).
thf(f1390,plain,
( spl31_7
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_7])]) ).
thf(f5638,plain,
( spl31_167
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_167])]) ).
thf(f6002,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)) )
| ( vAPP(list_a,nat,size_size_list_a,xs) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k) )
| ~ spl31_7
| ~ spl31_167 ),
inference(trivial_inequality_removal,[],[f5772]) ).
thf(f5772,plain,
( ( $true = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,xs)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)) )
| ( vAPP(list_a,nat,size_size_list_a,xs) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k) )
| ~ spl31_7
| ~ spl31_167 ),
inference(superposition,[],[f5639,f1392]) ).
thf(f1392,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)) = $false )
| ~ spl31_7 ),
inference(avatar_component_clause,[],[f1390]) ).
thf(f5639,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( X0 = X1 ) )
| ~ spl31_167 ),
inference(avatar_component_clause,[],[f5638]) ).
thf(f5707,plain,
( spl31_172
| ~ spl31_86
| ~ spl31_87 ),
inference(avatar_split_clause,[],[f2281,f2221,f2217,f5705]) ).
thf(f5705,plain,
( spl31_172
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X1) )
| ( zero_zero_nat = X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_172])]) ).
thf(f2217,plain,
( spl31_86
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_86])]) ).
thf(f2221,plain,
( spl31_87
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_87])]) ).
thf(f2281,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X1) )
| ( zero_zero_nat = X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_86
| ~ spl31_87 ),
inference(superposition,[],[f2222,f2218]) ).
thf(f2218,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_86 ),
inference(avatar_component_clause,[],[f2217]) ).
thf(f2222,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_87 ),
inference(avatar_component_clause,[],[f2221]) ).
thf(f5657,plain,
( spl31_125
| spl31_171
| ~ spl31_52 ),
inference(avatar_split_clause,[],[f1809,f1794,f5654,f2750]) ).
thf(f5654,plain,
( spl31_171
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_171])]) ).
thf(f1809,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat))) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_52 ),
inference(leibniz_equality_elimination,[],[f1795]) ).
thf(f5652,plain,
spl31_170,
inference(avatar_split_clause,[],[f1226,f5650]) ).
thf(f5650,plain,
( spl31_170
<=> ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_170])]) ).
thf(f1226,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $false ) ),
inference(binary_proxy_clausification,[],[f1225]) ).
thf(f1225,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
inference(equality_proxy_clausification,[],[f1224]) ).
thf(f1224,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
inference(not_proxy_clausification,[],[f1219]) ).
thf(f1219,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f775]) ).
thf(f775,plain,
! [X0: nat,X1: nat] : ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ),
inference(cnf_transformation,[],[f255]) ).
thf(f255,plain,
! [X0: nat,X1: nat] : ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ),
inference(fool_elimination,[],[f254]) ).
thf(f254,plain,
! [X0: nat,X1: nat] :
( ( ( X0 != X1 )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
inference(rectify,[],[f37]) ).
thf(f37,axiom,
! [X1: nat,X0: 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_nat,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_nat__neq__iff) ).
thf(f5648,plain,
( spl31_169
| ~ spl31_19
| ~ spl31_23
| ~ spl31_48 ),
inference(avatar_split_clause,[],[f1780,f1714,f1468,f1446,f5646]) ).
thf(f5646,plain,
( spl31_169
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_169])]) ).
thf(f1446,plain,
( spl31_19
<=> ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_19])]) ).
thf(f1780,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) )
| ~ spl31_19
| ~ spl31_23
| ~ spl31_48 ),
inference(trivial_inequality_removal,[],[f1779]) ).
thf(f1779,plain,
( ! [X0: nat] :
( ( $true = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) ) )
| ~ spl31_19
| ~ spl31_23
| ~ spl31_48 ),
inference(forward_demodulation,[],[f1773,f1447]) ).
thf(f1447,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) = $false )
| ~ spl31_19 ),
inference(avatar_component_clause,[],[f1446]) ).
thf(f1773,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) = $true ) )
| ~ spl31_23
| ~ spl31_48 ),
inference(trivial_inequality_removal,[],[f1768]) ).
thf(f1768,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) = $true ) )
| ~ spl31_23
| ~ spl31_48 ),
inference(superposition,[],[f1715,f1469]) ).
thf(f5644,plain,
( spl31_168
| ~ spl31_19
| ~ spl31_23
| ~ spl31_45 ),
inference(avatar_split_clause,[],[f1735,f1702,f1468,f1446,f5642]) ).
thf(f5642,plain,
( spl31_168
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_168])]) ).
thf(f1735,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) )
| ~ spl31_19
| ~ spl31_23
| ~ spl31_45 ),
inference(trivial_inequality_removal,[],[f1734]) ).
thf(f1734,plain,
( ! [X0: nat] :
( ( $true = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) ) )
| ~ spl31_19
| ~ spl31_23
| ~ spl31_45 ),
inference(forward_demodulation,[],[f1728,f1447]) ).
thf(f1728,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) = $true ) )
| ~ spl31_23
| ~ spl31_45 ),
inference(trivial_inequality_removal,[],[f1723]) ).
thf(f1723,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0)))) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) = $true ) )
| ~ spl31_23
| ~ spl31_45 ),
inference(superposition,[],[f1703,f1469]) ).
thf(f5640,plain,
spl31_167,
inference(avatar_split_clause,[],[f1223,f5638]) ).
thf(f1223,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ),
inference(binary_proxy_clausification,[],[f1222]) ).
thf(f1222,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
inference(equality_proxy_clausification,[],[f1221]) ).
thf(f1221,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
inference(not_proxy_clausification,[],[f1220]) ).
thf(f1220,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f775]) ).
thf(f5636,plain,
spl31_166,
inference(avatar_split_clause,[],[f1202,f5634]) ).
thf(f5634,plain,
( spl31_166
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( zero_zero_nat = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_166])]) ).
thf(f1202,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( zero_zero_nat = X1 ) ),
inference(equality_proxy_clausification,[],[f1201]) ).
thf(f1201,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) ) ),
inference(binary_proxy_clausification,[],[f1200]) ).
thf(f1200,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ) ),
inference(equality_proxy_clausification,[],[f1199]) ).
thf(f1199,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),divide_divide_nat,X0),X1)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f778]) ).
thf(f778,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,$o),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f261]) ).
thf(f261,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$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),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ),
inference(fool_elimination,[],[f260]) ).
thf(f260,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( zero_zero_nat = X1 ) ),
inference(rectify,[],[f123]) ).
thf(f123,axiom,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( zero_zero_nat = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_div__eq__0__conv) ).
thf(f5632,plain,
spl31_165,
inference(avatar_split_clause,[],[f1059,f5630]) ).
thf(f5630,plain,
( spl31_165
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
| ( zero_zero_nat = X0 )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_165])]) ).
thf(f1059,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
| ( zero_zero_nat = X0 )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f1058]) ).
thf(f1058,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
| ( zero_zero_nat = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) ) ),
inference(equality_proxy_clausification,[],[f1057]) ).
thf(f1057,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1056]) ).
thf(f1056,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ) ),
inference(equality_proxy_clausification,[],[f1055]) ).
thf(f1055,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ) ),
inference(binary_proxy_clausification,[],[f866]) ).
thf(f866,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ),
inference(cnf_transformation,[],[f379]) ).
thf(f379,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ),
inference(fool_elimination,[],[f378]) ).
thf(f378,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
= ( zero_zero_nat = X0 ) )
| ( X1 = X2 ) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X2: nat,X1: nat,X0: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0) )
= ( zero_zero_nat = X2 ) )
| ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_mult__cancel1) ).
thf(f5628,plain,
spl31_164,
inference(avatar_split_clause,[],[f1048,f5626]) ).
thf(f5626,plain,
( spl31_164
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) )
| ( zero_zero_nat = X1 )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_164])]) ).
thf(f1048,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) )
| ( zero_zero_nat = X1 )
| ( X0 = X2 ) ),
inference(equality_proxy_clausification,[],[f1047]) ).
thf(f1047,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) )
| ( zero_zero_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f1046]) ).
thf(f1046,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f1045]) ).
thf(f1045,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(equality_proxy_clausification,[],[f1044]) ).
thf(f1044,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(binary_proxy_clausification,[],[f867]) ).
thf(f867,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ),
inference(cnf_transformation,[],[f381]) ).
thf(f381,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ),
inference(fool_elimination,[],[f380]) ).
thf(f380,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) )
= ( zero_zero_nat = X1 ) )
| ( X0 = X2 ) ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
! [X1: nat,X2: nat,X0: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
= ( zero_zero_nat = X2 ) )
| ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_mult__cancel2) ).
thf(f5118,plain,
spl31_163,
inference(avatar_split_clause,[],[f1206,f5116]) ).
thf(f5116,plain,
( spl31_163
<=> ! [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,[spl31_163])]) ).
thf(f1206,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,[],[f1205]) ).
thf(f1205,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,[],[f1203]) ).
thf(f1203,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),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ) ),
inference(equality_proxy_clausification,[],[f1198]) ).
thf(f1198,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),vEQ(nat),zero_zero_nat),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f778]) ).
thf(f4949,plain,
( spl31_162
| ~ spl31_3
| ~ spl31_42 ),
inference(avatar_split_clause,[],[f1674,f1619,f1343,f4947]) ).
thf(f4947,plain,
( spl31_162
<=> ! [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,sK16,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_162])]) ).
thf(f1619,plain,
( spl31_42
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_42])]) ).
thf(f1674,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,sK16,X0)) ) )
| ~ spl31_3
| ~ spl31_42 ),
inference(trivial_inequality_removal,[],[f1673]) ).
thf(f1673,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,sK16,X0)) ) )
| ~ spl31_3
| ~ spl31_42 ),
inference(superposition,[],[f1620,f1344]) ).
thf(f1620,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,X1) ) )
| ~ spl31_42 ),
inference(avatar_component_clause,[],[f1619]) ).
thf(f4945,plain,
( spl31_161
| ~ spl31_3
| ~ spl31_41 ),
inference(avatar_split_clause,[],[f1663,f1615,f1343,f4943]) ).
thf(f4943,plain,
( spl31_161
<=> ! [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,sK15,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_161])]) ).
thf(f1615,plain,
( spl31_41
<=> ! [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,[spl31_41])]) ).
thf(f1663,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,sK15,X0)) ) )
| ~ spl31_3
| ~ spl31_41 ),
inference(trivial_inequality_removal,[],[f1662]) ).
thf(f1662,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,sK15,X0)) ) )
| ~ spl31_3
| ~ spl31_41 ),
inference(superposition,[],[f1616,f1344]) ).
thf(f1616,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_41 ),
inference(avatar_component_clause,[],[f1615]) ).
thf(f4941,plain,
( spl31_160
| ~ spl31_3
| ~ spl31_40 ),
inference(avatar_split_clause,[],[f1651,f1611,f1343,f4939]) ).
thf(f4939,plain,
( spl31_160
<=> ! [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,[spl31_160])]) ).
thf(f1611,plain,
( spl31_40
<=> ! [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,[spl31_40])]) ).
thf(f1651,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) ) )
| ~ spl31_3
| ~ spl31_40 ),
inference(trivial_inequality_removal,[],[f1650]) ).
thf(f1650,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) ) )
| ~ spl31_3
| ~ spl31_40 ),
inference(superposition,[],[f1612,f1344]) ).
thf(f1612,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) ) )
| ~ spl31_40 ),
inference(avatar_component_clause,[],[f1611]) ).
thf(f4937,plain,
( spl31_159
| ~ spl31_3
| ~ spl31_39 ),
inference(avatar_split_clause,[],[f1639,f1607,f1343,f4935]) ).
thf(f4935,plain,
( spl31_159
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_159])]) ).
thf(f1607,plain,
( spl31_39
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_39])]) ).
thf(f1639,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_3
| ~ spl31_39 ),
inference(trivial_inequality_removal,[],[f1638]) ).
thf(f1638,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_3
| ~ spl31_39 ),
inference(superposition,[],[f1608,f1344]) ).
thf(f1608,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_39 ),
inference(avatar_component_clause,[],[f1607]) ).
thf(f4933,plain,
( spl31_158
| ~ spl31_3
| ~ spl31_38 ),
inference(avatar_split_clause,[],[f1628,f1603,f1343,f4931]) ).
thf(f4931,plain,
( spl31_158
<=> ! [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,sK5,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_158])]) ).
thf(f1603,plain,
( spl31_38
<=> ! [X2: nat,X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK5,X0)) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_38])]) ).
thf(f1628,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,sK5,X0)) ) )
| ~ spl31_3
| ~ spl31_38 ),
inference(trivial_inequality_removal,[],[f1627]) ).
thf(f1627,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,sK5,X0)) ) )
| ~ spl31_3
| ~ spl31_38 ),
inference(superposition,[],[f1604,f1344]) ).
thf(f1604,plain,
( ! [X2: nat,X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK5,X0)) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) )
| ~ spl31_38 ),
inference(avatar_component_clause,[],[f1603]) ).
thf(f4929,plain,
spl31_157,
inference(avatar_split_clause,[],[f1275,f4927]) ).
thf(f4927,plain,
( spl31_157
<=> ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = $false )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_157])]) ).
thf(f1275,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = $false )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f1274]) ).
thf(f1274,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = $false )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(equality_proxy_clausification,[],[f1273]) ).
thf(f1273,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(binary_proxy_clausification,[],[f1272]) ).
thf(f1272,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = $false )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ) ),
inference(binary_proxy_clausification,[],[f742]) ).
thf(f742,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ),
inference(cnf_transformation,[],[f217]) ).
thf(f217,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) ),
inference(fool_elimination,[],[f173]) ).
thf(f173,axiom,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,suc,zero_zero_nat))
= ( vAPP(nat,nat,suc,zero_zero_nat) = X0 ) )
| ( zero_zero_nat = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_nat__leSuc0__conv) ).
thf(f4925,plain,
spl31_156,
inference(avatar_split_clause,[],[f1266,f4923]) ).
thf(f4923,plain,
( spl31_156
<=> ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_156])]) ).
thf(f1266,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f1265]) ).
thf(f1265,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(not_proxy_clausification,[],[f1264]) ).
thf(f1264,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = $true )
| ( vAPP(nat,nat,suc,zero_zero_nat) = X0 )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ) ),
inference(equality_proxy_clausification,[],[f1263]) ).
thf(f1263,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0) )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ) ),
inference(not_proxy_clausification,[],[f1262]) ).
thf(f1262,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = $true )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0)) )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ) ),
inference(binary_proxy_clausification,[],[f1254]) ).
thf(f1254,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = $true )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0))) ) ),
inference(binary_proxy_clausification,[],[f744]) ).
thf(f744,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0))) ),
inference(cnf_transformation,[],[f219]) ).
thf(f219,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0))),vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,zero_zero_nat)),X0))) ),
inference(fool_elimination,[],[f143]) ).
thf(f143,axiom,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0)
= ( vAPP(nat,nat,suc,zero_zero_nat) != X0 ) )
& ( zero_zero_nat != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_nat__grSuc0__conv) ).
thf(f4921,plain,
spl31_155,
inference(avatar_split_clause,[],[f1188,f4919]) ).
thf(f4919,plain,
( spl31_155
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( zero_zero_nat != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_155])]) ).
thf(f1188,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( zero_zero_nat != X1 ) ),
inference(equality_proxy_clausification,[],[f1185]) ).
thf(f1185,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) ) ),
inference(binary_proxy_clausification,[],[f1184]) ).
thf(f1184,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(equality_proxy_clausification,[],[f1178]) ).
thf(f1178,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),times_times_nat,X0),X1)) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(binary_proxy_clausification,[],[f780]) ).
thf(f780,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),times_times_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ),
inference(cnf_transformation,[],[f265]) ).
thf(f265,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ),
inference(fool_elimination,[],[f264]) ).
thf(f264,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
= ( zero_zero_nat = X1 ) )
| ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f104]) ).
thf(f104,axiom,
! [X7: nat,X9: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X9) )
= ( zero_zero_nat = X9 ) )
| ( zero_zero_nat = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_mult__eq__0__iff) ).
thf(f4710,plain,
( spl31_154
| ~ spl31_47 ),
inference(avatar_split_clause,[],[f1761,f1710,f4708]) ).
thf(f4708,plain,
( spl31_154
<=> ! [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,[spl31_154])]) ).
thf(f1761,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 ) )
| ~ spl31_47 ),
inference(equality_proxy_clausification,[],[f1760]) ).
thf(f1760,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,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl31_47 ),
inference(equality_proxy_clausification,[],[f1759]) ).
thf(f1759,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$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) ) )
| ~ spl31_47 ),
inference(equality_proxy_clausification,[],[f1752]) ).
thf(f1752,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,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl31_47 ),
inference(primitive_instantiation,[],[f1711]) ).
thf(f4706,plain,
( spl31_153
| ~ spl31_46 ),
inference(avatar_split_clause,[],[f1748,f1706,f4704]) ).
thf(f4704,plain,
( spl31_153
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_153])]) ).
thf(f1748,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) )
| ~ spl31_46 ),
inference(equality_proxy_clausification,[],[f1747]) ).
thf(f1747,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) != X0 )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl31_46 ),
inference(equality_proxy_clausification,[],[f1746]) ).
thf(f1746,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$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) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl31_46 ),
inference(equality_proxy_clausification,[],[f1739]) ).
thf(f1739,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,sK13,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,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl31_46 ),
inference(primitive_instantiation,[],[f1707]) ).
thf(f4702,plain,
( spl31_152
| ~ spl31_3
| ~ spl31_36 ),
inference(avatar_split_clause,[],[f1600,f1570,f1343,f4700]) ).
thf(f4700,plain,
( spl31_152
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_152])]) ).
thf(f1570,plain,
( spl31_36
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_36])]) ).
thf(f1600,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
| ~ spl31_3
| ~ spl31_36 ),
inference(trivial_inequality_removal,[],[f1599]) ).
thf(f1599,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
| ~ spl31_3
| ~ spl31_36 ),
inference(superposition,[],[f1571,f1344]) ).
thf(f1571,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true ) )
| ~ spl31_36 ),
inference(avatar_component_clause,[],[f1570]) ).
thf(f4653,plain,
( spl31_151
| ~ spl31_22
| ~ spl31_53 ),
inference(avatar_split_clause,[],[f1838,f1821,f1464,f4651]) ).
thf(f4651,plain,
( spl31_151
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_151])]) ).
thf(f1821,plain,
( spl31_53
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_53])]) ).
thf(f1838,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))) )
| ~ spl31_22
| ~ spl31_53 ),
inference(trivial_inequality_removal,[],[f1833]) ).
thf(f1833,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))) ) )
| ~ spl31_22
| ~ spl31_53 ),
inference(superposition,[],[f1822,f1465]) ).
thf(f1822,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) )
| ~ spl31_53 ),
inference(avatar_component_clause,[],[f1821]) ).
thf(f4562,plain,
spl31_150,
inference(avatar_split_clause,[],[f1187,f4560]) ).
thf(f4560,plain,
( spl31_150
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( zero_zero_nat != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_150])]) ).
thf(f1187,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( zero_zero_nat != X0 ) ),
inference(equality_proxy_clausification,[],[f1186]) ).
thf(f1186,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(binary_proxy_clausification,[],[f1184]) ).
thf(f4558,plain,
( ~ spl31_23
| ~ spl31_58
| ~ spl31_147 ),
inference(avatar_contradiction_clause,[],[f4557]) ).
thf(f4557,plain,
( $false
| ~ spl31_23
| ~ spl31_58
| ~ spl31_147 ),
inference(trivial_inequality_removal,[],[f4556]) ).
thf(f4556,plain,
( ( $true = $false )
| ~ spl31_23
| ~ spl31_58
| ~ spl31_147 ),
inference(forward_demodulation,[],[f4536,f1866]) ).
thf(f4536,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),zero_zero_nat) = $true )
| ~ spl31_23
| ~ spl31_147 ),
inference(superposition,[],[f1469,f4498]) ).
thf(f4498,plain,
( ( zero_zero_nat = vAPP(nat,nat,suc,zero_zero_nat) )
| ~ spl31_147 ),
inference(avatar_component_clause,[],[f4496]) ).
thf(f4496,plain,
( spl31_147
<=> ( zero_zero_nat = vAPP(nat,nat,suc,zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_147])]) ).
thf(f4555,plain,
( ~ spl31_22
| ~ spl31_58
| ~ spl31_147 ),
inference(avatar_contradiction_clause,[],[f4554]) ).
thf(f4554,plain,
( $false
| ~ spl31_22
| ~ spl31_58
| ~ spl31_147 ),
inference(trivial_inequality_removal,[],[f4553]) ).
thf(f4553,plain,
( ( $true = $false )
| ~ spl31_22
| ~ spl31_58
| ~ spl31_147 ),
inference(forward_demodulation,[],[f4535,f1866]) ).
thf(f4535,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),zero_zero_nat) = $true )
| ~ spl31_22
| ~ spl31_147 ),
inference(superposition,[],[f1465,f4498]) ).
thf(f4552,plain,
( ~ spl31_5
| ~ spl31_147 ),
inference(avatar_contradiction_clause,[],[f4551]) ).
thf(f4551,plain,
( $false
| ~ spl31_5
| ~ spl31_147 ),
inference(trivial_inequality_removal,[],[f4533]) ).
thf(f4533,plain,
( ( zero_zero_nat != zero_zero_nat )
| ~ spl31_5
| ~ spl31_147 ),
inference(superposition,[],[f1383,f4498]) ).
thf(f1383,plain,
( ! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) )
| ~ spl31_5 ),
inference(avatar_component_clause,[],[f1382]) ).
thf(f1382,plain,
( spl31_5
<=> ! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_5])]) ).
thf(f4550,plain,
( ~ spl31_6
| ~ spl31_147 ),
inference(avatar_contradiction_clause,[],[f4549]) ).
thf(f4549,plain,
( $false
| ~ spl31_6
| ~ spl31_147 ),
inference(trivial_inequality_removal,[],[f4534]) ).
thf(f4534,plain,
( ( zero_zero_nat != zero_zero_nat )
| ~ spl31_6
| ~ spl31_147 ),
inference(superposition,[],[f1387,f4498]) ).
thf(f4526,plain,
( spl31_147
| spl31_149
| ~ spl31_21
| ~ spl31_34 ),
inference(avatar_split_clause,[],[f1582,f1562,f1460,f4524,f4496]) ).
thf(f4524,plain,
( spl31_149
<=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_149])]) ).
thf(f1562,plain,
( spl31_34
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_34])]) ).
thf(f1582,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = X0 )
| ( zero_zero_nat = vAPP(nat,nat,suc,zero_zero_nat) ) )
| ~ spl31_21
| ~ spl31_34 ),
inference(superposition,[],[f1563,f1461]) ).
thf(f1563,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_34 ),
inference(avatar_component_clause,[],[f1562]) ).
thf(f4502,plain,
( spl31_147
| spl31_148
| ~ spl31_21
| ~ spl31_33 ),
inference(avatar_split_clause,[],[f1576,f1558,f1460,f4500,f4496]) ).
thf(f4500,plain,
( spl31_148
<=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_148])]) ).
thf(f1576,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = X0 )
| ( zero_zero_nat = vAPP(nat,nat,suc,zero_zero_nat) ) )
| ~ spl31_21
| ~ spl31_33 ),
inference(superposition,[],[f1559,f1461]) ).
thf(f4494,plain,
( spl31_146
| ~ spl31_3
| ~ spl31_32 ),
inference(avatar_split_clause,[],[f1554,f1548,f1343,f4492]) ).
thf(f4492,plain,
( spl31_146
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_146])]) ).
thf(f1548,plain,
( spl31_32
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_32])]) ).
thf(f1554,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $false ) )
| ~ spl31_3
| ~ spl31_32 ),
inference(trivial_inequality_removal,[],[f1553]) ).
thf(f1553,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $false ) )
| ~ spl31_3
| ~ spl31_32 ),
inference(superposition,[],[f1549,f1344]) ).
thf(f1549,plain,
( ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 ) )
| ~ spl31_32 ),
inference(avatar_component_clause,[],[f1548]) ).
thf(f4454,plain,
( spl31_145
| ~ spl31_16
| ~ spl31_67 ),
inference(avatar_split_clause,[],[f1980,f1971,f1430,f4452]) ).
thf(f4452,plain,
( spl31_145
<=> ! [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,[spl31_145])]) ).
thf(f1430,plain,
( spl31_16
<=> ! [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,[spl31_16])]) ).
thf(f1971,plain,
( spl31_67
<=> ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK25,X1),X0)) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_67])]) ).
thf(f1980,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)) )
| ~ spl31_16
| ~ spl31_67 ),
inference(trivial_inequality_removal,[],[f1977]) ).
thf(f1977,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)) ) )
| ~ spl31_16
| ~ spl31_67 ),
inference(superposition,[],[f1972,f1431]) ).
thf(f1431,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true )
| ~ spl31_16 ),
inference(avatar_component_clause,[],[f1430]) ).
thf(f1972,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK25,X1),X0)) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) )
| ~ spl31_67 ),
inference(avatar_component_clause,[],[f1971]) ).
thf(f4450,plain,
( spl31_144
| ~ spl31_48 ),
inference(avatar_split_clause,[],[f1778,f1714,f4448]) ).
thf(f4448,plain,
( spl31_144
<=> ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_144])]) ).
thf(f1778,plain,
( ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl31_48 ),
inference(equality_proxy_clausification,[],[f1762]) ).
thf(f1762,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,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl31_48 ),
inference(leibniz_equality_elimination,[],[f1715]) ).
thf(f4441,plain,
( spl31_143
| ~ spl31_45 ),
inference(avatar_split_clause,[],[f1733,f1702,f4439]) ).
thf(f4439,plain,
( spl31_143
<=> ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_143])]) ).
thf(f1733,plain,
( ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl31_45 ),
inference(equality_proxy_clausification,[],[f1717]) ).
thf(f1717,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,sK5,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl31_45 ),
inference(leibniz_equality_elimination,[],[f1703]) ).
thf(f4435,plain,
( spl31_142
| ~ spl31_42 ),
inference(avatar_split_clause,[],[f1678,f1619,f4433]) ).
thf(f4433,plain,
( spl31_142
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( zero_zero_nat = X0 )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_142])]) ).
thf(f1678,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( zero_zero_nat = X0 )
| ( X0 != X1 ) )
| ~ spl31_42 ),
inference(equality_proxy_clausification,[],[f1677]) ).
thf(f1677,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_42 ),
inference(equality_proxy_clausification,[],[f1676]) ).
thf(f1676,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK16,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_42 ),
inference(equality_proxy_clausification,[],[f1671]) ).
thf(f1671,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),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_42 ),
inference(primitive_instantiation,[],[f1620]) ).
thf(f4431,plain,
( spl31_141
| ~ spl31_41 ),
inference(avatar_split_clause,[],[f1667,f1615,f4429]) ).
thf(f4429,plain,
( spl31_141
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_141])]) ).
thf(f1667,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 )
| ( zero_zero_nat != X0 ) )
| ~ spl31_41 ),
inference(equality_proxy_clausification,[],[f1666]) ).
thf(f1666,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK15,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl31_41 ),
inference(equality_proxy_clausification,[],[f1665]) ).
thf(f1665,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$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) ) )
| ~ spl31_41 ),
inference(equality_proxy_clausification,[],[f1660]) ).
thf(f1660,plain,
( ! [X0: nat,X1: 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) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl31_41 ),
inference(primitive_instantiation,[],[f1616]) ).
thf(f4427,plain,
( spl31_140
| ~ spl31_40 ),
inference(avatar_split_clause,[],[f1655,f1611,f4425]) ).
thf(f4425,plain,
( spl31_140
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_140])]) ).
thf(f1655,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( X0 = X1 ) )
| ~ spl31_40 ),
inference(equality_proxy_clausification,[],[f1654]) ).
thf(f1654,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$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) ) )
| ~ spl31_40 ),
inference(equality_proxy_clausification,[],[f1653]) ).
thf(f1653,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) ) )
| ~ spl31_40 ),
inference(equality_proxy_clausification,[],[f1648]) ).
thf(f1648,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,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_40 ),
inference(primitive_instantiation,[],[f1612]) ).
thf(f4423,plain,
( spl31_139
| ~ spl31_39 ),
inference(avatar_split_clause,[],[f1643,f1607,f4421]) ).
thf(f4421,plain,
( spl31_139
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_139])]) ).
thf(f1643,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 )
| ( X0 = X1 ) )
| ~ spl31_39 ),
inference(equality_proxy_clausification,[],[f1642]) ).
thf(f1642,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
| ( vAPP(sTfun(nat,$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) ) )
| ~ spl31_39 ),
inference(equality_proxy_clausification,[],[f1641]) ).
thf(f1641,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,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_39 ),
inference(equality_proxy_clausification,[],[f1636]) ).
thf(f1636,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,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_39 ),
inference(primitive_instantiation,[],[f1608]) ).
thf(f4419,plain,
( spl31_138
| ~ spl31_6
| ~ spl31_123 ),
inference(avatar_split_clause,[],[f3752,f2742,f1386,f4417]) ).
thf(f4417,plain,
( spl31_138
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,sK6,vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_138])]) ).
thf(f2742,plain,
( spl31_123
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK6,vAPP(nat,nat,suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_123])]) ).
thf(f3752,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,sK6,vAPP(nat,nat,suc,X0)) )
| ~ spl31_6
| ~ spl31_123 ),
inference(superposition,[],[f1387,f2743]) ).
thf(f2743,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK6,vAPP(nat,nat,suc,X0))) )
| ~ spl31_123 ),
inference(avatar_component_clause,[],[f2742]) ).
thf(f4415,plain,
( spl31_137
| ~ spl31_38 ),
inference(avatar_split_clause,[],[f1632,f1603,f4413]) ).
thf(f4413,plain,
( spl31_137
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 != X1 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_137])]) ).
thf(f1632,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 != X1 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_38 ),
inference(equality_proxy_clausification,[],[f1631]) ).
thf(f1631,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK5,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl31_38 ),
inference(equality_proxy_clausification,[],[f1630]) ).
thf(f1630,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK5,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) ) )
| ~ spl31_38 ),
inference(equality_proxy_clausification,[],[f1625]) ).
thf(f1625,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK5,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,$o),vEQ(nat),X0),zero_zero_nat) ) )
| ~ spl31_38 ),
inference(primitive_instantiation,[],[f1604]) ).
thf(f4350,plain,
( spl31_136
| ~ spl31_23
| ~ spl31_43 ),
inference(avatar_split_clause,[],[f1692,f1680,f1468,f4348]) ).
thf(f1680,plain,
( spl31_43
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$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) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_43])]) ).
thf(f1692,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))) )
| ~ spl31_23
| ~ spl31_43 ),
inference(trivial_inequality_removal,[],[f1689]) ).
thf(f1689,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,vAPP(nat,nat,suc,X0))) ) )
| ~ spl31_23
| ~ spl31_43 ),
inference(superposition,[],[f1681,f1469]) ).
thf(f1681,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$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)) = $true ) )
| ~ spl31_43 ),
inference(avatar_component_clause,[],[f1680]) ).
thf(f3795,plain,
( spl31_135
| ~ spl31_3
| ~ spl31_28 ),
inference(avatar_split_clause,[],[f1530,f1494,f1343,f3793]) ).
thf(f3793,plain,
( spl31_135
<=> ! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) )
| ( $false = vAPP(list_P1467822637od_a_a,$o,X0,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_135])]) ).
thf(f1494,plain,
( spl31_28
<=> ! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) )
| ( $true != vAPP(list_P1467822637od_a_a,$o,X0,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_28])]) ).
thf(f1530,plain,
( ! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) )
| ( $false = vAPP(list_P1467822637od_a_a,$o,X0,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0)) ) )
| ~ spl31_3
| ~ spl31_28 ),
inference(trivial_inequality_removal,[],[f1529]) ).
thf(f1529,plain,
( ! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ( $true != $true )
| ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) )
| ( $false = vAPP(list_P1467822637od_a_a,$o,X0,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0)) ) )
| ~ spl31_3
| ~ spl31_28 ),
inference(superposition,[],[f1495,f1344]) ).
thf(f1495,plain,
( ! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ( $true != vAPP(list_P1467822637od_a_a,$o,X0,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0)) )
| ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) ) )
| ~ spl31_28 ),
inference(avatar_component_clause,[],[f1494]) ).
thf(f3791,plain,
( spl31_134
| ~ spl31_3
| ~ spl31_27 ),
inference(avatar_split_clause,[],[f1522,f1490,f1343,f3789]) ).
thf(f3789,plain,
( spl31_134
<=> ! [X0: list_a > $o,X1: list_a] :
( ( $true = vAPP(list_a,$o,X0,X1) )
| ( $false = vAPP(list_a,$o,X0,vAPP(sTfun(list_a,$o),list_a,sK11,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_134])]) ).
thf(f1490,plain,
( spl31_27
<=> ! [X0: list_a > $o,X1: list_a] :
( ( $true = vAPP(list_a,$o,X0,X1) )
| ( $true != vAPP(list_a,$o,X0,vAPP(sTfun(list_a,$o),list_a,sK11,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_27])]) ).
thf(f1522,plain,
( ! [X0: list_a > $o,X1: list_a] :
( ( $true = vAPP(list_a,$o,X0,X1) )
| ( $false = vAPP(list_a,$o,X0,vAPP(sTfun(list_a,$o),list_a,sK11,X0)) ) )
| ~ spl31_3
| ~ spl31_27 ),
inference(trivial_inequality_removal,[],[f1521]) ).
thf(f1521,plain,
( ! [X0: list_a > $o,X1: list_a] :
( ( $true != $true )
| ( $true = vAPP(list_a,$o,X0,X1) )
| ( $false = vAPP(list_a,$o,X0,vAPP(sTfun(list_a,$o),list_a,sK11,X0)) ) )
| ~ spl31_3
| ~ spl31_27 ),
inference(superposition,[],[f1491,f1344]) ).
thf(f1491,plain,
( ! [X0: list_a > $o,X1: list_a] :
( ( $true != vAPP(list_a,$o,X0,vAPP(sTfun(list_a,$o),list_a,sK11,X0)) )
| ( $true = vAPP(list_a,$o,X0,X1) ) )
| ~ spl31_27 ),
inference(avatar_component_clause,[],[f1490]) ).
thf(f3787,plain,
( spl31_133
| ~ spl31_3
| ~ spl31_26 ),
inference(avatar_split_clause,[],[f1513,f1486,f1343,f3785]) ).
thf(f3785,plain,
( spl31_133
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK10,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_133])]) ).
thf(f1486,plain,
( spl31_26
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK10,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_26])]) ).
thf(f1513,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK10,X0)) ) )
| ~ spl31_3
| ~ spl31_26 ),
inference(trivial_inequality_removal,[],[f1512]) ).
thf(f1512,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK10,X0)) ) )
| ~ spl31_3
| ~ spl31_26 ),
inference(superposition,[],[f1487,f1344]) ).
thf(f1487,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK10,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_26 ),
inference(avatar_component_clause,[],[f1486]) ).
thf(f3783,plain,
( spl31_132
| ~ spl31_3
| ~ spl31_25 ),
inference(avatar_split_clause,[],[f1503,f1482,f1343,f3781]) ).
thf(f3781,plain,
( spl31_132
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_132])]) ).
thf(f1482,plain,
( spl31_25
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_25])]) ).
thf(f1503,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)) ) )
| ~ spl31_3
| ~ spl31_25 ),
inference(trivial_inequality_removal,[],[f1502]) ).
thf(f1502,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)) ) )
| ~ spl31_3
| ~ spl31_25 ),
inference(superposition,[],[f1483,f1344]) ).
thf(f1483,plain,
( ! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)) )
| ( $true = vAPP(nat,$o,X0,X1) ) )
| ~ spl31_25 ),
inference(avatar_component_clause,[],[f1482]) ).
thf(f3779,plain,
( spl31_131
| ~ spl31_20
| ~ spl31_23 ),
inference(avatar_split_clause,[],[f1476,f1468,f1450,f3777]) ).
thf(f3777,plain,
( spl31_131
<=> ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK4,X0)),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_131])]) ).
thf(f1476,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK4,X0)),X0) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_20
| ~ spl31_23 ),
inference(superposition,[],[f1469,f1451]) ).
thf(f3775,plain,
( spl31_130
| ~ spl31_18
| ~ spl31_23 ),
inference(avatar_split_clause,[],[f1475,f1468,f1442,f3773]) ).
thf(f3773,plain,
( spl31_130
<=> ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK3,X0)),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_130])]) ).
thf(f1475,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK3,X0)),X0) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_18
| ~ spl31_23 ),
inference(superposition,[],[f1469,f1443]) ).
thf(f3771,plain,
( spl31_129
| ~ spl31_17
| ~ spl31_23 ),
inference(avatar_split_clause,[],[f1474,f1468,f1438,f3769]) ).
thf(f3769,plain,
( spl31_129
<=> ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK2,X0)),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_129])]) ).
thf(f1474,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK2,X0)),X0) )
| ( zero_zero_nat = X0 ) )
| ~ spl31_17
| ~ spl31_23 ),
inference(superposition,[],[f1469,f1439]) ).
thf(f3767,plain,
spl31_128,
inference(avatar_split_clause,[],[f1269,f3765]) ).
thf(f3765,plain,
( spl31_128
<=> ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = $false )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_128])]) ).
thf(f1269,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = $false )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f1268]) ).
thf(f1268,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(binary_proxy_clausification,[],[f743]) ).
thf(f743,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ),
inference(cnf_transformation,[],[f218]) ).
thf(f218,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,zero_zero_nat)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,zero_zero_nat))
= ( zero_zero_nat = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_less__Suc0) ).
thf(f3745,plain,
( spl31_127
| ~ spl31_6
| ~ spl31_117 ),
inference(avatar_split_clause,[],[f3615,f2718,f1386,f3743]) ).
thf(f3743,plain,
( spl31_127
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK6,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_127])]) ).
thf(f2718,plain,
( spl31_117
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_117])]) ).
thf(f3615,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK6,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_6
| ~ spl31_117 ),
inference(superposition,[],[f1387,f2719]) ).
thf(f2719,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_117 ),
inference(avatar_component_clause,[],[f2718]) ).
thf(f3727,plain,
( spl31_126
| spl31_125
| ~ spl31_40 ),
inference(avatar_split_clause,[],[f1656,f1611,f2750,f3724]) ).
thf(f3724,plain,
( spl31_126
<=> ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_126])]) ).
thf(f1656,plain,
( ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK14,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) )
| ~ spl31_40 ),
inference(equality_proxy_clausification,[],[f1645]) ).
thf(f1645,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)) ) )
| ~ spl31_40 ),
inference(leibniz_equality_elimination,[],[f1612]) ).
thf(f2876,plain,
( ~ spl31_19
| ~ spl31_23
| ~ spl31_125 ),
inference(avatar_contradiction_clause,[],[f2875]) ).
thf(f2875,plain,
( $false
| ~ spl31_19
| ~ spl31_23
| ~ spl31_125 ),
inference(trivial_inequality_removal,[],[f2874]) ).
thf(f2874,plain,
( ( $true = $false )
| ~ spl31_19
| ~ spl31_23
| ~ spl31_125 ),
inference(forward_demodulation,[],[f2785,f2757]) ).
thf(f2757,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $false )
| ~ spl31_19
| ~ spl31_125 ),
inference(superposition,[],[f1447,f2751]) ).
thf(f2751,plain,
( ! [X0: nat] : ( zero_zero_nat = X0 )
| ~ spl31_125 ),
inference(avatar_component_clause,[],[f2750]) ).
thf(f2785,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) = $true )
| ~ spl31_23
| ~ spl31_125 ),
inference(superposition,[],[f1469,f2751]) ).
thf(f2873,plain,
( ~ spl31_19
| ~ spl31_22
| ~ spl31_125 ),
inference(avatar_contradiction_clause,[],[f2872]) ).
thf(f2872,plain,
( $false
| ~ spl31_19
| ~ spl31_22
| ~ spl31_125 ),
inference(trivial_inequality_removal,[],[f2871]) ).
thf(f2871,plain,
( ( $true = $false )
| ~ spl31_19
| ~ spl31_22
| ~ spl31_125 ),
inference(forward_demodulation,[],[f2784,f2757]) ).
thf(f2784,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),zero_zero_nat) = $true )
| ~ spl31_22
| ~ spl31_125 ),
inference(superposition,[],[f1465,f2751]) ).
thf(f2868,plain,
( ~ spl31_19
| ~ spl31_22
| ~ spl31_125 ),
inference(avatar_contradiction_clause,[],[f2867]) ).
thf(f2867,plain,
( $false
| ~ spl31_19
| ~ spl31_22
| ~ spl31_125 ),
inference(trivial_inequality_removal,[],[f2866]) ).
thf(f2866,plain,
( ( $true = $false )
| ~ spl31_19
| ~ spl31_22
| ~ spl31_125 ),
inference(forward_demodulation,[],[f2759,f2757]) ).
thf(f2759,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) = $true )
| ~ spl31_22
| ~ spl31_125 ),
inference(superposition,[],[f1465,f2751]) ).
thf(f2865,plain,
( ~ spl31_5
| ~ spl31_125 ),
inference(avatar_contradiction_clause,[],[f2864]) ).
thf(f2864,plain,
( $false
| ~ spl31_5
| ~ spl31_125 ),
inference(trivial_inequality_removal,[],[f2782]) ).
thf(f2782,plain,
( ( zero_zero_nat != zero_zero_nat )
| ~ spl31_5
| ~ spl31_125 ),
inference(superposition,[],[f1383,f2751]) ).
thf(f2752,plain,
( spl31_124
| spl31_125
| ~ spl31_39 ),
inference(avatar_split_clause,[],[f1644,f1607,f2750,f2746]) ).
thf(f2746,plain,
( spl31_124
<=> ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_124])]) ).
thf(f1644,plain,
( ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat = vAPP(sTfun(nat,$o),nat,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) )
| ~ spl31_39 ),
inference(equality_proxy_clausification,[],[f1633]) ).
thf(f1633,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,sK13,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat)) ) )
| ~ spl31_39 ),
inference(leibniz_equality_elimination,[],[f1608]) ).
thf(f2744,plain,
( spl31_123
| ~ spl31_22
| ~ spl31_32 ),
inference(avatar_split_clause,[],[f1556,f1548,f1464,f2742]) ).
thf(f1556,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK6,vAPP(nat,nat,suc,X0))) )
| ~ spl31_22
| ~ spl31_32 ),
inference(trivial_inequality_removal,[],[f1551]) ).
thf(f1551,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK6,vAPP(nat,nat,suc,X0))) ) )
| ~ spl31_22
| ~ spl31_32 ),
inference(superposition,[],[f1549,f1465]) ).
thf(f2740,plain,
( spl31_122
| ~ spl31_28 ),
inference(avatar_split_clause,[],[f1532,f1494,f2738]) ).
thf(f2738,plain,
( spl31_122
<=> ! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a] :
( ( vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,$o),vEQ(list_P1467822637od_a_a),X0)) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_122])]) ).
thf(f1532,plain,
( ! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a] :
( ( vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,$o),vEQ(list_P1467822637od_a_a),X0)) != X0 )
| ( X0 = X1 ) )
| ~ spl31_28 ),
inference(equality_proxy_clausification,[],[f1531]) ).
thf(f1531,plain,
( ! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a] :
( ( vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,$o),vEQ(list_P1467822637od_a_a),X0)) != X0 )
| ( $true = vAPP(list_P1467822637od_a_a,$o,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,$o),vEQ(list_P1467822637od_a_a),X0),X1) ) )
| ~ spl31_28 ),
inference(equality_proxy_clausification,[],[f1528]) ).
thf(f1528,plain,
( ! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a] :
( ( $true != vAPP(list_P1467822637od_a_a,$o,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,$o),vEQ(list_P1467822637od_a_a),X0),vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,$o),vEQ(list_P1467822637od_a_a),X0))) )
| ( $true = vAPP(list_P1467822637od_a_a,$o,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,$o),vEQ(list_P1467822637od_a_a),X0),X1) ) )
| ~ spl31_28 ),
inference(primitive_instantiation,[],[f1495]) ).
thf(f2736,plain,
( spl31_121
| ~ spl31_27 ),
inference(avatar_split_clause,[],[f1524,f1490,f2734]) ).
thf(f2734,plain,
( spl31_121
<=> ! [X0: list_a,X1: list_a] :
( ( vAPP(sTfun(list_a,$o),list_a,sK11,vAPP(list_a,sTfun(list_a,$o),vEQ(list_a),X0)) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_121])]) ).
thf(f1524,plain,
( ! [X0: list_a,X1: list_a] :
( ( vAPP(sTfun(list_a,$o),list_a,sK11,vAPP(list_a,sTfun(list_a,$o),vEQ(list_a),X0)) != X0 )
| ( X0 = X1 ) )
| ~ spl31_27 ),
inference(equality_proxy_clausification,[],[f1523]) ).
thf(f1523,plain,
( ! [X0: list_a,X1: list_a] :
( ( vAPP(sTfun(list_a,$o),list_a,sK11,vAPP(list_a,sTfun(list_a,$o),vEQ(list_a),X0)) != X0 )
| ( $true = vAPP(list_a,$o,vAPP(list_a,sTfun(list_a,$o),vEQ(list_a),X0),X1) ) )
| ~ spl31_27 ),
inference(equality_proxy_clausification,[],[f1520]) ).
thf(f1520,plain,
( ! [X0: list_a,X1: list_a] :
( ( $true != vAPP(list_a,$o,vAPP(list_a,sTfun(list_a,$o),vEQ(list_a),X0),vAPP(sTfun(list_a,$o),list_a,sK11,vAPP(list_a,sTfun(list_a,$o),vEQ(list_a),X0))) )
| ( $true = vAPP(list_a,$o,vAPP(list_a,sTfun(list_a,$o),vEQ(list_a),X0),X1) ) )
| ~ spl31_27 ),
inference(primitive_instantiation,[],[f1491]) ).
thf(f2732,plain,
( spl31_120
| ~ spl31_26 ),
inference(avatar_split_clause,[],[f1516,f1486,f2730]) ).
thf(f2730,plain,
( spl31_120
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK10,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_120])]) ).
thf(f1516,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK10,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) )
| ~ spl31_26 ),
inference(equality_proxy_clausification,[],[f1515]) ).
thf(f1515,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK10,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_26 ),
inference(equality_proxy_clausification,[],[f1510]) ).
thf(f1510,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK10,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_26 ),
inference(primitive_instantiation,[],[f1487]) ).
thf(f2728,plain,
( spl31_119
| ~ spl31_25 ),
inference(avatar_split_clause,[],[f1506,f1482,f2726]) ).
thf(f2726,plain,
( spl31_119
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK9,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_119])]) ).
thf(f1506,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK9,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( X0 = X1 ) )
| ~ spl31_25 ),
inference(equality_proxy_clausification,[],[f1505]) ).
thf(f1505,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK9,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_25 ),
inference(equality_proxy_clausification,[],[f1500]) ).
thf(f1500,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK9,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl31_25 ),
inference(primitive_instantiation,[],[f1483]) ).
thf(f2724,plain,
spl31_118,
inference(avatar_split_clause,[],[f1183,f2722]) ).
thf(f1183,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( zero_zero_nat = X1 )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f1182]) ).
thf(f1182,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( zero_zero_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(equality_proxy_clausification,[],[f1181]) ).
thf(f1181,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(binary_proxy_clausification,[],[f1180]) ).
thf(f1180,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(equality_proxy_clausification,[],[f1179]) ).
thf(f1179,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),times_times_nat,X0),X1)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(binary_proxy_clausification,[],[f780]) ).
thf(f2720,plain,
( spl31_117
| ~ spl31_32
| ~ spl31_107 ),
inference(avatar_split_clause,[],[f2697,f2507,f1548,f2718]) ).
thf(f2507,plain,
( spl31_107
<=> ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_107])]) ).
thf(f2697,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_32
| ~ spl31_107 ),
inference(trivial_inequality_removal,[],[f2621]) ).
thf(f2621,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_32
| ~ spl31_107 ),
inference(superposition,[],[f1549,f2508]) ).
thf(f2508,plain,
( ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
| ( zero_zero_nat = X0 ) )
| ~ spl31_107 ),
inference(avatar_component_clause,[],[f2507]) ).
thf(f2706,plain,
( spl31_116
| ~ spl31_23
| ~ spl31_35 ),
inference(avatar_split_clause,[],[f1594,f1566,f1468,f2704]) ).
thf(f2704,plain,
( spl31_116
<=> ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_116])]) ).
thf(f1566,plain,
( spl31_35
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_35])]) ).
thf(f1594,plain,
( ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,X0)) )
| ~ spl31_23
| ~ spl31_35 ),
inference(trivial_inequality_removal,[],[f1591]) ).
thf(f1591,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,suc,X0)) ) )
| ~ spl31_23
| ~ spl31_35 ),
inference(superposition,[],[f1567,f1469]) ).
thf(f1567,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
| ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) ) )
| ~ spl31_35 ),
inference(avatar_component_clause,[],[f1566]) ).
thf(f2611,plain,
spl31_115,
inference(avatar_split_clause,[],[f716,f2608]) ).
thf(f2608,plain,
( spl31_115
<=> ( ord_less_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(nat,sTfun(nat,sTfun($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,vIMP)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,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,[spl31_115])]) ).
thf(f716,plain,
ord_less_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),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,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat))))),vAPP(sTfun(nat,sTfun(nat,$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,$o)),bCOMB,vNOT)),vEQ(nat)))),
inference(cnf_transformation,[],[f201]) ).
thf(f201,plain,
ord_less_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(nat,sTfun(nat,sTfun($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,vIMP)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,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,[],[f200]) ).
thf(f200,plain,
( ord_less_nat
= ( ^ [X0: nat,X1: nat] :
! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0)
=> ( X1 != X2 ) ) ) ),
inference(rectify,[],[f170]) ).
thf(f170,axiom,
( ord_less_nat
= ( ^ [X33: nat,X41: nat] :
! [X42: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X42),X33)
=> ( X41 != X42 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_greater__le__neq__conv) ).
thf(f2606,plain,
spl31_114,
inference(avatar_split_clause,[],[f713,f2603]) ).
thf(f2603,plain,
( spl31_114
<=> ( ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),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,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_nat))))),vAPP(sTfun(nat,sTfun(nat,$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,$o)),bCOMB,vNOT)),vEQ(nat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_114])]) ).
thf(f713,plain,
ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(nat,sTfun(nat,sTfun($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,vIMP)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_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,[],[f195]) ).
thf(f195,plain,
ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),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,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_nat))))),vAPP(sTfun(nat,sTfun(nat,$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,$o)),bCOMB,vNOT)),vEQ(nat)))),
inference(fool_elimination,[],[f194]) ).
thf(f194,plain,
( ord_less_eq_nat
= ( ^ [X0: nat,X1: nat] :
! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0)
=> ( X1 != X2 ) ) ) ),
inference(rectify,[],[f168]) ).
thf(f168,axiom,
( ord_less_eq_nat
= ( ^ [X33: nat,X41: nat] :
! [X42: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X42),X33)
=> ( X41 != X42 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_ge__less__neq__conv) ).
thf(f2585,plain,
spl31_113,
inference(avatar_split_clause,[],[f715,f2582]) ).
thf(f2582,plain,
( spl31_113
<=> ( ord_less_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),cCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($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,vIMP)),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,[spl31_113])]) ).
thf(f715,plain,
ord_less_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),cCOMB,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,$o))),bCOMB,vIMP)),ord_less_eq_nat)))),vAPP(sTfun(nat,sTfun(nat,$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,$o)),bCOMB,vNOT)),vEQ(nat)))),
inference(cnf_transformation,[],[f199]) ).
thf(f199,plain,
ord_less_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),cCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($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,vIMP)),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,[],[f198]) ).
thf(f198,plain,
( ord_less_nat
= ( ^ [X0: nat,X1: nat] :
! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( X0 != X2 ) ) ) ),
inference(rectify,[],[f169]) ).
thf(f169,axiom,
( ord_less_nat
= ( ^ [X41: nat,X33: nat] :
! [X42: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X33),X42)
=> ( X41 != X42 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_less__ge__neq__conv) ).
thf(f2580,plain,
spl31_112,
inference(avatar_split_clause,[],[f712,f2577]) ).
thf(f2577,plain,
( spl31_112
<=> ( ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),cCOMB,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,$o))),bCOMB,vIMP)),ord_less_nat)))),vAPP(sTfun(nat,sTfun(nat,$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,$o)),bCOMB,vNOT)),vEQ(nat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_112])]) ).
thf(f712,plain,
ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),cCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($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,vIMP)),ord_less_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,[],[f193]) ).
thf(f193,plain,
ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),cCOMB,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,$o))),bCOMB,vIMP)),ord_less_nat)))),vAPP(sTfun(nat,sTfun(nat,$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,$o)),bCOMB,vNOT)),vEQ(nat)))),
inference(fool_elimination,[],[f192]) ).
thf(f192,plain,
( ord_less_eq_nat
= ( ^ [X0: nat,X1: nat] :
! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( X0 != X2 ) ) ) ),
inference(rectify,[],[f171]) ).
thf(f171,axiom,
( ord_less_eq_nat
= ( ^ [X41: nat,X33: nat] :
! [X42: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X33),X42)
=> ( X41 != X42 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_le__greater__neq__conv) ).
thf(f2568,plain,
spl31_111,
inference(avatar_split_clause,[],[f886,f2566]) ).
thf(f2566,plain,
( spl31_111
<=> ! [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,sK19,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK20,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,sK21,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK22,X0)),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_111])]) ).
thf(f886,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,sK19,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK20,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,sK21,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK22,X0)),zero_zero_nat) ) ),
inference(cnf_transformation,[],[f692]) ).
thf(f692,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,sK19,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK20,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK20,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,sK21,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK22,X0)),zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22])],[f688,f691,f690,f689]) ).
thf(f689,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,sK19,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK20,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK20,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f690,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,sK21,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f691,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,sK22,X0)),zero_zero_nat) ) ),
introduced(choice_axiom,[]) ).
thf(f688,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,[],[f609]) ).
thf(f609,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,[],[f608]) ).
thf(f608,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,[],[f405]) ).
thf(f405,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,[],[f404]) ).
thf(f404,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,[],[f47]) ).
thf(f47,axiom,
! [X12: nat > nat > $o,X1: nat,X0: nat] :
( ! [X19: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X19),zero_zero_nat)
=> ( ! [X20: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,zero_zero_nat),vAPP(nat,nat,suc,X20))
=> ( ! [X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X19),X20)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,vAPP(nat,nat,suc,X19)),vAPP(nat,nat,suc,X20)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_diff__induct) ).
thf(f2553,plain,
spl31_110,
inference(avatar_split_clause,[],[f885,f2551]) ).
thf(f2551,plain,
( spl31_110
<=> ! [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,sK19,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK20,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,sK21,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK22,X0)),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_110])]) ).
thf(f885,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,sK19,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK20,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,sK21,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK22,X0)),zero_zero_nat) ) ),
inference(cnf_transformation,[],[f692]) ).
thf(f2523,plain,
spl31_109,
inference(avatar_split_clause,[],[f888,f2521]) ).
thf(f2521,plain,
( spl31_109
<=> ! [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,sK24,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK24,X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_109])]) ).
thf(f888,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,sK24,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK24,X0)))) ) ),
inference(cnf_transformation,[],[f696]) ).
thf(f696,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,sK24,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK24,X0)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f612,f695]) ).
thf(f695,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,sK24,X0))),vAPP(nat,nat,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,nat),nat,sK24,X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f612,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,[],[f611]) ).
thf(f611,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,[],[f409]) ).
thf(f409,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,$o),ord_less_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ) ),
inference(fool_elimination,[],[f408]) ).
thf(f408,plain,
! [X0: nat > nat,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(nat,$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,$o),ord_less_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
! [X29: nat > nat,X0: nat,X30: nat] :
( ! [X13: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X29,X13)),vAPP(nat,nat,X29,vAPP(nat,nat,suc,X13)))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X30)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X29,X0)),vAPP(nat,nat,X29,X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_lift__Suc__mono__less) ).
thf(f2513,plain,
spl31_108,
inference(avatar_split_clause,[],[f909,f2511]) ).
thf(f2511,plain,
( spl31_108
<=> ! [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,sK30,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X2))) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_108])]) ).
thf(f909,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,sK30,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X2))) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f708]) ).
thf(f708,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,sK30,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X2))) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f652,f707]) ).
thf(f707,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,sK30,X2)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X2))) ) ),
introduced(choice_axiom,[]) ).
thf(f652,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,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(definition_folding,[],[f630,f651]) ).
thf(f651,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(f630,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,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(flattening,[],[f629]) ).
thf(f629,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,$o),X2,X3),vAPP(nat,nat,suc,X3)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f433]) ).
thf(f433,plain,
! [X0: nat,X1: nat,X2: nat > nat > $o] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( ! [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,[],[f432]) ).
thf(f432,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,[],[f62]) ).
thf(f62,axiom,
! [X21: nat,X22: nat,X12: nat > nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X21),X22)
=> ( ! [X23: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X23),vAPP(nat,nat,suc,X23))
=> ( ! [X23: nat,X24: nat,X25: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X23),X24)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X24),X25)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X23),X24)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X24),X25)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X23),X25) ) ) ) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X12,X21),X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_less__Suc__induct) ).
thf(f2509,plain,
spl31_107,
inference(avatar_split_clause,[],[f1317,f2507]) ).
thf(f1317,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f1316]) ).
thf(f1316,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(not_proxy_clausification,[],[f1312]) ).
thf(f1312,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ) ),
inference(binary_proxy_clausification,[],[f734]) ).
thf(f734,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ),
inference(cnf_transformation,[],[f205]) ).
thf(f205,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)) ),
inference(fool_elimination,[],[f204]) ).
thf(f204,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
! [X7: nat] :
( ( zero_zero_nat != X7 )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_bot__nat__0_Onot__eq__extremum) ).
thf(f2499,plain,
spl31_106,
inference(avatar_split_clause,[],[f853,f2497]) ).
thf(f2497,plain,
( spl31_106
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_106])]) ).
thf(f853,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) != $true ) ),
inference(cnf_transformation,[],[f592]) ).
thf(f592,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) != $true ) ),
inference(flattening,[],[f591]) ).
thf(f591,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) != $true ) ),
inference(ennf_transformation,[],[f365]) ).
thf(f365,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) = $true )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true ) ) ),
inference(fool_elimination,[],[f364]) ).
thf(f364,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) ) ),
inference(rectify,[],[f97]) ).
thf(f97,axiom,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_one__less__mult) ).
thf(f2457,plain,
spl31_105,
inference(avatar_split_clause,[],[f1331,f2455]) ).
thf(f2455,plain,
( spl31_105
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_105])]) ).
thf(f1331,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(trivial_inequality_removal,[],[f1330]) ).
thf(f1330,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(forward_demodulation,[],[f1329,f764]) ).
thf(f764,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true ),
inference(cnf_transformation,[],[f245]) ).
thf(f245,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true ),
inference(fool_elimination,[],[f244]) ).
thf(f244,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0),
inference(rectify,[],[f167]) ).
thf(f167,axiom,
! [X10: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_zero__le) ).
thf(f1329,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(trivial_inequality_removal,[],[f1328]) ).
thf(f1328,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(forward_demodulation,[],[f918,f764]) ).
thf(f918,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) )
| ( $true != vAPP(nat,$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,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f646]) ).
thf(f646,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) )
| ( $true != vAPP(nat,$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,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(flattening,[],[f645]) ).
thf(f645,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) )
| ( $true != vAPP(nat,$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,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f451]) ).
thf(f451,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) ) ) ) ) ),
inference(fool_elimination,[],[f450]) ).
thf(f450,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) ) ) ) ),
inference(rectify,[],[f182]) ).
thf(f182,axiom,
! [X7: nat,X9: nat,X8: nat,X43: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X9)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X8),X43)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X7)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X8)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X8)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X9),X43)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_mult__mono_H) ).
thf(f2453,plain,
spl31_104,
inference(avatar_split_clause,[],[f911,f2451]) ).
thf(f2451,plain,
( spl31_104
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_104])]) ).
thf(f911,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f634]) ).
thf(f634,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(flattening,[],[f633]) ).
thf(f633,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f437]) ).
thf(f437,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ) ) ),
inference(fool_elimination,[],[f436]) ).
thf(f436,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ) ),
inference(rectify,[],[f121]) ).
thf(f121,axiom,
! [X7: nat,X9: nat,X8: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X7),X9)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X8)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X8)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X9),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_mult__strict__right__mono) ).
thf(f2449,plain,
spl31_103,
inference(avatar_split_clause,[],[f910,f2447]) ).
thf(f2447,plain,
( spl31_103
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_103])]) ).
thf(f910,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f632]) ).
thf(f632,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(flattening,[],[f631]) ).
thf(f631,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f435]) ).
thf(f435,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(fool_elimination,[],[f434]) ).
thf(f434,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(rectify,[],[f120]) ).
thf(f120,axiom,
! [X7: nat,X9: nat,X8: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X7),X9)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X8)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X8),X7)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X8),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_mult__strict__left__mono) ).
thf(f2445,plain,
spl31_102,
inference(avatar_split_clause,[],[f895,f2443]) ).
thf(f2443,plain,
( spl31_102
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_102])]) ).
thf(f895,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f620]) ).
thf(f620,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f619]) ).
thf(f619,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f423]) ).
thf(f423,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$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),divide_divide_nat,X1),X0)),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ) ),
inference(fool_elimination,[],[f422]) ).
thf(f422,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ),
inference(rectify,[],[f127]) ).
thf(f127,axiom,
! [X1: nat,X0: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_div__less__imp__less__mult) ).
thf(f2441,plain,
spl31_101,
inference(avatar_split_clause,[],[f1283,f2439]) ).
thf(f2439,plain,
( spl31_101
<=> ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $true )
| ( zero_zero_nat != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_101])]) ).
thf(f1283,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $true )
| ( zero_zero_nat != X0 ) ),
inference(equality_proxy_clausification,[],[f1280]) ).
thf(f1280,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(binary_proxy_clausification,[],[f741]) ).
thf(f741,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ),
inference(cnf_transformation,[],[f216]) ).
thf(f216,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ),
inference(fool_elimination,[],[f159]) ).
thf(f159,axiom,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat)
= ( zero_zero_nat = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_le__zero__eq) ).
thf(f2410,plain,
spl31_100,
inference(avatar_split_clause,[],[f903,f2408]) ).
thf(f2408,plain,
( spl31_100
<=> ! [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,$o),sTfun(nat,nat),sK26,X2),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_100])]) ).
thf(f903,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,$o),sTfun(nat,nat),sK26,X2),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f702]) ).
thf(f702,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,$o),sTfun(nat,nat),sK26,X2),X1)) )
& ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK26,X2),X1)) = X1 ) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f650,f701]) ).
thf(f701,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,$o),sTfun(nat,nat),sK26,X2),X1)) )
& ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK26,X2),X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f650,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 ) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(definition_folding,[],[f628,f649]) ).
thf(f649,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(f628,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 ) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(flattening,[],[f627]) ).
thf(f627,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 ) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f431]) ).
thf(f431,plain,
! [X0: nat,X1: nat,X2: nat > $o] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( ! [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,[],[f430]) ).
thf(f430,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,[],[f61]) ).
thf(f61,axiom,
! [X21: nat,X22: nat,X12: nat > $o] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X21),X22)
=> ( ! [X23: nat] :
( ( vAPP(nat,nat,suc,X23) = X22 )
=> vAPP(nat,$o,X12,X23) )
=> ( ! [X23: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X23),X22)
=> ( vAPP(nat,$o,X12,vAPP(nat,nat,suc,X23))
=> vAPP(nat,$o,X12,X23) ) )
=> vAPP(nat,$o,X12,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_strict__inc__induct) ).
thf(f2406,plain,
spl31_99,
inference(avatar_split_clause,[],[f902,f2404]) ).
thf(f2404,plain,
( spl31_99
<=> ! [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),sK26,X2),X1)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_99])]) ).
thf(f902,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),sK26,X2),X1)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f702]) ).
thf(f2402,plain,
spl31_98,
inference(avatar_split_clause,[],[f891,f2400]) ).
thf(f2400,plain,
( spl31_98
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_98])]) ).
thf(f891,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f615]) ).
thf(f615,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f415]) ).
thf(f415,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(fool_elimination,[],[f414]) ).
thf(f414,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(rectify,[],[f98]) ).
thf(f98,axiom,
! [X2: nat,X1: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_nat__mult__div__cancel1) ).
thf(f2386,plain,
spl31_97,
inference(avatar_split_clause,[],[f838,f2384]) ).
thf(f2384,plain,
( spl31_97
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_97])]) ).
thf(f838,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f573]) ).
thf(f573,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f572]) ).
thf(f572,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f337]) ).
thf(f337,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) = $true )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) = $true ) ) ),
inference(fool_elimination,[],[f336]) ).
thf(f336,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(rectify,[],[f95]) ).
thf(f95,axiom,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_n__less__n__mult__m) ).
thf(f2382,plain,
spl31_96,
inference(avatar_split_clause,[],[f837,f2380]) ).
thf(f2380,plain,
( spl31_96
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_96])]) ).
thf(f837,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f571]) ).
thf(f571,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f570]) ).
thf(f570,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f335]) ).
thf(f335,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1) = $true )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = $true ) ) ),
inference(fool_elimination,[],[f334]) ).
thf(f334,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) ) ),
inference(rectify,[],[f96]) ).
thf(f96,axiom,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,zero_zero_nat)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_n__less__m__mult__n) ).
thf(f2378,plain,
spl31_95,
inference(avatar_split_clause,[],[f1282,f2376]) ).
thf(f2376,plain,
( spl31_95
<=> ! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $false )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_95])]) ).
thf(f1282,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $false )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f1281]) ).
thf(f1281,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(binary_proxy_clausification,[],[f741]) ).
thf(f2366,plain,
spl31_94,
inference(avatar_split_clause,[],[f839,f2364]) ).
thf(f2364,plain,
( spl31_94
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0))),X0)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_94])]) ).
thf(f839,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0))),X0)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f574]) ).
thf(f574,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0))),X0)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f339]) ).
thf(f339,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0))),X0)) ) ),
inference(fool_elimination,[],[f338]) ).
thf(f338,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0))),X0)) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X1: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1))),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_less__div__Suc__mult) ).
thf(f2330,plain,
spl31_93,
inference(avatar_split_clause,[],[f860,f2328]) ).
thf(f2328,plain,
( spl31_93
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_93])]) ).
thf(f860,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(cnf_transformation,[],[f601]) ).
thf(f601,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(flattening,[],[f600]) ).
thf(f600,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(ennf_transformation,[],[f377]) ).
thf(f377,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true ) ) ),
inference(fool_elimination,[],[f376]) ).
thf(f376,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(rectify,[],[f119]) ).
thf(f119,axiom,
! [X9: nat,X7: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X9),X7))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X7)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_zero__less__mult__pos2) ).
thf(f2326,plain,
spl31_92,
inference(avatar_split_clause,[],[f859,f2324]) ).
thf(f2324,plain,
( spl31_92
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_92])]) ).
thf(f859,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(cnf_transformation,[],[f599]) ).
thf(f599,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(flattening,[],[f598]) ).
thf(f598,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(ennf_transformation,[],[f375]) ).
thf(f375,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true ) ) ),
inference(fool_elimination,[],[f374]) ).
thf(f374,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(rectify,[],[f118]) ).
thf(f118,axiom,
! [X7: nat,X9: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X9))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X7)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_zero__less__mult__pos) ).
thf(f2322,plain,
spl31_91,
inference(avatar_split_clause,[],[f834,f2320]) ).
thf(f2320,plain,
( spl31_91
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_91])]) ).
thf(f834,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f565]) ).
thf(f565,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(flattening,[],[f564]) ).
thf(f564,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f329]) ).
thf(f329,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ) ),
inference(fool_elimination,[],[f328]) ).
thf(f328,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(rectify,[],[f116]) ).
thf(f116,axiom,
! [X7: nat,X9: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X7)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X9)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_mult__pos__pos) ).
thf(f2235,plain,
spl31_90,
inference(avatar_split_clause,[],[f1327,f2233]) ).
thf(f2233,plain,
( spl31_90
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_90])]) ).
thf(f1327,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(trivial_inequality_removal,[],[f1326]) ).
thf(f1326,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(forward_demodulation,[],[f897,f764]) ).
thf(f897,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),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f624]) ).
thf(f624,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),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(flattening,[],[f623]) ).
thf(f623,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),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f427]) ).
thf(f427,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ) ) ),
inference(fool_elimination,[],[f426]) ).
thf(f426,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ) ),
inference(rectify,[],[f180]) ).
thf(f180,axiom,
! [X7: nat,X9: nat,X8: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X9)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X8)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X8)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X9),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_mult__right__mono) ).
thf(f2231,plain,
spl31_89,
inference(avatar_split_clause,[],[f1325,f2229]) ).
thf(f2229,plain,
( spl31_89
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_89])]) ).
thf(f1325,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(trivial_inequality_removal,[],[f1324]) ).
thf(f1324,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(forward_demodulation,[],[f896,f764]) ).
thf(f896,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),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f622]) ).
thf(f622,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),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(flattening,[],[f621]) ).
thf(f621,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),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f425]) ).
thf(f425,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(fool_elimination,[],[f424]) ).
thf(f424,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(rectify,[],[f174]) ).
thf(f174,axiom,
! [X7: nat,X9: nat,X8: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X9)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X8)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X8),X7)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X8),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_ordered__comm__semiring__class_Ocomm__mult__left__mono) ).
thf(f2227,plain,
spl31_88,
inference(avatar_split_clause,[],[f916,f2225]) ).
thf(f916,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),divide_divide_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f643]) ).
thf(f643,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),divide_divide_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f447]) ).
thf(f447,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X2)),X1) ) ),
inference(fool_elimination,[],[f446]) ).
thf(f446,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X2)),X1) ),
inference(rectify,[],[f94]) ).
thf(f94,axiom,
! [X1: nat,X21: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X21),X0))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Euclidean__Division_Oless__mult__imp__div__less) ).
thf(f2223,plain,
spl31_87,
inference(avatar_split_clause,[],[f881,f2221]) ).
thf(f881,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f604]) ).
thf(f604,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f514]) ).
thf(f514,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( zero_zero_nat != X0 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ),
inference(rectify,[],[f26]) ).
thf(f26,axiom,
! [X8: nat,X7: nat,X9: nat] :
( ( zero_zero_nat != X8 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X7),X9) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X8)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X9),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_div__mult__mult2) ).
thf(f2219,plain,
spl31_86,
inference(avatar_split_clause,[],[f878,f2217]) ).
thf(f878,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f602]) ).
thf(f602,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( zero_zero_nat = X0 ) )
& ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( zero_zero_nat != X0 ) ) ),
inference(ennf_transformation,[],[f512]) ).
thf(f512,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( zero_zero_nat != X0 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) )
& ( ( zero_zero_nat = X0 )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X2: nat,X1: nat,X0: nat] :
( ( ( zero_zero_nat != X2 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0) ) )
& ( ( zero_zero_nat = X2 )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_nat__mult__div__cancel__disj) ).
thf(f2213,plain,
spl31_85,
inference(avatar_split_clause,[],[f899,f2211]) ).
thf(f2211,plain,
( spl31_85
<=> ! [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),sK25,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,[spl31_85])]) ).
thf(f899,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),sK25,X1),X0)),X1) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f700]) ).
thf(f700,plain,
! [X0: nat > $o,X1: nat] :
( ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK25,X1),X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK25,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),sK25,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,[sK25])],[f698,f699]) ).
thf(f699,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),sK25,X1),X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK25,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),sK25,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f698,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,[],[f697]) ).
thf(f697,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,[],[f649]) ).
thf(f2110,plain,
spl31_84,
inference(avatar_split_clause,[],[f915,f2108]) ).
thf(f2108,plain,
( spl31_84
<=> ! [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,$o),ord_less_nat,X1),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_84])]) ).
thf(f915,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,$o),ord_less_nat,X1),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f642]) ).
thf(f642,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,$o),ord_less_nat,X1),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(flattening,[],[f641]) ).
thf(f641,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,$o),ord_less_nat,X1),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f445]) ).
thf(f445,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X2) ) ) ),
inference(fool_elimination,[],[f444]) ).
thf(f444,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$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,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X2) ) ),
inference(rectify,[],[f63]) ).
thf(f63,axiom,
! [X21: nat,X22: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X21),X22)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X22),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X21)),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_less__trans__Suc) ).
thf(f2106,plain,
spl31_83,
inference(avatar_split_clause,[],[f863,f2104]) ).
thf(f2104,plain,
( spl31_83
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_83])]) ).
thf(f863,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) ),
inference(cnf_transformation,[],[f509]) ).
thf(f509,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) ),
inference(rectify,[],[f135]) ).
thf(f135,axiom,
! [X7: nat,X9: nat,X8: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X9),X8)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X9)),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_mult_Oassoc) ).
thf(f2102,plain,
spl31_82,
inference(avatar_split_clause,[],[f862,f2100]) ).
thf(f2100,plain,
( spl31_82
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_82])]) ).
thf(f862,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(cnf_transformation,[],[f508]) ).
thf(f508,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(rectify,[],[f133]) ).
thf(f133,axiom,
! [X9: nat,X7: nat,X8: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X9),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X8)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X9),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_mult_Oleft__commute) ).
thf(f2098,plain,
spl31_81,
inference(avatar_split_clause,[],[f861,f2096]) ).
thf(f861,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X2) ),
inference(cnf_transformation,[],[f507]) ).
thf(f507,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1)),X2) ),
inference(rectify,[],[f80]) ).
thf(f80,axiom,
! [X1: nat,X0: nat,X28: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X28)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0)),X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_div__mult2__eq) ).
thf(f2094,plain,
spl31_80,
inference(avatar_split_clause,[],[f847,f2092]) ).
thf(f2092,plain,
( spl31_80
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_80])]) ).
thf(f847,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f685]) ).
thf(f685,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) ) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f585,f684]) ).
thf(f684,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),sK17,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f585,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,suc,X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(flattening,[],[f584]) ).
thf(f584,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,suc,X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f355]) ).
thf(f355,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( ( vAPP(nat,nat,suc,X0) != X1 )
=> ~ ! [X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
=> ( vAPP(nat,nat,suc,X2) != X1 ) ) ) ),
inference(fool_elimination,[],[f354]) ).
thf(f354,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$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,$o),ord_less_nat,X0),X2)
=> ( vAPP(nat,nat,suc,X2) != X1 ) ) ) ),
inference(rectify,[],[f76]) ).
thf(f76,axiom,
! [X21: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X21),X2)
=> ( ( vAPP(nat,nat,suc,X21) != X2 )
=> ~ ! [X24: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X21),X24)
=> ( vAPP(nat,nat,suc,X24) != X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Nat_OlessE) ).
thf(f2090,plain,
spl31_79,
inference(avatar_split_clause,[],[f1218,f2088]) ).
thf(f2088,plain,
( spl31_79
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_79])]) ).
thf(f1218,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) ) ),
inference(equality_proxy_clausification,[],[f1217]) ).
thf(f1217,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(equality_proxy_clausification,[],[f1213]) ).
thf(f1213,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,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(binary_proxy_clausification,[],[f776]) ).
thf(f776,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(cnf_transformation,[],[f257]) ).
thf(f257,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(fool_elimination,[],[f256]) ).
thf(f256,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f14]) ).
thf(f14,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_13_nat_Oinject) ).
thf(f2084,plain,
spl31_78,
inference(avatar_split_clause,[],[f900,f2082]) ).
thf(f2082,plain,
( spl31_78
<=> ! [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),sK25,X1),X0))) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_78])]) ).
thf(f900,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),sK25,X1),X0))) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f700]) ).
thf(f2072,plain,
spl31_77,
inference(avatar_split_clause,[],[f817,f2070]) ).
thf(f2070,plain,
( spl31_77
<=> ! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a,X3: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) )
| ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X3)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_77])]) ).
thf(f817,plain,
! [X3: list_P1467822637od_a_a,X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) )
| ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X3)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0))) ) ),
inference(cnf_transformation,[],[f675]) ).
thf(f675,plain,
! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) )
| ( ( $true != vAPP(list_P1467822637od_a_a,$o,X0,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0)) )
& ! [X3: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X3)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0))) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f546,f674]) ).
thf(f674,plain,
! [X0: list_P1467822637od_a_a > $o] :
( ? [X2: list_P1467822637od_a_a] :
( ( $true != vAPP(list_P1467822637od_a_a,$o,X0,X2) )
& ! [X3: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X3)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X2)) ) ) )
=> ( ( $true != vAPP(list_P1467822637od_a_a,$o,X0,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0)) )
& ! [X3: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X3)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0))) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f546,plain,
! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) )
| ? [X2: list_P1467822637od_a_a] :
( ( $true != vAPP(list_P1467822637od_a_a,$o,X0,X2) )
& ! [X3: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X3)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X2)) ) ) ) ),
inference(ennf_transformation,[],[f307]) ).
thf(f307,plain,
! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ! [X2: list_P1467822637od_a_a] :
( ! [X3: list_P1467822637od_a_a] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X3)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X2)) )
=> ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X3) ) )
=> ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X2) ) )
=> ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) ) ),
inference(fool_elimination,[],[f306]) ).
thf(f306,plain,
! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ! [X2: list_P1467822637od_a_a] :
( ! [X3: list_P1467822637od_a_a] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X3)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X2))
=> vAPP(list_P1467822637od_a_a,$o,X0,X3) )
=> vAPP(list_P1467822637od_a_a,$o,X0,X2) )
=> vAPP(list_P1467822637od_a_a,$o,X0,X1) ),
inference(rectify,[],[f144]) ).
thf(f144,axiom,
! [X12: list_P1467822637od_a_a > $o,X35: list_P1467822637od_a_a] :
( ! [X36: list_P1467822637od_a_a] :
( ! [X37: list_P1467822637od_a_a] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X37)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X36))
=> vAPP(list_P1467822637od_a_a,$o,X12,X37) )
=> vAPP(list_P1467822637od_a_a,$o,X12,X36) )
=> vAPP(list_P1467822637od_a_a,$o,X12,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_length__induct) ).
thf(f2068,plain,
spl31_76,
inference(avatar_split_clause,[],[f815,f2066]) ).
thf(f2066,plain,
( spl31_76
<=> ! [X0: list_a > $o,X1: list_a,X3: list_a] :
( ( $true = vAPP(list_a,$o,X0,X1) )
| ( $true = vAPP(list_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,X3)),vAPP(list_a,nat,size_size_list_a,vAPP(sTfun(list_a,$o),list_a,sK11,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_76])]) ).
thf(f815,plain,
! [X3: list_a,X0: list_a > $o,X1: list_a] :
( ( $true = vAPP(list_a,$o,X0,X1) )
| ( $true = vAPP(list_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,X3)),vAPP(list_a,nat,size_size_list_a,vAPP(sTfun(list_a,$o),list_a,sK11,X0))) ) ),
inference(cnf_transformation,[],[f673]) ).
thf(f673,plain,
! [X0: list_a > $o,X1: list_a] :
( ( $true = vAPP(list_a,$o,X0,X1) )
| ( ( $true != vAPP(list_a,$o,X0,vAPP(sTfun(list_a,$o),list_a,sK11,X0)) )
& ! [X3: list_a] :
( ( $true = vAPP(list_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,X3)),vAPP(list_a,nat,size_size_list_a,vAPP(sTfun(list_a,$o),list_a,sK11,X0))) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f545,f672]) ).
thf(f672,plain,
! [X0: list_a > $o] :
( ? [X2: list_a] :
( ( $true != vAPP(list_a,$o,X0,X2) )
& ! [X3: list_a] :
( ( $true = vAPP(list_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,X3)),vAPP(list_a,nat,size_size_list_a,X2)) ) ) )
=> ( ( $true != vAPP(list_a,$o,X0,vAPP(sTfun(list_a,$o),list_a,sK11,X0)) )
& ! [X3: list_a] :
( ( $true = vAPP(list_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,X3)),vAPP(list_a,nat,size_size_list_a,vAPP(sTfun(list_a,$o),list_a,sK11,X0))) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f545,plain,
! [X0: list_a > $o,X1: list_a] :
( ( $true = vAPP(list_a,$o,X0,X1) )
| ? [X2: list_a] :
( ( $true != vAPP(list_a,$o,X0,X2) )
& ! [X3: list_a] :
( ( $true = vAPP(list_a,$o,X0,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,X3)),vAPP(list_a,nat,size_size_list_a,X2)) ) ) ) ),
inference(ennf_transformation,[],[f305]) ).
thf(f305,plain,
! [X0: list_a > $o,X1: list_a] :
( ! [X2: list_a] :
( ! [X3: list_a] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,X3)),vAPP(list_a,nat,size_size_list_a,X2)) )
=> ( $true = vAPP(list_a,$o,X0,X3) ) )
=> ( $true = vAPP(list_a,$o,X0,X2) ) )
=> ( $true = vAPP(list_a,$o,X0,X1) ) ),
inference(fool_elimination,[],[f304]) ).
thf(f304,plain,
! [X0: list_a > $o,X1: list_a] :
( ! [X2: list_a] :
( ! [X3: list_a] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,X3)),vAPP(list_a,nat,size_size_list_a,X2))
=> vAPP(list_a,$o,X0,X3) )
=> vAPP(list_a,$o,X0,X2) )
=> vAPP(list_a,$o,X0,X1) ),
inference(rectify,[],[f145]) ).
thf(f145,axiom,
! [X12: list_a > $o,X35: list_a] :
( ! [X36: list_a] :
( ! [X37: list_a] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(list_a,nat,size_size_list_a,X37)),vAPP(list_a,nat,size_size_list_a,X36))
=> vAPP(list_a,$o,X12,X37) )
=> vAPP(list_a,$o,X12,X36) )
=> vAPP(list_a,$o,X12,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_length__induct) ).
thf(f2054,plain,
spl31_75,
inference(avatar_split_clause,[],[f1216,f2052]) ).
thf(f2052,plain,
( spl31_75
<=> ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_75])]) ).
thf(f1216,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) ) ),
inference(equality_proxy_clausification,[],[f1215]) ).
thf(f1215,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(equality_proxy_clausification,[],[f1214]) ).
thf(f1214,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,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(binary_proxy_clausification,[],[f776]) ).
thf(f2033,plain,
spl31_74,
inference(avatar_split_clause,[],[f908,f2031]) ).
thf(f908,plain,
! [X0: nat > nat > $o] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f706]) ).
thf(f706,plain,
! [X0: nat > nat > $o] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)) ) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29])],[f704,f705]) ).
thf(f705,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,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f704,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,[],[f703]) ).
thf(f703,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,[],[f651]) ).
thf(f2029,plain,
spl31_73,
inference(avatar_split_clause,[],[f907,f2027]) ).
thf(f2027,plain,
( spl31_73
<=> ! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_73])]) ).
thf(f907,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f706]) ).
thf(f2025,plain,
spl31_72,
inference(avatar_split_clause,[],[f906,f2023]) ).
thf(f2023,plain,
( spl31_72
<=> ! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_72])]) ).
thf(f906,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f706]) ).
thf(f2021,plain,
spl31_71,
inference(avatar_split_clause,[],[f905,f2019]) ).
thf(f2019,plain,
( spl31_71
<=> ! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_71])]) ).
thf(f905,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f706]) ).
thf(f2017,plain,
spl31_70,
inference(avatar_split_clause,[],[f904,f2015]) ).
thf(f2015,plain,
( spl31_70
<=> ! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_70])]) ).
thf(f904,plain,
! [X0: nat > nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK27,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK28,X0)) )
| ( $true != vAPP(sTfun(nat,sTfun(nat,$o)),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f706]) ).
thf(f2013,plain,
spl31_69,
inference(avatar_split_clause,[],[f855,f2011]) ).
thf(f855,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) != $true ) ),
inference(cnf_transformation,[],[f687]) ).
thf(f687,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) ) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f595,f686]) ).
thf(f686,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),sK18,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f595,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,suc,X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) != $true ) ),
inference(ennf_transformation,[],[f369]) ).
thf(f369,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $true )
=> ~ ! [X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
=> ( vAPP(nat,nat,suc,X2) != X1 ) ) ),
inference(fool_elimination,[],[f368]) ).
thf(f368,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1)
=> ~ ! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2)
=> ( vAPP(nat,nat,suc,X2) != X1 ) ) ),
inference(rectify,[],[f74]) ).
thf(f74,axiom,
! [X21: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X21)),X2)
=> ~ ! [X24: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X21),X24)
=> ( vAPP(nat,nat,suc,X24) != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Suc__lessE) ).
thf(f2009,plain,
spl31_68,
inference(avatar_split_clause,[],[f825,f2007]) ).
thf(f825,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,sK15,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f681]) ).
thf(f681,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,sK15,X0)) ) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,X0)) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f552,f680]) ).
thf(f680,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,sK15,X0)) ) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK15,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(sTfun(nat,$o),nat,sK15,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f552,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,[],[f551]) ).
thf(f551,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,[],[f505]) ).
thf(f505,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,[],[f313]) ).
thf(f313,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,[],[f312]) ).
thf(f312,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,[],[f54]) ).
thf(f54,axiom,
! [X12: nat > $o,X0: nat] :
( vAPP(nat,$o,X12,zero_zero_nat)
=> ( ! [X13: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X13)
=> ( ~ vAPP(nat,$o,X12,X13)
=> ? [X14: nat] :
( ~ vAPP(nat,$o,X12,X14)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13) ) ) )
=> vAPP(nat,$o,X12,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_infinite__descent0) ).
thf(f1973,plain,
spl31_67,
inference(avatar_split_clause,[],[f901,f1971]) ).
thf(f901,plain,
! [X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK25,X1),X0)) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f700]) ).
thf(f1955,plain,
spl31_66,
inference(avatar_split_clause,[],[f849,f1953]) ).
thf(f849,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $true )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f587]) ).
thf(f587,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $true )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(flattening,[],[f586]) ).
thf(f586,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $true )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f357]) ).
thf(f357,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( ( vAPP(nat,nat,suc,X0) != X1 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) = $true ) ) ),
inference(fool_elimination,[],[f356]) ).
thf(f356,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( ( vAPP(nat,nat,suc,X0) != X1 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
! [X1: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)
=> ( ( vAPP(nat,nat,suc,X1) != X0 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Suc__lessI) ).
thf(f1951,plain,
spl31_65,
inference(avatar_split_clause,[],[f848,f1949]) ).
thf(f848,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK17,X1),X0)) = X1 )
| ( vAPP(nat,nat,suc,X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f685]) ).
thf(f1907,plain,
spl31_64,
inference(avatar_split_clause,[],[f1321,f1905]) ).
thf(f1321,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),times_times_nat,X0),X1)),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) ) ),
inference(trivial_inequality_removal,[],[f1320]) ).
thf(f1320,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),times_times_nat,X0),X1)),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) ) ),
inference(forward_demodulation,[],[f807,f764]) ).
thf(f807,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),times_times_nat,X0),X1)),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f539]) ).
thf(f539,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),times_times_nat,X0),X1)),zero_zero_nat) )
| ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) != $true ) )
& ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) != $true ) ) ) ),
inference(ennf_transformation,[],[f295]) ).
thf(f295,plain,
! [X0: nat,X1: nat] :
( ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) = $true ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) = $true ) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) ) ),
inference(fool_elimination,[],[f294]) ).
thf(f294,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) ) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) ),
inference(rectify,[],[f179]) ).
thf(f179,axiom,
! [X7: nat,X9: nat] :
( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X9)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),zero_zero_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X7) ) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X9)),zero_zero_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_split__mult__neg__le) ).
thf(f1903,plain,
spl31_63,
inference(avatar_split_clause,[],[f1319,f1901]) ).
thf(f1319,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) != $true ) ),
inference(trivial_inequality_removal,[],[f1318]) ).
thf(f1318,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) != $true ) ),
inference(forward_demodulation,[],[f808,f764]) ).
thf(f808,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),times_times_nat,X0),X1)),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) != $true ) ),
inference(cnf_transformation,[],[f539]) ).
thf(f1899,plain,
spl31_62,
inference(avatar_split_clause,[],[f832,f1897]) ).
thf(f832,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f562]) ).
thf(f562,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f325]) ).
thf(f325,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 ) ),
inference(fool_elimination,[],[f324]) ).
thf(f324,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_div__mult__self1__is__m) ).
thf(f1895,plain,
spl31_61,
inference(avatar_split_clause,[],[f831,f1893]) ).
thf(f831,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f561]) ).
thf(f561,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f323]) ).
thf(f323,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 ) ),
inference(fool_elimination,[],[f322]) ).
thf(f322,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_div__mult__self__is__m) ).
thf(f1875,plain,
spl31_60,
inference(avatar_split_clause,[],[f774,f1873]) ).
thf(f774,plain,
! [X0: list_a,X1: list_a] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(list_a,list_P1467822637od_a_a,vAPP(list_a,sTfun(list_a,list_P1467822637od_a_a),product_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X0)),vAPP(list_a,nat,size_size_list_a,X1)) ),
inference(cnf_transformation,[],[f489]) ).
thf(f489,plain,
! [X0: list_a,X1: list_a] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(list_a,list_P1467822637od_a_a,vAPP(list_a,sTfun(list_a,list_P1467822637od_a_a),product_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X0)),vAPP(list_a,nat,size_size_list_a,X1)) ),
inference(rectify,[],[f156]) ).
thf(f156,axiom,
! [X35: list_a,X38: list_a] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(list_a,list_P1467822637od_a_a,vAPP(list_a,sTfun(list_a,list_P1467822637od_a_a),product_a_a,X35),X38)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X35)),vAPP(list_a,nat,size_size_list_a,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_length__product) ).
thf(f1871,plain,
spl31_59,
inference(avatar_split_clause,[],[f773,f1869]) ).
thf(f773,plain,
! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a] : ( vAPP(list_P1891567085od_a_a,nat,size_s1052379225od_a_a,vAPP(list_P1467822637od_a_a,list_P1891567085od_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,list_P1891567085od_a_a),produc1055075589od_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X0)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) ),
inference(cnf_transformation,[],[f488]) ).
thf(f488,plain,
! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a] : ( vAPP(list_P1891567085od_a_a,nat,size_s1052379225od_a_a,vAPP(list_P1467822637od_a_a,list_P1891567085od_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,list_P1891567085od_a_a),produc1055075589od_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X0)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) ),
inference(rectify,[],[f155]) ).
thf(f155,axiom,
! [X35: list_P1467822637od_a_a,X38: list_P1467822637od_a_a] : ( vAPP(list_P1891567085od_a_a,nat,size_s1052379225od_a_a,vAPP(list_P1467822637od_a_a,list_P1891567085od_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_P1467822637od_a_a,list_P1891567085od_a_a),produc1055075589od_a_a,X35),X38)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X35)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_length__product) ).
thf(f1867,plain,
( spl31_58
| ~ spl31_3
| ~ spl31_15 ),
inference(avatar_split_clause,[],[f1436,f1423,f1343,f1865]) ).
thf(f1423,plain,
( spl31_15
<=> ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) != $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_15])]) ).
thf(f1436,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) = $false )
| ~ spl31_3
| ~ spl31_15 ),
inference(trivial_inequality_removal,[],[f1435]) ).
thf(f1435,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) = $false ) )
| ~ spl31_3
| ~ spl31_15 ),
inference(superposition,[],[f1424,f1344]) ).
thf(f1424,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) != $true )
| ~ spl31_15 ),
inference(avatar_component_clause,[],[f1423]) ).
thf(f1863,plain,
spl31_57,
inference(avatar_split_clause,[],[f772,f1861]) ).
thf(f772,plain,
! [X0: list_a,X1: list_P1467822637od_a_a] : ( vAPP(list_P1458844246od_a_a,nat,size_s1875148994od_a_a,vAPP(list_P1467822637od_a_a,list_P1458844246od_a_a,vAPP(list_a,sTfun(list_P1467822637od_a_a,list_P1458844246od_a_a),produc16441326od_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X0)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) ),
inference(cnf_transformation,[],[f487]) ).
thf(f487,plain,
! [X0: list_a,X1: list_P1467822637od_a_a] : ( vAPP(list_P1458844246od_a_a,nat,size_s1875148994od_a_a,vAPP(list_P1467822637od_a_a,list_P1458844246od_a_a,vAPP(list_a,sTfun(list_P1467822637od_a_a,list_P1458844246od_a_a),produc16441326od_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X0)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1)) ),
inference(rectify,[],[f153]) ).
thf(f153,axiom,
! [X35: list_a,X38: list_P1467822637od_a_a] : ( vAPP(list_P1458844246od_a_a,nat,size_s1875148994od_a_a,vAPP(list_P1467822637od_a_a,list_P1458844246od_a_a,vAPP(list_a,sTfun(list_P1467822637od_a_a,list_P1458844246od_a_a),produc16441326od_a_a,X35),X38)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_a,nat,size_size_list_a,X35)),vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_length__product) ).
thf(f1859,plain,
spl31_56,
inference(avatar_split_clause,[],[f771,f1857]) ).
thf(f771,plain,
! [X0: list_P1467822637od_a_a,X1: list_a] : ( vAPP(list_P319927492_a_a_a,nat,size_s736232240_a_a_a,vAPP(list_a,list_P319927492_a_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_a,list_P319927492_a_a_a),produc778776796_a_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X0)),vAPP(list_a,nat,size_size_list_a,X1)) ),
inference(cnf_transformation,[],[f486]) ).
thf(f486,plain,
! [X0: list_P1467822637od_a_a,X1: list_a] : ( vAPP(list_P319927492_a_a_a,nat,size_s736232240_a_a_a,vAPP(list_a,list_P319927492_a_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_a,list_P319927492_a_a_a),produc778776796_a_a_a,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X0)),vAPP(list_a,nat,size_size_list_a,X1)) ),
inference(rectify,[],[f154]) ).
thf(f154,axiom,
! [X35: list_P1467822637od_a_a,X38: list_a] : ( vAPP(list_P319927492_a_a_a,nat,size_s736232240_a_a_a,vAPP(list_a,list_P319927492_a_a_a,vAPP(list_P1467822637od_a_a,sTfun(list_a,list_P319927492_a_a_a),produc778776796_a_a_a,X35),X38)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X35)),vAPP(list_a,nat,size_size_list_a,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_length__product) ).
thf(f1831,plain,
spl31_55,
inference(avatar_split_clause,[],[f858,f1829]) ).
thf(f858,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(cnf_transformation,[],[f597]) ).
thf(f597,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(ennf_transformation,[],[f373]) ).
thf(f373,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ),
inference(fool_elimination,[],[f372]) ).
thf(f372,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$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,$o),ord_less_nat,X0),X1) ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X1: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Suc__less__SucD) ).
thf(f1827,plain,
spl31_54,
inference(avatar_split_clause,[],[f856,f1825]) ).
thf(f856,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK18,X1),X0)) = X1 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1) != $true ) ),
inference(cnf_transformation,[],[f687]) ).
thf(f1823,plain,
spl31_53,
inference(avatar_split_clause,[],[f852,f1821]) ).
thf(f852,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f590]) ).
thf(f590,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f363]) ).
thf(f363,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(fool_elimination,[],[f362]) ).
thf(f362,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
! [X1: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),vAPP(nat,nat,suc,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Suc__mono) ).
thf(f1796,plain,
spl31_52,
inference(avatar_split_clause,[],[f823,f1794]) ).
thf(f823,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,sK15,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f681]) ).
thf(f1792,plain,
spl31_51,
inference(avatar_split_clause,[],[f813,f1790]) ).
thf(f813,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,sK10,X0)) ) ),
inference(cnf_transformation,[],[f671]) ).
thf(f671,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK10,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,sK10,X0)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f544,f670]) ).
thf(f670,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,sK10,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,sK10,X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f544,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,[],[f303]) ).
thf(f303,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,[],[f302]) ).
thf(f302,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,[],[f32]) ).
thf(f32,axiom,
! [X12: nat > $o,X0: nat] :
( ! [X13: nat] :
( ! [X14: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13)
=> vAPP(nat,$o,X12,X14) )
=> vAPP(nat,$o,X12,X13) )
=> vAPP(nat,$o,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_nat__less__induct) ).
thf(f1788,plain,
spl31_50,
inference(avatar_split_clause,[],[f812,f1786]) ).
thf(f812,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,sK9,X0)) ) ),
inference(cnf_transformation,[],[f669]) ).
thf(f669,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,sK9,X0)) ) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f543,f668]) ).
thf(f668,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,sK9,X0)) ) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f543,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,[],[f504]) ).
thf(f504,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,[],[f301]) ).
thf(f301,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,[],[f300]) ).
thf(f300,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,[],[f31]) ).
thf(f31,axiom,
! [X12: nat > $o,X0: nat] :
( ! [X13: nat] :
( ~ vAPP(nat,$o,X12,X13)
=> ? [X14: nat] :
( ~ vAPP(nat,$o,X12,X14)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13) ) )
=> vAPP(nat,$o,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_infinite__descent) ).
thf(f1784,plain,
spl31_49,
inference(avatar_split_clause,[],[f810,f1782]) ).
thf(f1782,plain,
( spl31_49
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( 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) = $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_49])]) ).
thf(f810,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,$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) = $true ) ),
inference(cnf_transformation,[],[f542]) ).
thf(f542,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,$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) = $true ) ),
inference(flattening,[],[f541]) ).
thf(f541,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,$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) = $true ) ),
inference(ennf_transformation,[],[f503]) ).
thf(f503,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$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)) = $true )
=> ( X0 = X1 ) ) ),
inference(flattening,[],[f299]) ).
thf(f299,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$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)) = $true )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f298]) ).
thf(f298,plain,
! [X0: nat,X1: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f65]) ).
thf(f65,axiom,
! [X0: nat,X1: nat] :
( ~ vAPP(nat,$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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__antisym) ).
thf(f1716,plain,
spl31_48,
inference(avatar_split_clause,[],[f826,f1714]) ).
thf(f826,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,sK16,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f683]) ).
thf(f683,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,X0))) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f554,f682]) ).
thf(f682,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,sK16,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK16,X0))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f554,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,[],[f553]) ).
thf(f553,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,[],[f315]) ).
thf(f315,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,[],[f314]) ).
thf(f314,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,[],[f46]) ).
thf(f46,axiom,
! [X12: nat > $o,X2: nat] :
( vAPP(nat,$o,X12,X2)
=> ( ! [X13: nat] :
( vAPP(nat,$o,X12,vAPP(nat,nat,suc,X13))
=> vAPP(nat,$o,X12,X13) )
=> vAPP(nat,$o,X12,zero_zero_nat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_zero__induct) ).
thf(f1712,plain,
spl31_47,
inference(avatar_split_clause,[],[f822,f1710]) ).
thf(f822,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,[],[f679]) ).
thf(f679,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])],[f550,f678]) ).
thf(f678,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(f550,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,[],[f549]) ).
thf(f549,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,[],[f311]) ).
thf(f311,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,[],[f310]) ).
thf(f310,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,[],[f41]) ).
thf(f41,axiom,
! [X12: nat > $o,X3: nat] :
( vAPP(nat,$o,X12,zero_zero_nat)
=> ( ! [X18: nat] :
( vAPP(nat,$o,X12,X18)
=> vAPP(nat,$o,X12,vAPP(nat,nat,suc,X18)) )
=> vAPP(nat,$o,X12,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_old_Onat_Oinducts) ).
thf(f1708,plain,
spl31_46,
inference(avatar_split_clause,[],[f820,f1706]) ).
thf(f820,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,sK13,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f677]) ).
thf(f677,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,sK13,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f548,f676]) ).
thf(f676,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,sK13,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f548,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,[],[f547]) ).
thf(f547,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,[],[f309]) ).
thf(f309,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,[],[f308]) ).
thf(f308,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,[],[f48]) ).
thf(f48,axiom,
! [X12: nat > $o,X0: nat] :
( vAPP(nat,$o,X12,zero_zero_nat)
=> ( ! [X13: nat] :
( vAPP(nat,$o,X12,X13)
=> vAPP(nat,$o,X12,vAPP(nat,nat,suc,X13)) )
=> vAPP(nat,$o,X12,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_nat__induct) ).
thf(f1704,plain,
spl31_45,
inference(avatar_split_clause,[],[f753,f1702]) ).
thf(f753,plain,
! [X2: nat,X0: nat > $o] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,X0))) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f661]) ).
thf(f661,plain,
! [X0: nat > $o] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK5,X0))) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK5,X0)) ) )
| ! [X2: nat] : ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f659,f660]) ).
thf(f660,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,sK5,X0))) )
& ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK5,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f659,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,[],[f522]) ).
thf(f522,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,[],[f521]) ).
thf(f521,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,[],[f475]) ).
thf(f475,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,[],[f227]) ).
thf(f227,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,[],[f226]) ).
thf(f226,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,[],[f151]) ).
thf(f151,axiom,
! [X12: nat > $o] :
( ~ vAPP(nat,$o,X12,zero_zero_nat)
=> ( ? [X39: nat] : vAPP(nat,$o,X12,X39)
=> ? [X13: nat] :
( vAPP(nat,$o,X12,vAPP(nat,nat,suc,X13))
& ~ vAPP(nat,$o,X12,X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_exists__least__lemma) ).
thf(f1686,plain,
spl31_44,
inference(avatar_split_clause,[],[f857,f1684]) ).
thf(f857,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$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) != $true ) ),
inference(cnf_transformation,[],[f596]) ).
thf(f596,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$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) != $true ) ),
inference(ennf_transformation,[],[f371]) ).
thf(f371,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$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) = $true ) ),
inference(fool_elimination,[],[f370]) ).
thf(f370,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X0)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
inference(rectify,[],[f75]) ).
thf(f75,axiom,
! [X1: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,suc,X1)),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Suc__lessD) ).
thf(f1682,plain,
spl31_43,
inference(avatar_split_clause,[],[f851,f1680]) ).
thf(f851,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$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) != $true ) ),
inference(cnf_transformation,[],[f589]) ).
thf(f589,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$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) != $true ) ),
inference(ennf_transformation,[],[f361]) ).
thf(f361,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$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)) = $true ) ),
inference(fool_elimination,[],[f360]) ).
thf(f360,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f71]) ).
thf(f71,axiom,
! [X1: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,suc,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__SucI) ).
thf(f1621,plain,
spl31_42,
inference(avatar_split_clause,[],[f827,f1619]) ).
thf(f827,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK16,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f683]) ).
thf(f1617,plain,
spl31_41,
inference(avatar_split_clause,[],[f824,f1615]) ).
thf(f824,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,[],[f681]) ).
thf(f1613,plain,
spl31_40,
inference(avatar_split_clause,[],[f821,f1611]) ).
thf(f821,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,[],[f679]) ).
thf(f1609,plain,
spl31_39,
inference(avatar_split_clause,[],[f819,f1607]) ).
thf(f819,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK13,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f677]) ).
thf(f1605,plain,
spl31_38,
inference(avatar_split_clause,[],[f752,f1603]) ).
thf(f752,plain,
! [X2: nat,X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK5,X0)) )
| ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f661]) ).
thf(f1588,plain,
( spl31_37
| ~ spl31_6
| ~ spl31_20 ),
inference(avatar_split_clause,[],[f1457,f1450,f1386,f1586]) ).
thf(f1586,plain,
( spl31_37
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK4,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_37])]) ).
thf(f1457,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK4,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_6
| ~ spl31_20 ),
inference(superposition,[],[f1387,f1451]) ).
thf(f1572,plain,
spl31_36,
inference(avatar_split_clause,[],[f850,f1570]) ).
thf(f850,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f588]) ).
thf(f588,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f359]) ).
thf(f359,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) = $true ) ),
inference(fool_elimination,[],[f358]) ).
thf(f358,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ),
inference(rectify,[],[f141]) ).
thf(f141,axiom,
! [X1: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_gr__implies__gr0) ).
thf(f1568,plain,
spl31_35,
inference(avatar_split_clause,[],[f846,f1566]) ).
thf(f846,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f583]) ).
thf(f583,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f353]) ).
thf(f353,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) ) ),
inference(fool_elimination,[],[f352]) ).
thf(f352,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),X1) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X1: nat,X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_div__less) ).
thf(f1564,plain,
spl31_34,
inference(avatar_split_clause,[],[f796,f1562]) ).
thf(f796,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f527]) ).
thf(f527,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f492]) ).
thf(f492,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X0) = X1 ) ),
inference(rectify,[],[f100]) ).
thf(f100,axiom,
! [X7: nat,X9: nat] :
( ( zero_zero_nat != X7 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X9)),X7) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_nonzero__mult__div__cancel__left) ).
thf(f1560,plain,
spl31_33,
inference(avatar_split_clause,[],[f795,f1558]) ).
thf(f795,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f526]) ).
thf(f526,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f491]) ).
thf(f491,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X0 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X0) = X1 ) ),
inference(rectify,[],[f99]) ).
thf(f99,axiom,
! [X9: nat,X7: nat] :
( ( zero_zero_nat != X9 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X9)),X9) = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_nonzero__mult__div__cancel__right) ).
thf(f1550,plain,
spl31_32,
inference(avatar_split_clause,[],[f754,f1548]) ).
thf(f754,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(cnf_transformation,[],[f663]) ).
thf(f663,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f523,f662]) ).
thf(f662,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK6,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f523,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) != $true ) ),
inference(ennf_transformation,[],[f229]) ).
thf(f229,plain,
! [X0: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) = $true )
=> ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(fool_elimination,[],[f228]) ).
thf(f228,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(rectify,[],[f84]) ).
thf(f84,axiom,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ? [X17: nat] : ( vAPP(nat,nat,suc,X17) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_gr0__implies__Suc) ).
thf(f1546,plain,
spl31_31,
inference(avatar_split_clause,[],[f714,f1543]) ).
thf(f1543,plain,
( spl31_31
<=> ( times_times_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,times_times_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_31])]) ).
thf(f714,plain,
times_times_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,times_times_nat),
inference(cnf_transformation,[],[f197]) ).
thf(f197,plain,
times_times_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,times_times_nat),
inference(fool_elimination,[],[f196]) ).
thf(f196,plain,
( times_times_nat
= ( ^ [X0: nat,X1: nat] : vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) ) ),
inference(rectify,[],[f134]) ).
thf(f134,axiom,
( times_times_nat
= ( ^ [X33: nat,X34: nat] : vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X34),X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_mult_Ocommute) ).
thf(f1541,plain,
( spl31_30
| ~ spl31_6
| ~ spl31_18 ),
inference(avatar_split_clause,[],[f1455,f1442,f1386,f1539]) ).
thf(f1539,plain,
( spl31_30
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK3,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_30])]) ).
thf(f1455,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK3,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_6
| ~ spl31_18 ),
inference(superposition,[],[f1387,f1443]) ).
thf(f1537,plain,
spl31_29,
inference(avatar_split_clause,[],[f711,f1534]) ).
thf(f711,plain,
vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(list_a,nat,size_size_list_a,xs)),k) = vAPP(nat,nat,suc,n),
inference(cnf_transformation,[],[f184]) ).
thf(f184,axiom,
vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,vAPP(list_a,nat,size_size_list_a,xs)),k) = vAPP(nat,nat,suc,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f1496,plain,
spl31_28,
inference(avatar_split_clause,[],[f818,f1494]) ).
thf(f818,plain,
! [X0: list_P1467822637od_a_a > $o,X1: list_P1467822637od_a_a] :
( ( $true = vAPP(list_P1467822637od_a_a,$o,X0,X1) )
| ( $true != vAPP(list_P1467822637od_a_a,$o,X0,vAPP(sTfun(list_P1467822637od_a_a,$o),list_P1467822637od_a_a,sK12,X0)) ) ),
inference(cnf_transformation,[],[f675]) ).
thf(f1492,plain,
spl31_27,
inference(avatar_split_clause,[],[f816,f1490]) ).
thf(f816,plain,
! [X0: list_a > $o,X1: list_a] :
( ( $true = vAPP(list_a,$o,X0,X1) )
| ( $true != vAPP(list_a,$o,X0,vAPP(sTfun(list_a,$o),list_a,sK11,X0)) ) ),
inference(cnf_transformation,[],[f673]) ).
thf(f1488,plain,
spl31_26,
inference(avatar_split_clause,[],[f814,f1486]) ).
thf(f814,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK10,X0)) ) ),
inference(cnf_transformation,[],[f671]) ).
thf(f1484,plain,
spl31_25,
inference(avatar_split_clause,[],[f811,f1482]) ).
thf(f811,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK9,X0)) ) ),
inference(cnf_transformation,[],[f669]) ).
thf(f1480,plain,
( spl31_24
| ~ spl31_6
| ~ spl31_17 ),
inference(avatar_split_clause,[],[f1453,f1438,f1386,f1478]) ).
thf(f1478,plain,
( spl31_24
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK2,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_24])]) ).
thf(f1453,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK2,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl31_6
| ~ spl31_17 ),
inference(superposition,[],[f1387,f1439]) ).
thf(f1470,plain,
spl31_23,
inference(avatar_split_clause,[],[f768,f1468]) ).
thf(f768,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X0)) = $true ),
inference(cnf_transformation,[],[f253]) ).
thf(f253,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X0)) = $true ),
inference(fool_elimination,[],[f252]) ).
thf(f252,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X0)),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_lessI) ).
thf(f1466,plain,
spl31_22,
inference(avatar_split_clause,[],[f767,f1464]) ).
thf(f767,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) = $true ),
inference(cnf_transformation,[],[f251]) ).
thf(f251,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)) = $true ),
inference(fool_elimination,[],[f250]) ).
thf(f250,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,suc,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zero__less__Suc) ).
thf(f1462,plain,
spl31_21,
inference(avatar_split_clause,[],[f733,f1460]) ).
thf(f733,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,[],[f471]) ).
thf(f471,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,[],[f5]) ).
thf(f5,axiom,
! [X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X1),vAPP(nat,nat,suc,zero_zero_nat)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_div__by__Suc__0) ).
thf(f1452,plain,
spl31_20,
inference(avatar_split_clause,[],[f749,f1450]) ).
thf(f749,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f658]) ).
thf(f658,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f518,f657]) ).
thf(f657,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK4,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f518,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f474]) ).
thf(f474,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(rectify,[],[f40]) ).
thf(f40,axiom,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ? [X17: nat] : ( vAPP(nat,nat,suc,X17) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_not0__implies__Suc) ).
thf(f1448,plain,
( spl31_19
| ~ spl31_3
| ~ spl31_14 ),
inference(avatar_split_clause,[],[f1434,f1419,f1343,f1446]) ).
thf(f1419,plain,
( spl31_14
<=> ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) != $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_14])]) ).
thf(f1434,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) = $false )
| ~ spl31_3
| ~ spl31_14 ),
inference(trivial_inequality_removal,[],[f1433]) ).
thf(f1433,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) = $false ) )
| ~ spl31_3
| ~ spl31_14 ),
inference(superposition,[],[f1420,f1344]) ).
thf(f1420,plain,
( ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) != $true )
| ~ spl31_14 ),
inference(avatar_component_clause,[],[f1419]) ).
thf(f1444,plain,
spl31_18,
inference(avatar_split_clause,[],[f748,f1442]) ).
thf(f748,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK3,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f656]) ).
thf(f656,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])],[f517,f655]) ).
thf(f655,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(f517,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f473]) ).
thf(f473,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ~ ! [X1: nat] : ( vAPP(nat,nat,suc,X1) != X0 ) ),
inference(rectify,[],[f42]) ).
thf(f42,axiom,
! [X11: nat] :
( ( zero_zero_nat != X11 )
=> ~ ! [X18: nat] : ( vAPP(nat,nat,suc,X18) != X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_old_Onat_Oexhaust) ).
thf(f1440,plain,
spl31_17,
inference(avatar_split_clause,[],[f747,f1438]) ).
thf(f747,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK2,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f654]) ).
thf(f654,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])],[f516,f653]) ).
thf(f653,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(f516,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f472]) ).
thf(f472,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ~ ! [X1: nat] : ( vAPP(nat,nat,suc,X1) != X0 ) ),
inference(rectify,[],[f150]) ).
thf(f150,axiom,
! [X10: nat] :
( ( zero_zero_nat != X10 )
=> ~ ! [X13: nat] : ( vAPP(nat,nat,suc,X13) != X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_list__decode_Ocases) ).
thf(f1432,plain,
spl31_16,
inference(avatar_split_clause,[],[f764,f1430]) ).
thf(f1425,plain,
spl31_15,
inference(avatar_split_clause,[],[f760,f1423]) ).
thf(f760,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) != $true ),
inference(cnf_transformation,[],[f481]) ).
thf(f481,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) != $true ),
inference(flattening,[],[f241]) ).
thf(f241,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) != $true ),
inference(fool_elimination,[],[f240]) ).
thf(f240,plain,
! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0),
inference(rectify,[],[f33]) ).
thf(f33,axiom,
! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_less__irrefl__nat) ).
thf(f1421,plain,
spl31_14,
inference(avatar_split_clause,[],[f755,f1419]) ).
thf(f755,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) != $true ),
inference(cnf_transformation,[],[f476]) ).
thf(f476,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) != $true ),
inference(flattening,[],[f231]) ).
thf(f231,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) != $true ),
inference(fool_elimination,[],[f230]) ).
thf(f230,plain,
! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat),
inference(rectify,[],[f53]) ).
thf(f53,axiom,
! [X7: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X7),zero_zero_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_bot__nat__0_Oextremum__strict) ).
thf(f1417,plain,
spl31_13,
inference(avatar_split_clause,[],[f731,f1415]) ).
thf(f1415,plain,
( spl31_13
<=> ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_13])]) ).
thf(f731,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f469]) ).
thf(f469,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),zero_zero_nat) ),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
! [X1: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),zero_zero_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_mult__0__right) ).
thf(f1413,plain,
spl31_12,
inference(avatar_split_clause,[],[f729,f1411]) ).
thf(f1411,plain,
( spl31_12
<=> ! [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,[spl31_12])]) ).
thf(f729,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f467]) ).
thf(f467,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X0),zero_zero_nat) ),
inference(rectify,[],[f129]) ).
thf(f129,axiom,
! [X7: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,X7),zero_zero_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_bits__div__by__0) ).
thf(f1409,plain,
spl31_11,
inference(avatar_split_clause,[],[f727,f1407]) ).
thf(f1407,plain,
( spl31_11
<=> ! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,zero_zero_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_11])]) ).
thf(f727,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,zero_zero_nat),X0) ),
inference(cnf_transformation,[],[f466]) ).
thf(f466,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,zero_zero_nat),X0) ),
inference(rectify,[],[f102]) ).
thf(f102,axiom,
! [X7: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,zero_zero_nat),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_mult__zero__left) ).
thf(f1405,plain,
spl31_10,
inference(avatar_split_clause,[],[f725,f1403]) ).
thf(f1403,plain,
( spl31_10
<=> ! [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,[spl31_10])]) ).
thf(f725,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,zero_zero_nat),X0) ),
inference(cnf_transformation,[],[f464]) ).
thf(f464,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,zero_zero_nat),X0) ),
inference(rectify,[],[f128]) ).
thf(f128,axiom,
! [X7: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide_nat,zero_zero_nat),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_bits__div__0) ).
thf(f1401,plain,
spl31_9,
inference(avatar_split_clause,[],[f763,f1399]) ).
thf(f763,plain,
! [X0: nat] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(nat,list_P1467822637od_a_a,sK8,X0)) = X0 ),
inference(cnf_transformation,[],[f667]) ).
thf(f667,plain,
! [X0: nat] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(nat,list_P1467822637od_a_a,sK8,X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f484,f666]) ).
thf(f666,plain,
! [X0: nat] :
( ? [X1: list_P1467822637od_a_a] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1) = X0 )
=> ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,vAPP(nat,list_P1467822637od_a_a,sK8,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f484,plain,
! [X0: nat] :
? [X1: list_P1467822637od_a_a] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X1) = X0 ),
inference(rectify,[],[f146]) ).
thf(f146,axiom,
! [X0: nat] :
? [X36: list_P1467822637od_a_a] : ( vAPP(list_P1467822637od_a_a,nat,size_s642698393od_a_a,X36) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Ex__list__of__length) ).
thf(f1397,plain,
spl31_8,
inference(avatar_split_clause,[],[f762,f1395]) ).
thf(f762,plain,
! [X0: nat] : ( vAPP(list_a,nat,size_size_list_a,vAPP(nat,list_a,sK7,X0)) = X0 ),
inference(cnf_transformation,[],[f665]) ).
thf(f665,plain,
! [X0: nat] : ( vAPP(list_a,nat,size_size_list_a,vAPP(nat,list_a,sK7,X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f483,f664]) ).
thf(f664,plain,
! [X0: nat] :
( ? [X1: list_a] : ( vAPP(list_a,nat,size_size_list_a,X1) = X0 )
=> ( vAPP(list_a,nat,size_size_list_a,vAPP(nat,list_a,sK7,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f483,plain,
! [X0: nat] :
? [X1: list_a] : ( vAPP(list_a,nat,size_size_list_a,X1) = X0 ),
inference(rectify,[],[f147]) ).
thf(f147,axiom,
! [X0: nat] :
? [X36: list_a] : ( vAPP(list_a,nat,size_size_list_a,X36) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Ex__list__of__length) ).
thf(f1393,plain,
( spl31_7
| ~ spl31_3
| spl31_4 ),
inference(avatar_split_clause,[],[f1380,f1375,f1343,f1390]) ).
thf(f1375,plain,
( spl31_4
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_4])]) ).
thf(f1380,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)) = $false )
| ~ spl31_3
| spl31_4 ),
inference(trivial_inequality_removal,[],[f1379]) ).
thf(f1379,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)) = $false )
| ~ spl31_3
| spl31_4 ),
inference(superposition,[],[f1377,f1344]) ).
thf(f1377,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)) != $true )
| spl31_4 ),
inference(avatar_component_clause,[],[f1375]) ).
thf(f1388,plain,
spl31_6,
inference(avatar_split_clause,[],[f724,f1386]) ).
thf(f724,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(cnf_transformation,[],[f28]) ).
thf(f28,axiom,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_n__not__Suc__n) ).
thf(f1384,plain,
spl31_5,
inference(avatar_split_clause,[],[f718,f1382]) ).
thf(f718,plain,
! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) ),
inference(cnf_transformation,[],[f458]) ).
thf(f458,plain,
! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) ),
inference(rectify,[],[f45]) ).
thf(f45,axiom,
! [X1: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Suc__neq__Zero) ).
thf(f1378,plain,
~ spl31_4,
inference(avatar_split_clause,[],[f709,f1375]) ).
thf(f709,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)) != $true,
inference(cnf_transformation,[],[f456]) ).
thf(f456,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)) != $true,
inference(flattening,[],[f191]) ).
thf(f191,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)) != $true,
inference(fool_elimination,[],[f190]) ).
thf(f190,plain,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)),
inference(rectify,[],[f187]) ).
thf(f187,negated_conjecture,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)),
inference(negated_conjecture,[],[f186]) ).
thf(f186,conjecture,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,n),k)),vAPP(list_a,nat,size_size_list_a,xs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(f1345,plain,
spl31_3,
inference(avatar_split_clause,[],[f189,f1343]) ).
thf(f189,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1341,plain,
~ spl31_2,
inference(avatar_split_clause,[],[f188,f1338]) ).
thf(f1338,plain,
( spl31_2
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_2])]) ).
thf(f188,plain,
$true != $false,
introduced(fool_axiom,[]) ).
thf(f1336,plain,
~ spl31_1,
inference(avatar_split_clause,[],[f710,f1333]) ).
thf(f710,plain,
zero_zero_nat != k,
inference(cnf_transformation,[],[f185]) ).
thf(f185,axiom,
zero_zero_nat != k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP103^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 19:21:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (22619)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (22624)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)
% 0.15/0.38 % (22622)WARNING: value z3 for option sas not known
% 0.15/0.38 % (22620)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (22621)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (22623)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (22622)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)
% 0.15/0.38 % (22625)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)
% 0.15/0.38 % (22626)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)
% 0.15/0.40 % (22626)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.40 % Exception at run slice level% Exception at run slice level
% 0.15/0.40
% 0.15/0.40 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.42 % (22627)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.42 % (22628)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)
% 0.15/0.42 % (22629)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.43 % (22627)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.43 % (22628)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.44 % Exception at run slice level
% 0.21/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.45 % (22630)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)
% 2.01/0.64 % (22624)First to succeed.
% 2.11/0.66 % (22624)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22619"
% 2.11/0.66 % (22624)Refutation found. Thanks to Tanya!
% 2.11/0.66 % SZS status Theorem for theBenchmark
% 2.11/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 2.11/0.67 % (22624)------------------------------
% 2.11/0.67 % (22624)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.11/0.67 % (22624)Termination reason: Refutation
% 2.11/0.67
% 2.11/0.67 % (22624)Memory used [KB]: 4135
% 2.11/0.67 % (22624)Time elapsed: 0.282 s
% 2.11/0.67 % (22624)Instructions burned: 889 (million)
% 2.11/0.67 % (22619)Success in time 0.3 s
%------------------------------------------------------------------------------