TSTP Solution File: SYO500^1.004 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO500^1.004 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:11:34 EDT 2024
% Result : Theorem 1.48s 0.59s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 89
% Syntax : Number of formulae : 1262 ( 5 unt; 13 typ; 0 def)
% Number of atoms : 12445 (1037 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 6520 (2992 ~;3454 |; 0 &; 0 @)
% ( 74 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 22 ( 21 >; 1 *; 0 +; 0 <<)
% Number of symbols : 91 ( 88 usr; 77 con; 0-6 aty)
% Number of variables : 35 ( 0 ^ 29 !; 0 ?; 35 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: $o ).
thf(func_def_1,type,
f0: $o > $o ).
thf(func_def_2,type,
f1: $o > $o ).
thf(func_def_3,type,
f2: $o > $o ).
thf(func_def_4,type,
f3: $o > $o ).
thf(func_def_9,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_10,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_12,type,
vOR: $o > $o > $o ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f7591,plain,
$false,
inference(avatar_sat_refutation,[],[f17,f26,f95,f104,f113,f122,f135,f145,f154,f156,f159,f162,f304,f372,f407,f409,f436,f446,f451,f456,f485,f620,f652,f665,f675,f677,f700,f701,f728,f908,f930,f939,f961,f971,f983,f1108,f1109,f1114,f1126,f1225,f1265,f1305,f1315,f1320,f1367,f1370,f1378,f1502,f1535,f1537,f1541,f1619,f1695,f1783,f1804,f1883,f1917,f1943,f1950,f1974,f2016,f2139,f2184,f2197,f2211,f2283,f2305,f2355,f2417,f2419,f2458,f2551,f2564,f2590,f2640,f2648,f2659,f2665,f2673,f2682,f2685,f2774,f2799,f2803,f2846,f2847,f2952,f2977,f3010,f3027,f3031,f3043,f3064,f3156,f3157,f3189,f3246,f3266,f3324,f3336,f3365,f3369,f3395,f3404,f3408,f3410,f3455,f3495,f3532,f3540,f3617,f3672,f3692,f3722,f3755,f3788,f3791,f3795,f3808,f3819,f3827,f3838,f3926,f3955,f3963,f3964,f3969,f3997,f4031,f4095,f4097,f4109,f4110,f4113,f4135,f4163,f4195,f4210,f4213,f4246,f4283,f4367,f4420,f4449,f4472,f4480,f4517,f4519,f4619,f4622,f4845,f4871,f4872,f4879,f4924,f4958,f4969,f4978,f4981,f4984,f5074,f5076,f5080,f5092,f5094,f5111,f5137,f5203,f5357,f5362,f5373,f5487,f5491,f5525,f5573,f5621,f5722,f5730,f5754,f5756,f5766,f5772,f5784,f5797,f5865,f5866,f5927,f5973,f5977,f6004,f6170,f6284,f6426,f6442,f6443,f6481,f6559,f6630,f6635,f6683,f6696,f6764,f6775,f6870,f6872,f6902,f6913,f6974,f6990,f7058,f7092,f7099,f7104,f7127,f7150,f7157,f7163,f7181,f7246,f7253,f7267,f7296,f7304,f7330,f7333,f7360,f7374,f7398,f7433,f7438,f7446,f7452,f7462,f7475,f7550,f7555,f7577,f7584]) ).
thf(f7584,plain,
( ~ spl0_4
| spl0_20
| ~ spl0_39
| spl0_47 ),
inference(avatar_contradiction_clause,[],[f7583]) ).
thf(f7583,plain,
( $false
| ~ spl0_4
| spl0_20
| ~ spl0_39
| spl0_47 ),
inference(subsumption_resolution,[],[f7582,f7415]) ).
thf(f7415,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_20
| ~ spl0_39 ),
inference(forward_demodulation,[],[f138,f601]) ).
thf(f601,plain,
( ( vAPP($o,$o,f3,x) = $true )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f599]) ).
thf(f599,plain,
( spl0_39
<=> ( vAPP($o,$o,f3,x) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
thf(f138,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) != $false )
| spl0_20 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f137,plain,
( spl0_20
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f7582,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_4
| ~ spl0_39
| spl0_47 ),
inference(subsumption_resolution,[],[f7523,f937]) ).
thf(f937,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_47 ),
inference(avatar_component_clause,[],[f936]) ).
thf(f936,plain,
( spl0_47
<=> ( $false = vAPP($o,$o,f0,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
thf(f7523,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(superposition,[],[f7495,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f7495,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(forward_demodulation,[],[f25,f601]) ).
thf(f25,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) = $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f23,plain,
( spl0_4
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f7577,plain,
( ~ spl0_4
| spl0_21
| ~ spl0_23
| ~ spl0_39
| spl0_47 ),
inference(avatar_contradiction_clause,[],[f7576]) ).
thf(f7576,plain,
( $false
| ~ spl0_4
| spl0_21
| ~ spl0_23
| ~ spl0_39
| spl0_47 ),
inference(subsumption_resolution,[],[f7575,f937]) ).
thf(f7575,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| spl0_21
| ~ spl0_23
| ~ spl0_39 ),
inference(forward_demodulation,[],[f7574,f153]) ).
thf(f153,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f151]) ).
thf(f151,plain,
( spl0_23
<=> ( $true = vAPP($o,$o,f0,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f7574,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_4
| spl0_21
| ~ spl0_39 ),
inference(subsumption_resolution,[],[f7520,f7367]) ).
thf(f7367,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| spl0_21
| ~ spl0_39 ),
inference(backward_demodulation,[],[f143,f601]) ).
thf(f143,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))) != $false )
| spl0_21 ),
inference(avatar_component_clause,[],[f142]) ).
thf(f142,plain,
( spl0_21
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f7520,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(superposition,[],[f7495,f4]) ).
thf(f7555,plain,
( ~ spl0_4
| spl0_15
| ~ spl0_23
| ~ spl0_39
| spl0_47 ),
inference(avatar_contradiction_clause,[],[f7554]) ).
thf(f7554,plain,
( $false
| ~ spl0_4
| spl0_15
| ~ spl0_23
| ~ spl0_39
| spl0_47 ),
inference(subsumption_resolution,[],[f7553,f937]) ).
thf(f7553,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| spl0_15
| ~ spl0_23
| ~ spl0_39 ),
inference(forward_demodulation,[],[f7552,f153]) ).
thf(f7552,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_4
| spl0_15
| ~ spl0_23
| ~ spl0_39 ),
inference(forward_demodulation,[],[f7551,f153]) ).
thf(f7551,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_4
| spl0_15
| ~ spl0_39 ),
inference(subsumption_resolution,[],[f7517,f6821]) ).
thf(f6821,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_15
| ~ spl0_39 ),
inference(forward_demodulation,[],[f116,f601]) ).
thf(f116,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))) != $false )
| spl0_15 ),
inference(avatar_component_clause,[],[f115]) ).
thf(f115,plain,
( spl0_15
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f7517,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(superposition,[],[f7495,f4]) ).
thf(f7550,plain,
( ~ spl0_4
| spl0_13
| ~ spl0_23
| ~ spl0_39
| spl0_47
| ~ spl0_69 ),
inference(avatar_contradiction_clause,[],[f7549]) ).
thf(f7549,plain,
( $false
| ~ spl0_4
| spl0_13
| ~ spl0_23
| ~ spl0_39
| spl0_47
| ~ spl0_69 ),
inference(subsumption_resolution,[],[f7548,f937]) ).
thf(f7548,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| spl0_13
| ~ spl0_23
| ~ spl0_39
| ~ spl0_69 ),
inference(forward_demodulation,[],[f7547,f153]) ).
thf(f7547,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_4
| spl0_13
| ~ spl0_39
| ~ spl0_69 ),
inference(forward_demodulation,[],[f7546,f2612]) ).
thf(f2612,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f2610]) ).
thf(f2610,plain,
( spl0_69
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
thf(f7546,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| spl0_13
| ~ spl0_39 ),
inference(subsumption_resolution,[],[f7516,f7365]) ).
thf(f7365,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| spl0_13
| ~ spl0_39 ),
inference(backward_demodulation,[],[f107,f601]) ).
thf(f107,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))) != $false )
| spl0_13 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f106,plain,
( spl0_13
<=> ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f7516,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(superposition,[],[f7495,f4]) ).
thf(f7475,plain,
( spl0_53
| ~ spl0_58
| ~ spl0_60
| ~ spl0_79
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f7426,f4358,f4160,f2158,f1910,f1508]) ).
thf(f1508,plain,
( spl0_53
<=> ( $false = vAPP($o,$o,f0,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
thf(f1910,plain,
( spl0_58
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
thf(f2158,plain,
( spl0_60
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
thf(f4160,plain,
( spl0_79
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
thf(f4358,plain,
( spl0_81
<=> ( $true = vAPP($o,$o,f3,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
thf(f7426,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_58
| ~ spl0_60
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7425,f1912]) ).
thf(f1912,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1910]) ).
thf(f7425,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_60
| ~ spl0_79
| ~ spl0_81 ),
inference(backward_demodulation,[],[f2160,f7424]) ).
thf(f7424,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7423,f4360]) ).
thf(f4360,plain,
( ( $true = vAPP($o,$o,f3,$true) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f4358]) ).
thf(f7423,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f4162,f4360]) ).
thf(f4162,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f4160]) ).
thf(f2160,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f2158]) ).
thf(f7462,plain,
( ~ spl0_11
| ~ spl0_39
| spl0_75 ),
inference(avatar_contradiction_clause,[],[f7461]) ).
thf(f7461,plain,
( $false
| ~ spl0_11
| ~ spl0_39
| spl0_75 ),
inference(subsumption_resolution,[],[f7460,f3953]) ).
thf(f3953,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| spl0_75 ),
inference(avatar_component_clause,[],[f3952]) ).
thf(f3952,plain,
( spl0_75
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
thf(f7460,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_11
| ~ spl0_39 ),
inference(forward_demodulation,[],[f99,f601]) ).
thf(f99,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))) = $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f97,plain,
( spl0_11
<=> ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f7452,plain,
( ~ spl0_38
| ~ spl0_39
| spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f7451]) ).
thf(f7451,plain,
( $false
| ~ spl0_38
| ~ spl0_39
| spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f7450,f2429]) ).
thf(f2429,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| spl0_65 ),
inference(avatar_component_clause,[],[f2428]) ).
thf(f2428,plain,
( spl0_65
<=> ( $false = vAPP($o,$o,f1,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
thf(f7450,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_38
| ~ spl0_39
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7449,f7424]) ).
thf(f7449,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| ~ spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7448,f4360]) ).
thf(f7448,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))) )
| ~ spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7447,f4360]) ).
thf(f7447,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f455,f601]) ).
thf(f455,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))) = $false )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f453]) ).
thf(f453,plain,
( spl0_38
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
thf(f7446,plain,
( ~ spl0_29
| ~ spl0_46
| spl0_78 ),
inference(avatar_contradiction_clause,[],[f7445]) ).
thf(f7445,plain,
( $false
| ~ spl0_29
| ~ spl0_46
| spl0_78 ),
inference(subsumption_resolution,[],[f7443,f4105]) ).
thf(f4105,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_78 ),
inference(avatar_component_clause,[],[f4103]) ).
thf(f4103,plain,
( spl0_78
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
thf(f7443,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_29
| ~ spl0_46 ),
inference(backward_demodulation,[],[f276,f934]) ).
thf(f934,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f932]) ).
thf(f932,plain,
( spl0_46
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
thf(f276,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f274,plain,
( spl0_29
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
thf(f7438,plain,
( ~ spl0_65
| ~ spl0_44
| spl0_66 ),
inference(avatar_split_clause,[],[f7437,f2544,f634,f2428]) ).
thf(f634,plain,
( spl0_44
<=> ( $false = vAPP($o,$o,f2,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
thf(f2544,plain,
( spl0_66
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
thf(f7437,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_44
| spl0_66 ),
inference(forward_demodulation,[],[f7436,f635]) ).
thf(f635,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f634]) ).
thf(f7436,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_44
| spl0_66 ),
inference(forward_demodulation,[],[f7435,f635]) ).
thf(f7435,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_44
| spl0_66 ),
inference(forward_demodulation,[],[f2545,f635]) ).
thf(f2545,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| spl0_66 ),
inference(avatar_component_clause,[],[f2544]) ).
thf(f7433,plain,
( ~ spl0_70
| ~ spl0_44
| spl0_72 ),
inference(avatar_split_clause,[],[f7432,f2679,f634,f2614]) ).
thf(f2614,plain,
( spl0_70
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
thf(f2679,plain,
( spl0_72
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
thf(f7432,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_44
| spl0_72 ),
inference(forward_demodulation,[],[f2680,f635]) ).
thf(f2680,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| spl0_72 ),
inference(avatar_component_clause,[],[f2679]) ).
thf(f7398,plain,
( spl0_8
| ~ spl0_23
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f7397]) ).
thf(f7397,plain,
( $false
| spl0_8
| ~ spl0_23
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f7396,f153]) ).
thf(f7396,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_8
| ~ spl0_73 ),
inference(backward_demodulation,[],[f84,f3921]) ).
thf(f3921,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f3919]) ).
thf(f3919,plain,
( spl0_73
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
thf(f84,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_8 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f83,plain,
( spl0_8
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f7374,plain,
( ~ spl0_79
| spl0_30
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f7347,f1307,f284,f4160]) ).
thf(f284,plain,
( spl0_30
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
thf(f1307,plain,
( spl0_51
<=> ( $true = vAPP($o,$o,f3,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
thf(f7347,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| spl0_30
| ~ spl0_51 ),
inference(forward_demodulation,[],[f285,f1309]) ).
thf(f1309,plain,
( ( $true = vAPP($o,$o,f3,$false) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1307]) ).
thf(f285,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) )
| spl0_30 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f7360,plain,
( ~ spl0_4
| ~ spl0_22
| ~ spl0_23
| spl0_47 ),
inference(avatar_contradiction_clause,[],[f7359]) ).
thf(f7359,plain,
( $false
| ~ spl0_4
| ~ spl0_22
| ~ spl0_23
| spl0_47 ),
inference(subsumption_resolution,[],[f7358,f937]) ).
thf(f7358,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| ~ spl0_22
| ~ spl0_23 ),
inference(forward_demodulation,[],[f7357,f153]) ).
thf(f7357,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_4
| ~ spl0_22 ),
inference(backward_demodulation,[],[f25,f149]) ).
thf(f149,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))) = $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f147]) ).
thf(f147,plain,
( spl0_22
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f7333,plain,
( ~ spl0_23
| spl0_73
| ~ spl0_74 ),
inference(avatar_contradiction_clause,[],[f7332]) ).
thf(f7332,plain,
( $false
| ~ spl0_23
| spl0_73
| ~ spl0_74 ),
inference(subsumption_resolution,[],[f7331,f153]) ).
thf(f7331,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_73
| ~ spl0_74 ),
inference(forward_demodulation,[],[f3920,f3925]) ).
thf(f3925,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f3923]) ).
thf(f3923,plain,
( spl0_74
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
thf(f3920,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_73 ),
inference(avatar_component_clause,[],[f3919]) ).
thf(f7330,plain,
( ~ spl0_23
| ~ spl0_41
| spl0_47
| ~ spl0_51
| ~ spl0_60
| ~ spl0_77 ),
inference(avatar_contradiction_clause,[],[f7329]) ).
thf(f7329,plain,
( $false
| ~ spl0_23
| ~ spl0_41
| spl0_47
| ~ spl0_51
| ~ spl0_60
| ~ spl0_77 ),
inference(subsumption_resolution,[],[f7328,f937]) ).
thf(f7328,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_23
| ~ spl0_41
| ~ spl0_51
| ~ spl0_60
| ~ spl0_77 ),
inference(forward_demodulation,[],[f7327,f153]) ).
thf(f7327,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_23
| ~ spl0_41
| ~ spl0_51
| ~ spl0_60
| ~ spl0_77 ),
inference(forward_demodulation,[],[f7324,f153]) ).
thf(f7324,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_41
| ~ spl0_51
| ~ spl0_60
| ~ spl0_77 ),
inference(backward_demodulation,[],[f2160,f7323]) ).
thf(f7323,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_41
| ~ spl0_51
| ~ spl0_77 ),
inference(forward_demodulation,[],[f7322,f1309]) ).
thf(f7322,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_41
| ~ spl0_77 ),
inference(forward_demodulation,[],[f4100,f619]) ).
thf(f619,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f617]) ).
thf(f617,plain,
( spl0_41
<=> ( $false = vAPP($o,$o,f3,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
thf(f4100,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f4099]) ).
thf(f4099,plain,
( spl0_77
<=> ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
thf(f7304,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| ~ spl0_44
| ~ spl0_51
| spl0_55
| ~ spl0_65
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f7303]) ).
thf(f7303,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| ~ spl0_44
| ~ spl0_51
| spl0_55
| ~ spl0_65
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f7302,f7274]) ).
thf(f7274,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51
| ~ spl0_65
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7273,f2430]) ).
thf(f2430,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f2428]) ).
thf(f7273,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51
| ~ spl0_65
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7272,f2430]) ).
thf(f7272,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7271,f7212]) ).
thf(f7212,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_41
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7203,f1309]) ).
thf(f7203,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_41
| ~ spl0_79 ),
inference(backward_demodulation,[],[f4162,f619]) ).
thf(f7271,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7270,f1309]) ).
thf(f7270,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7269,f619]) ).
thf(f7269,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7268,f1309]) ).
thf(f7268,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f12,f72]) ).
thf(f72,plain,
( ( x = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f70,plain,
( spl0_5
<=> ( x = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f12,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))) = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
thf(f10,plain,
( spl0_1
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f7302,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| ~ spl0_44
| spl0_55
| ~ spl0_65 ),
inference(forward_demodulation,[],[f7301,f2430]) ).
thf(f7301,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_44
| spl0_55 ),
inference(forward_demodulation,[],[f7300,f635]) ).
thf(f7300,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_44
| spl0_55 ),
inference(forward_demodulation,[],[f7299,f635]) ).
thf(f7299,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_44
| spl0_55 ),
inference(forward_demodulation,[],[f1897,f635]) ).
thf(f1897,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_55 ),
inference(avatar_component_clause,[],[f1896]) ).
thf(f1896,plain,
( spl0_55
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
thf(f7296,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| spl0_47
| ~ spl0_51
| ~ spl0_58
| ~ spl0_65
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f7295]) ).
thf(f7295,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| spl0_47
| ~ spl0_51
| ~ spl0_58
| ~ spl0_65
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f7294,f937]) ).
thf(f7294,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51
| ~ spl0_58
| ~ spl0_65
| ~ spl0_79 ),
inference(forward_demodulation,[],[f1912,f7274]) ).
thf(f7267,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39
| ~ spl0_51 ),
inference(avatar_contradiction_clause,[],[f7266]) ).
thf(f7266,plain,
( $false
| spl0_2
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39
| ~ spl0_51 ),
inference(subsumption_resolution,[],[f7265,f153]) ).
thf(f7265,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_2
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7264,f153]) ).
thf(f7264,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_2
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7263,f153]) ).
thf(f7263,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| spl0_2
| ~ spl0_5
| ~ spl0_18
| ~ spl0_39
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7262,f6817]) ).
thf(f6817,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_18
| ~ spl0_39 ),
inference(forward_demodulation,[],[f130,f601]) ).
thf(f130,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))) = $true )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f128,plain,
( spl0_18
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f7262,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_2
| ~ spl0_5
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7261,f1309]) ).
thf(f7261,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f15,f72]) ).
thf(f15,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) != $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f14,plain,
( spl0_2
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f7253,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39
| spl0_47
| ~ spl0_51 ),
inference(avatar_contradiction_clause,[],[f7252]) ).
thf(f7252,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39
| spl0_47
| ~ spl0_51 ),
inference(subsumption_resolution,[],[f7251,f937]) ).
thf(f7251,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7250,f153]) ).
thf(f7250,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7249,f153]) ).
thf(f7249,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18
| ~ spl0_39
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7248,f6817]) ).
thf(f7248,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7247,f1309]) ).
thf(f7247,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f25,f72]) ).
thf(f7246,plain,
( spl0_8
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39 ),
inference(avatar_contradiction_clause,[],[f7245]) ).
thf(f7245,plain,
( $false
| spl0_8
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39 ),
inference(subsumption_resolution,[],[f7244,f153]) ).
thf(f7244,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_8
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39 ),
inference(forward_demodulation,[],[f7243,f153]) ).
thf(f7243,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_8
| ~ spl0_18
| ~ spl0_23
| ~ spl0_39 ),
inference(forward_demodulation,[],[f7242,f153]) ).
thf(f7242,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| spl0_8
| ~ spl0_18
| ~ spl0_39 ),
inference(forward_demodulation,[],[f84,f6817]) ).
thf(f7181,plain,
( ~ spl0_29
| ~ spl0_46
| spl0_53
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[],[f7180]) ).
thf(f7180,plain,
( $false
| ~ spl0_29
| ~ spl0_46
| spl0_53
| ~ spl0_65 ),
inference(subsumption_resolution,[],[f7179,f1510]) ).
thf(f1510,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_53 ),
inference(avatar_component_clause,[],[f1508]) ).
thf(f7179,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_29
| ~ spl0_46
| ~ spl0_65 ),
inference(forward_demodulation,[],[f7177,f2430]) ).
thf(f7177,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_29
| ~ spl0_46 ),
inference(backward_demodulation,[],[f276,f934]) ).
thf(f7163,plain,
( ~ spl0_25
| spl0_53
| ~ spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f7162]) ).
thf(f7162,plain,
( $false
| ~ spl0_25
| spl0_53
| ~ spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f7161,f1510]) ).
thf(f7161,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_25
| ~ spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7160,f2430]) ).
thf(f7160,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_25
| ~ spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7159,f2430]) ).
thf(f7159,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_25
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7135,f7138]) ).
thf(f7138,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7132,f4360]) ).
thf(f7132,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| ~ spl0_79
| ~ spl0_81 ),
inference(backward_demodulation,[],[f4162,f4360]) ).
thf(f7135,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_25
| ~ spl0_81 ),
inference(backward_demodulation,[],[f252,f4360]) ).
thf(f252,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f250]) ).
thf(f250,plain,
( spl0_25
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f7157,plain,
( ~ spl0_50
| spl0_53
| ~ spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f7156]) ).
thf(f7156,plain,
( $false
| ~ spl0_50
| spl0_53
| ~ spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f7155,f1510]) ).
thf(f7155,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_50
| ~ spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7154,f2430]) ).
thf(f7154,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_50
| ~ spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7153,f2430]) ).
thf(f7153,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_50
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7152,f7138]) ).
thf(f7152,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_50
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7151,f4360]) ).
thf(f7151,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_50
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7133,f4360]) ).
thf(f7133,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_50
| ~ spl0_81 ),
inference(backward_demodulation,[],[f1113,f4360]) ).
thf(f1113,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1111]) ).
thf(f1111,plain,
( spl0_50
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
thf(f7150,plain,
( ~ spl0_12
| spl0_47
| ~ spl0_58
| ~ spl0_79
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f7149]) ).
thf(f7149,plain,
( $false
| ~ spl0_12
| spl0_47
| ~ spl0_58
| ~ spl0_79
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f7148,f937]) ).
thf(f7148,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_12
| ~ spl0_58
| ~ spl0_79
| ~ spl0_81 ),
inference(backward_demodulation,[],[f1912,f7147]) ).
thf(f7147,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_12
| ~ spl0_58
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7141,f1912]) ).
thf(f7141,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_12
| ~ spl0_79
| ~ spl0_81 ),
inference(backward_demodulation,[],[f103,f7138]) ).
thf(f103,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f101,plain,
( spl0_12
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f7127,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_32
| ~ spl0_51
| spl0_53
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[],[f7126]) ).
thf(f7126,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_32
| ~ spl0_51
| spl0_53
| ~ spl0_65 ),
inference(subsumption_resolution,[],[f7125,f1510]) ).
thf(f7125,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_32
| ~ spl0_51
| ~ spl0_65 ),
inference(forward_demodulation,[],[f7124,f2430]) ).
thf(f7124,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_32
| ~ spl0_51 ),
inference(backward_demodulation,[],[f7073,f7028]) ).
thf(f7028,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_32
| ~ spl0_51 ),
inference(forward_demodulation,[],[f299,f1309]) ).
thf(f299,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f297,plain,
( spl0_32
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
thf(f7073,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7072,f1309]) ).
thf(f7072,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f21,f72]) ).
thf(f21,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))) = $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f19,plain,
( spl0_3
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f7104,plain,
( ~ spl0_53
| ~ spl0_58
| spl0_62 ),
inference(avatar_split_clause,[],[f7103,f2168,f1910,f1508]) ).
thf(f2168,plain,
( spl0_62
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
thf(f7103,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_58
| spl0_62 ),
inference(forward_demodulation,[],[f2169,f1912]) ).
thf(f2169,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_62 ),
inference(avatar_component_clause,[],[f2168]) ).
thf(f7099,plain,
( ~ spl0_53
| ~ spl0_65
| spl0_78 ),
inference(avatar_split_clause,[],[f7098,f4103,f2428,f1508]) ).
thf(f7098,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_65
| spl0_78 ),
inference(forward_demodulation,[],[f4105,f2430]) ).
thf(f7092,plain,
( spl0_53
| ~ spl0_3
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51
| ~ spl0_65
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f7078,f4160,f2428,f1307,f617,f70,f19,f1508]) ).
thf(f7078,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51
| ~ spl0_65
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7077,f2430]) ).
thf(f7077,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51
| ~ spl0_65
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7076,f2430]) ).
thf(f7076,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7075,f6985]) ).
thf(f6985,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_41
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f6984,f1309]) ).
thf(f6984,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_41
| ~ spl0_79 ),
inference(forward_demodulation,[],[f4162,f619]) ).
thf(f7075,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7074,f1309]) ).
thf(f7074,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_41
| ~ spl0_51 ),
inference(forward_demodulation,[],[f7073,f619]) ).
thf(f7058,plain,
( ~ spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_53
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f7057]) ).
thf(f7057,plain,
( $false
| ~ spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_53
| ~ spl0_79 ),
inference(trivial_inequality_removal,[],[f7056]) ).
thf(f7056,plain,
( ( $true = $false )
| ~ spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_53
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7055,f1509]) ).
thf(f1509,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1508]) ).
thf(f7055,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_53
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7054,f1509]) ).
thf(f7054,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_53
| ~ spl0_79 ),
inference(forward_demodulation,[],[f7053,f1509]) ).
thf(f7053,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f103,f6985]) ).
thf(f6990,plain,
( ~ spl0_64
| ~ spl0_69
| spl0_71 ),
inference(avatar_split_clause,[],[f6989,f2645,f2610,f2181]) ).
thf(f2181,plain,
( spl0_64
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
thf(f2645,plain,
( spl0_71
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
thf(f6989,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_69
| spl0_71 ),
inference(forward_demodulation,[],[f2646,f2612]) ).
thf(f2646,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_71 ),
inference(avatar_component_clause,[],[f2645]) ).
thf(f6974,plain,
( spl0_23
| spl0_47 ),
inference(avatar_contradiction_clause,[],[f6973]) ).
thf(f6973,plain,
( $false
| spl0_23
| spl0_47 ),
inference(subsumption_resolution,[],[f6969,f937]) ).
thf(f6969,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| spl0_23 ),
inference(trivial_inequality_removal,[],[f6968]) ).
thf(f6968,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f0,$true) )
| spl0_23 ),
inference(superposition,[],[f152,f4]) ).
thf(f152,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_23 ),
inference(avatar_component_clause,[],[f151]) ).
thf(f6913,plain,
( spl0_31
| ~ spl0_46
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f6912]) ).
thf(f6912,plain,
( $false
| spl0_31
| ~ spl0_46
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f6905,f1509]) ).
thf(f6905,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_31
| ~ spl0_46 ),
inference(backward_demodulation,[],[f289,f934]) ).
thf(f289,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_31 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f288,plain,
( spl0_31
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
thf(f6902,plain,
( ~ spl0_53
| spl0_58 ),
inference(avatar_contradiction_clause,[],[f6901]) ).
thf(f6901,plain,
( $false
| ~ spl0_53
| spl0_58 ),
inference(subsumption_resolution,[],[f6900,f1509]) ).
thf(f6900,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_53
| spl0_58 ),
inference(forward_demodulation,[],[f1911,f1509]) ).
thf(f1911,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_58 ),
inference(avatar_component_clause,[],[f1910]) ).
thf(f6872,plain,
( spl0_64
| ~ spl0_69
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f6871,f2645,f2610,f2181]) ).
thf(f6871,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_69
| ~ spl0_71 ),
inference(forward_demodulation,[],[f2647,f2612]) ).
thf(f2647,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f2645]) ).
thf(f6870,plain,
( spl0_64
| ~ spl0_20
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44
| ~ spl0_77
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f6840,f4358,f4099,f634,f622,f599,f137,f2181]) ).
thf(f622,plain,
( spl0_42
<=> ( $false = vAPP($o,$o,f2,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
thf(f6840,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_20
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44
| ~ spl0_77
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6839,f6767]) ).
thf(f6767,plain,
( ( $true = vAPP($o,$o,f1,$false) )
| ~ spl0_42
| ~ spl0_77
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6766,f623]) ).
thf(f623,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f622]) ).
thf(f6766,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_77
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6765,f4360]) ).
thf(f6765,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| ~ spl0_77
| ~ spl0_81 ),
inference(forward_demodulation,[],[f4100,f4360]) ).
thf(f6839,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_20
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44 ),
inference(forward_demodulation,[],[f6838,f635]) ).
thf(f6838,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_20
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44 ),
inference(forward_demodulation,[],[f6707,f635]) ).
thf(f6707,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_20
| ~ spl0_39
| ~ spl0_42 ),
inference(forward_demodulation,[],[f6706,f623]) ).
thf(f6706,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_20
| ~ spl0_39 ),
inference(forward_demodulation,[],[f139,f601]) ).
thf(f139,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) = $false )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f6775,plain,
( spl0_44
| ~ spl0_42
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f6774,f3952,f622,f634]) ).
thf(f6774,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_42
| ~ spl0_75 ),
inference(forward_demodulation,[],[f3954,f623]) ).
thf(f3954,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f3952]) ).
thf(f6764,plain,
( ~ spl0_65
| ~ spl0_42
| spl0_79
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f6763,f4358,f4160,f622,f2428]) ).
thf(f6763,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_42
| spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6762,f623]) ).
thf(f6762,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6761,f4360]) ).
thf(f6761,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f4161,f4360]) ).
thf(f4161,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| spl0_79 ),
inference(avatar_component_clause,[],[f4160]) ).
thf(f6696,plain,
( spl0_25
| ~ spl0_42
| ~ spl0_53
| ~ spl0_65
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f6695]) ).
thf(f6695,plain,
( $false
| spl0_25
| ~ spl0_42
| ~ spl0_53
| ~ spl0_65
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f6694,f1509]) ).
thf(f6694,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_25
| ~ spl0_42
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6693,f2430]) ).
thf(f6693,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_25
| ~ spl0_42
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6692,f2430]) ).
thf(f6692,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_25
| ~ spl0_42
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6691,f2430]) ).
thf(f6691,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_25
| ~ spl0_42
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6690,f623]) ).
thf(f6690,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_25
| ~ spl0_81 ),
inference(forward_demodulation,[],[f251,f4360]) ).
thf(f251,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_25 ),
inference(avatar_component_clause,[],[f250]) ).
thf(f6683,plain,
( ~ spl0_42
| spl0_50
| ~ spl0_53
| ~ spl0_65
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f6682]) ).
thf(f6682,plain,
( $false
| ~ spl0_42
| spl0_50
| ~ spl0_53
| ~ spl0_65
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f6681,f1509]) ).
thf(f6681,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_42
| spl0_50
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6680,f2430]) ).
thf(f6680,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_42
| spl0_50
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6679,f2430]) ).
thf(f6679,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_42
| spl0_50
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6678,f2430]) ).
thf(f6678,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_42
| spl0_50
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6677,f623]) ).
thf(f6677,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_50
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6676,f4360]) ).
thf(f6676,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_50
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6675,f4360]) ).
thf(f6675,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| spl0_50
| ~ spl0_81 ),
inference(forward_demodulation,[],[f1112,f4360]) ).
thf(f1112,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| spl0_50 ),
inference(avatar_component_clause,[],[f1111]) ).
thf(f6635,plain,
( spl0_14
| ~ spl0_10
| ~ spl0_42
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f6623,f1504,f622,f92,f110]) ).
thf(f110,plain,
( spl0_14
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f92,plain,
( spl0_10
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f1504,plain,
( spl0_52
<=> ( $true = vAPP($o,$o,f2,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
thf(f6623,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_10
| ~ spl0_42
| ~ spl0_52 ),
inference(forward_demodulation,[],[f6622,f1505]) ).
thf(f1505,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1504]) ).
thf(f6622,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_10
| ~ spl0_42 ),
inference(forward_demodulation,[],[f94,f623]) ).
thf(f94,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f6630,plain,
( spl0_79
| ~ spl0_37
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f6628,f599,f448,f4160]) ).
thf(f448,plain,
( spl0_37
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
thf(f6628,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| ~ spl0_37
| ~ spl0_39 ),
inference(backward_demodulation,[],[f450,f601]) ).
thf(f450,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x))))) = $false )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f448]) ).
thf(f6559,plain,
( spl0_65
| ~ spl0_41
| ~ spl0_42
| ~ spl0_51
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f6558,f4160,f1307,f622,f617,f2428]) ).
thf(f6558,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_41
| ~ spl0_42
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f6557,f623]) ).
thf(f6557,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_41
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f6556,f1309]) ).
thf(f6556,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_41
| ~ spl0_79 ),
inference(forward_demodulation,[],[f4162,f619]) ).
thf(f6481,plain,
( ~ spl0_14
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f6480]) ).
thf(f6480,plain,
( $false
| ~ spl0_14
| ~ spl0_71 ),
inference(trivial_inequality_removal,[],[f6479]) ).
thf(f6479,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_71 ),
inference(backward_demodulation,[],[f112,f2647]) ).
thf(f112,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f6443,plain,
( ~ spl0_46
| ~ spl0_52
| spl0_72 ),
inference(avatar_split_clause,[],[f6436,f2679,f1504,f932]) ).
thf(f6436,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_52
| spl0_72 ),
inference(backward_demodulation,[],[f2680,f1505]) ).
thf(f6442,plain,
( ~ spl0_29
| spl0_43
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f6434,f1504,f628,f274]) ).
thf(f628,plain,
( spl0_43
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
thf(f6434,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| spl0_43
| ~ spl0_52 ),
inference(backward_demodulation,[],[f629,f1505]) ).
thf(f629,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_43 ),
inference(avatar_component_clause,[],[f628]) ).
thf(f6426,plain,
( ~ spl0_44
| ~ spl0_42
| spl0_75 ),
inference(avatar_split_clause,[],[f6425,f3952,f622,f634]) ).
thf(f6425,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_42
| spl0_75 ),
inference(forward_demodulation,[],[f3953,f623]) ).
thf(f6284,plain,
( ~ spl0_2
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44
| ~ spl0_62
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[],[f6283]) ).
thf(f6283,plain,
( $false
| ~ spl0_2
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44
| ~ spl0_62
| ~ spl0_65 ),
inference(trivial_inequality_removal,[],[f6282]) ).
thf(f6282,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44
| ~ spl0_62
| ~ spl0_65 ),
inference(forward_demodulation,[],[f6224,f2170]) ).
thf(f2170,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f2168]) ).
thf(f6224,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_2
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44
| ~ spl0_65 ),
inference(forward_demodulation,[],[f6056,f2430]) ).
thf(f6056,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_2
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44 ),
inference(forward_demodulation,[],[f6055,f635]) ).
thf(f6055,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_2
| ~ spl0_39
| ~ spl0_42
| ~ spl0_44 ),
inference(forward_demodulation,[],[f6054,f635]) ).
thf(f6054,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_2
| ~ spl0_39
| ~ spl0_42 ),
inference(forward_demodulation,[],[f6053,f623]) ).
thf(f6053,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_2
| ~ spl0_39 ),
inference(forward_demodulation,[],[f16,f601]) ).
thf(f16,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f6170,plain,
( spl0_65
| ~ spl0_44
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f6169,f2544,f634,f2428]) ).
thf(f6169,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_44
| ~ spl0_66 ),
inference(forward_demodulation,[],[f6168,f635]) ).
thf(f6168,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_44
| ~ spl0_66 ),
inference(forward_demodulation,[],[f6167,f635]) ).
thf(f6167,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_44
| ~ spl0_66 ),
inference(forward_demodulation,[],[f2546,f635]) ).
thf(f2546,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f2544]) ).
thf(f6004,plain,
( ~ spl0_47
| ~ spl0_19
| spl0_67 ),
inference(avatar_split_clause,[],[f6003,f2548,f132,f936]) ).
thf(f132,plain,
( spl0_19
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f2548,plain,
( spl0_67
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
thf(f6003,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| ~ spl0_19
| spl0_67 ),
inference(forward_demodulation,[],[f2549,f134]) ).
thf(f134,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f2549,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| spl0_67 ),
inference(avatar_component_clause,[],[f2548]) ).
thf(f5977,plain,
( spl0_36
| ~ spl0_39
| ~ spl0_42
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f5976]) ).
thf(f5976,plain,
( $false
| spl0_36
| ~ spl0_39
| ~ spl0_42
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5975,f623]) ).
thf(f5975,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_36
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5974,f4360]) ).
thf(f5974,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| spl0_36
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5130,f4360]) ).
thf(f5130,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| spl0_36
| ~ spl0_39 ),
inference(forward_demodulation,[],[f444,f601]) ).
thf(f444,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))) != $false )
| spl0_36 ),
inference(avatar_component_clause,[],[f443]) ).
thf(f443,plain,
( spl0_36
<=> ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
thf(f5973,plain,
( ~ spl0_30
| ~ spl0_32
| spl0_65 ),
inference(avatar_contradiction_clause,[],[f5972]) ).
thf(f5972,plain,
( $false
| ~ spl0_30
| ~ spl0_32
| spl0_65 ),
inference(subsumption_resolution,[],[f5971,f2429]) ).
thf(f5971,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_30
| ~ spl0_32 ),
inference(backward_demodulation,[],[f299,f286]) ).
thf(f286,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f5927,plain,
( ~ spl0_42
| spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f5926]) ).
thf(f5926,plain,
( $false
| ~ spl0_42
| spl0_65
| ~ spl0_79
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5925,f2429]) ).
thf(f5925,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_42
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5924,f623]) ).
thf(f5924,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5909,f4360]) ).
thf(f5909,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| ~ spl0_79
| ~ spl0_81 ),
inference(backward_demodulation,[],[f4162,f4360]) ).
thf(f5866,plain,
( spl0_5
| ~ spl0_41
| spl0_7 ),
inference(avatar_split_clause,[],[f5233,f79,f617,f70]) ).
thf(f79,plain,
( spl0_7
<=> ( vAPP($o,$o,f3,x) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f5233,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( x = $false )
| spl0_7 ),
inference(superposition,[],[f80,f4]) ).
thf(f80,plain,
( ( vAPP($o,$o,f3,x) != $false )
| spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f5865,plain,
( spl0_5
| spl0_81
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f5269,f599,f4358,f70]) ).
thf(f5269,plain,
( ( $true = vAPP($o,$o,f3,$true) )
| ( x = $false )
| ~ spl0_39 ),
inference(superposition,[],[f601,f4]) ).
thf(f5797,plain,
( ~ spl0_65
| spl0_15
| ~ spl0_39
| ~ spl0_44
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f5796,f3952,f634,f599,f115,f2428]) ).
thf(f5796,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| spl0_15
| ~ spl0_39
| ~ spl0_44
| ~ spl0_75 ),
inference(forward_demodulation,[],[f5791,f635]) ).
thf(f5791,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| spl0_15
| ~ spl0_39
| ~ spl0_75 ),
inference(backward_demodulation,[],[f5156,f3954]) ).
thf(f5156,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_15
| ~ spl0_39 ),
inference(forward_demodulation,[],[f116,f601]) ).
thf(f5784,plain,
( ~ spl0_44
| ~ spl0_55
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f5783]) ).
thf(f5783,plain,
( $false
| ~ spl0_44
| ~ spl0_55
| ~ spl0_78 ),
inference(trivial_inequality_removal,[],[f5782]) ).
thf(f5782,plain,
( ( $true = $false )
| ~ spl0_44
| ~ spl0_55
| ~ spl0_78 ),
inference(backward_demodulation,[],[f5230,f4104]) ).
thf(f4104,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f4103]) ).
thf(f5230,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_44
| ~ spl0_55 ),
inference(forward_demodulation,[],[f5229,f635]) ).
thf(f5229,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_44
| ~ spl0_55 ),
inference(forward_demodulation,[],[f5228,f635]) ).
thf(f5228,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_44
| ~ spl0_55 ),
inference(forward_demodulation,[],[f1898,f635]) ).
thf(f1898,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1896]) ).
thf(f5772,plain,
( spl0_65
| ~ spl0_61
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f5114,f2544,f2164,f2428]) ).
thf(f2164,plain,
( spl0_61
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
thf(f5114,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_61
| ~ spl0_66 ),
inference(backward_demodulation,[],[f2546,f2166]) ).
thf(f2166,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f2164]) ).
thf(f5766,plain,
( ~ spl0_42
| spl0_28
| ~ spl0_41
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f5607,f1307,f617,f270,f622]) ).
thf(f270,plain,
( spl0_28
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
thf(f5607,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_28
| ~ spl0_41
| ~ spl0_51 ),
inference(forward_demodulation,[],[f5585,f1309]) ).
thf(f5585,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| spl0_28
| ~ spl0_41
| ~ spl0_51 ),
inference(backward_demodulation,[],[f5138,f619]) ).
thf(f5138,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| spl0_28
| ~ spl0_51 ),
inference(forward_demodulation,[],[f271,f1309]) ).
thf(f271,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| spl0_28 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f5756,plain,
( spl0_27
| ~ spl0_31
| ~ spl0_41
| ~ spl0_51
| ~ spl0_77 ),
inference(avatar_contradiction_clause,[],[f5755]) ).
thf(f5755,plain,
( $false
| spl0_27
| ~ spl0_31
| ~ spl0_41
| ~ spl0_51
| ~ spl0_77 ),
inference(subsumption_resolution,[],[f5749,f290]) ).
thf(f290,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f5749,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_27
| ~ spl0_41
| ~ spl0_51
| ~ spl0_77 ),
inference(backward_demodulation,[],[f260,f5746]) ).
thf(f5746,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_41
| ~ spl0_51
| ~ spl0_77 ),
inference(forward_demodulation,[],[f5745,f1309]) ).
thf(f5745,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_41
| ~ spl0_77 ),
inference(forward_demodulation,[],[f4100,f619]) ).
thf(f260,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_27 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f259,plain,
( spl0_27
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
thf(f5754,plain,
( ~ spl0_1
| ~ spl0_31
| ~ spl0_39
| ~ spl0_41
| ~ spl0_51
| ~ spl0_77 ),
inference(avatar_contradiction_clause,[],[f5753]) ).
thf(f5753,plain,
( $false
| ~ spl0_1
| ~ spl0_31
| ~ spl0_39
| ~ spl0_41
| ~ spl0_51
| ~ spl0_77 ),
inference(trivial_inequality_removal,[],[f5752]) ).
thf(f5752,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_39
| ~ spl0_41
| ~ spl0_51
| ~ spl0_77 ),
inference(forward_demodulation,[],[f5748,f290]) ).
thf(f5748,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_41
| ~ spl0_51
| ~ spl0_77 ),
inference(backward_demodulation,[],[f5744,f5746]) ).
thf(f5744,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_41
| ~ spl0_51 ),
inference(backward_demodulation,[],[f5741,f1309]) ).
thf(f5741,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_41 ),
inference(backward_demodulation,[],[f5178,f619]) ).
thf(f5178,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_1
| ~ spl0_39 ),
inference(forward_demodulation,[],[f12,f601]) ).
thf(f5730,plain,
( spl0_13
| ~ spl0_39
| ~ spl0_41
| ~ spl0_44
| ~ spl0_51
| spl0_77
| spl0_79 ),
inference(avatar_contradiction_clause,[],[f5729]) ).
thf(f5729,plain,
( $false
| spl0_13
| ~ spl0_39
| ~ spl0_41
| ~ spl0_44
| ~ spl0_51
| spl0_77
| spl0_79 ),
inference(subsumption_resolution,[],[f5708,f635]) ).
thf(f5708,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_13
| ~ spl0_39
| ~ spl0_41
| ~ spl0_51
| spl0_77
| spl0_79 ),
inference(backward_demodulation,[],[f4930,f5693]) ).
thf(f5693,plain,
( ! [X0: $o] : ( $false = X0 )
| ~ spl0_41
| ~ spl0_51
| spl0_77
| spl0_79 ),
inference(subsumption_resolution,[],[f5692,f5659]) ).
thf(f5659,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,X0)) )
| ( $false = X0 ) )
| ~ spl0_41
| ~ spl0_51
| spl0_79 ),
inference(superposition,[],[f5606,f4]) ).
thf(f5606,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_41
| ~ spl0_51
| spl0_79 ),
inference(forward_demodulation,[],[f5582,f1309]) ).
thf(f5582,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_41
| spl0_79 ),
inference(backward_demodulation,[],[f4161,f619]) ).
thf(f5692,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,X0)) )
| ( $false = X0 ) )
| ~ spl0_41
| ~ spl0_51
| spl0_77 ),
inference(duplicate_literal_removal,[],[f5691]) ).
thf(f5691,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,X0)) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl0_41
| ~ spl0_51
| spl0_77 ),
inference(binary_proxy_clausification,[],[f5684]) ).
thf(f5684,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,X0)) != X0 )
| ( $false = X0 ) )
| ~ spl0_41
| ~ spl0_51
| spl0_77 ),
inference(superposition,[],[f5605,f4]) ).
thf(f5605,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_41
| ~ spl0_51
| spl0_77 ),
inference(forward_demodulation,[],[f5581,f1309]) ).
thf(f5581,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_41
| spl0_77 ),
inference(backward_demodulation,[],[f4101,f619]) ).
thf(f4101,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| spl0_77 ),
inference(avatar_component_clause,[],[f4099]) ).
thf(f4930,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| spl0_13
| ~ spl0_39 ),
inference(backward_demodulation,[],[f107,f601]) ).
thf(f5722,plain,
( ~ spl0_41
| ~ spl0_51
| spl0_77
| spl0_79 ),
inference(avatar_contradiction_clause,[],[f5721]) ).
thf(f5721,plain,
( $false
| ~ spl0_41
| ~ spl0_51
| spl0_77
| spl0_79 ),
inference(trivial_inequality_removal,[],[f5712]) ).
thf(f5712,plain,
( ( $true = $false )
| ~ spl0_41
| ~ spl0_51
| spl0_77
| spl0_79 ),
inference(backward_demodulation,[],[f1309,f5693]) ).
thf(f5621,plain,
( ~ spl0_46
| ~ spl0_31
| spl0_53 ),
inference(avatar_split_clause,[],[f5299,f1508,f288,f932]) ).
thf(f5299,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_31
| spl0_53 ),
inference(trivial_inequality_removal,[],[f5298]) ).
thf(f5298,plain,
( ( $false != $false )
| ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_31
| spl0_53 ),
inference(constrained_superposition,[],[f1510,f290]) ).
thf(f5573,plain,
( spl0_32
| ~ spl0_38
| ~ spl0_39
| ~ spl0_51 ),
inference(avatar_contradiction_clause,[],[f5572]) ).
thf(f5572,plain,
( $false
| spl0_32
| ~ spl0_38
| ~ spl0_39
| ~ spl0_51 ),
inference(subsumption_resolution,[],[f5429,f5547]) ).
thf(f5547,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f455,f601]) ).
thf(f5429,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| spl0_32
| ~ spl0_51 ),
inference(forward_demodulation,[],[f298,f1309]) ).
thf(f298,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| spl0_32 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f5525,plain,
( ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| spl0_42
| ~ spl0_47
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f5524]) ).
thf(f5524,plain,
( $false
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| spl0_42
| ~ spl0_47
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f5523]) ).
thf(f5523,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| spl0_42
| ~ spl0_47
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5522,f938]) ).
thf(f938,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f936]) ).
thf(f5522,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| spl0_42
| ~ spl0_47
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5521,f5498]) ).
thf(f5498,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| ~ spl0_47
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f5497]) ).
thf(f5497,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| ~ spl0_47
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5477,f5493]) ).
thf(f5493,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_47
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f5492]) ).
thf(f5492,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_47
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5463,f938]) ).
thf(f5463,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_81 ),
inference(superposition,[],[f5180,f4]) ).
thf(f5180,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5179,f4360]) ).
thf(f5179,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5178,f4360]) ).
thf(f5477,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ( $true = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| ~ spl0_81 ),
inference(binary_proxy_clausification,[],[f5476]) ).
thf(f5476,plain,
( ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f5466]) ).
thf(f5466,plain,
( ( $true = $false )
| ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| ~ spl0_81 ),
inference(constrained_superposition,[],[f5180,f303]) ).
thf(f303,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f301,plain,
( spl0_33
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
thf(f5521,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| spl0_42
| ~ spl0_47
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5520,f5498]) ).
thf(f5520,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_39
| spl0_42
| ~ spl0_47
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5519,f5498]) ).
thf(f5519,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_1
| ~ spl0_39
| spl0_42
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5457,f624]) ).
thf(f624,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_42 ),
inference(avatar_component_clause,[],[f622]) ).
thf(f5457,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_81 ),
inference(superposition,[],[f5180,f4]) ).
thf(f5491,plain,
( ~ spl0_1
| ~ spl0_33
| spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f5490]) ).
thf(f5490,plain,
( $false
| ~ spl0_1
| ~ spl0_33
| spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f5489]) ).
thf(f5489,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_33
| spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5488,f303]) ).
thf(f5488,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_1
| spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5461,f5426]) ).
thf(f5426,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5425,f4360]) ).
thf(f5425,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))) )
| spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5424,f4360]) ).
thf(f5424,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f454,f601]) ).
thf(f454,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))) != $false )
| spl0_38 ),
inference(avatar_component_clause,[],[f453]) ).
thf(f5461,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_81 ),
inference(superposition,[],[f5180,f4]) ).
thf(f5487,plain,
( ~ spl0_1
| ~ spl0_31
| ~ spl0_39
| spl0_79
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f5486]) ).
thf(f5486,plain,
( $false
| ~ spl0_1
| ~ spl0_31
| ~ spl0_39
| spl0_79
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f5485]) ).
thf(f5485,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_39
| spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5484,f290]) ).
thf(f5484,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_1
| ~ spl0_39
| spl0_79
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5459,f5108]) ).
thf(f5108,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| spl0_79
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5105,f4360]) ).
thf(f5105,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| spl0_79
| ~ spl0_81 ),
inference(backward_demodulation,[],[f4161,f4360]) ).
thf(f5459,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_1
| ~ spl0_39
| ~ spl0_81 ),
inference(superposition,[],[f5180,f4]) ).
thf(f5373,plain,
( ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| ~ spl0_47
| spl0_53
| ~ spl0_68
| spl0_77
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f5372]) ).
thf(f5372,plain,
( $false
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| ~ spl0_47
| spl0_53
| ~ spl0_68
| spl0_77
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f5371]) ).
thf(f5371,plain,
( ( $true = $false )
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| ~ spl0_47
| spl0_53
| ~ spl0_68
| spl0_77
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5370,f938]) ).
thf(f5370,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| spl0_53
| ~ spl0_68
| spl0_77
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5369,f5364]) ).
thf(f5364,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| spl0_53
| spl0_77
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5363,f5215]) ).
thf(f5215,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| spl0_77
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5214,f4360]) ).
thf(f5214,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| spl0_77
| ~ spl0_81 ),
inference(forward_demodulation,[],[f4101,f4360]) ).
thf(f5363,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| spl0_53
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5348,f1510]) ).
thf(f5348,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(binary_proxy_clausification,[],[f5343]) ).
thf(f5343,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) != vAPP($o,$o,f1,$true) )
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(constrained_superposition,[],[f290,f5207]) ).
thf(f5207,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| ~ spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5206,f4360]) ).
thf(f5206,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))) )
| ~ spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5090,f4360]) ).
thf(f5090,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f455,f601]) ).
thf(f5369,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| spl0_53
| ~ spl0_68
| spl0_77
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5366,f5364]) ).
thf(f5366,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| spl0_53
| ~ spl0_68
| spl0_77
| ~ spl0_81 ),
inference(backward_demodulation,[],[f2558,f5364]) ).
thf(f2558,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f2556]) ).
thf(f2556,plain,
( spl0_68
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
thf(f5362,plain,
( ~ spl0_38
| ~ spl0_39
| spl0_49
| spl0_79
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f5361]) ).
thf(f5361,plain,
( $false
| ~ spl0_38
| ~ spl0_39
| spl0_49
| spl0_79
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5351,f5108]) ).
thf(f5351,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_38
| ~ spl0_39
| spl0_49
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f5339]) ).
thf(f5339,plain,
( ( $false != $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_38
| ~ spl0_39
| spl0_49
| ~ spl0_81 ),
inference(superposition,[],[f5256,f5207]) ).
thf(f5256,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f1,X0) )
| ( $false = X0 ) )
| spl0_49 ),
inference(superposition,[],[f959,f4]) ).
thf(f959,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| spl0_49 ),
inference(avatar_component_clause,[],[f958]) ).
thf(f958,plain,
( spl0_49
<=> ( $false = vAPP($o,$o,f1,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
thf(f5357,plain,
( ~ spl0_38
| ~ spl0_39
| spl0_42
| spl0_46
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f5356]) ).
thf(f5356,plain,
( $false
| ~ spl0_38
| ~ spl0_39
| spl0_42
| spl0_46
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5355,f624]) ).
thf(f5355,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_38
| ~ spl0_39
| spl0_46
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f5334,f933]) ).
thf(f933,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_46 ),
inference(avatar_component_clause,[],[f932]) ).
thf(f5334,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_38
| ~ spl0_39
| ~ spl0_81 ),
inference(superposition,[],[f5207,f4]) ).
thf(f5203,plain,
( ~ spl0_27
| spl0_3
| ~ spl0_39
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f5170,f4358,f599,f19,f259]) ).
thf(f5170,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_3
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5169,f4360]) ).
thf(f5169,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_3
| ~ spl0_39
| ~ spl0_81 ),
inference(forward_demodulation,[],[f5168,f4360]) ).
thf(f5168,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| spl0_3
| ~ spl0_39 ),
inference(forward_demodulation,[],[f20,f601]) ).
thf(f20,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))) != $false )
| spl0_3 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f5137,plain,
( ~ spl0_33
| ~ spl0_47
| ~ spl0_55
| ~ spl0_66
| spl0_71 ),
inference(avatar_contradiction_clause,[],[f5136]) ).
thf(f5136,plain,
( $false
| ~ spl0_33
| ~ spl0_47
| ~ spl0_55
| ~ spl0_66
| spl0_71 ),
inference(subsumption_resolution,[],[f5135,f938]) ).
thf(f5135,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| ~ spl0_33
| ~ spl0_55
| ~ spl0_66
| spl0_71 ),
inference(forward_demodulation,[],[f5134,f5100]) ).
thf(f5100,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_55
| ~ spl0_66 ),
inference(backward_demodulation,[],[f1898,f2546]) ).
thf(f5134,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_33
| spl0_71 ),
inference(backward_demodulation,[],[f2646,f303]) ).
thf(f5111,plain,
( spl0_65
| ~ spl0_48
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f5110,f2679,f944,f2428]) ).
thf(f944,plain,
( spl0_48
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
thf(f5110,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_48
| ~ spl0_72 ),
inference(backward_demodulation,[],[f946,f2681]) ).
thf(f2681,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f2679]) ).
thf(f946,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f944]) ).
thf(f5094,plain,
( spl0_65
| spl0_49
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f4231,f2614,f958,f2428]) ).
thf(f4231,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_70 ),
inference(superposition,[],[f2616,f4]) ).
thf(f2616,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f2614]) ).
thf(f5092,plain,
( spl0_49
| ~ spl0_38
| ~ spl0_39
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f5091,f4099,f599,f453,f958]) ).
thf(f5091,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_38
| ~ spl0_39
| ~ spl0_77 ),
inference(forward_demodulation,[],[f5090,f4100]) ).
thf(f5080,plain,
( ~ spl0_19
| spl0_41
| ~ spl0_47
| spl0_81 ),
inference(avatar_contradiction_clause,[],[f5079]) ).
thf(f5079,plain,
( $false
| ~ spl0_19
| spl0_41
| ~ spl0_47
| spl0_81 ),
inference(trivial_inequality_removal,[],[f5062]) ).
thf(f5062,plain,
( ( $true = $false )
| ~ spl0_19
| spl0_41
| ~ spl0_47
| spl0_81 ),
inference(backward_demodulation,[],[f4174,f5049]) ).
thf(f5049,plain,
( ! [X0: $o] : ( $false = X0 )
| spl0_41
| spl0_81 ),
inference(subsumption_resolution,[],[f5048,f4527]) ).
thf(f4527,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f3,X0) )
| ( $false = X0 ) )
| spl0_41 ),
inference(superposition,[],[f618,f4]) ).
thf(f618,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| spl0_41 ),
inference(avatar_component_clause,[],[f617]) ).
thf(f5048,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f3,X0) )
| ( $false = X0 ) )
| spl0_81 ),
inference(duplicate_literal_removal,[],[f5047]) ).
thf(f5047,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f3,X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| spl0_81 ),
inference(binary_proxy_clausification,[],[f5041]) ).
thf(f5041,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f3,X0) != X0 )
| ( $false = X0 ) )
| spl0_81 ),
inference(superposition,[],[f4359,f4]) ).
thf(f4359,plain,
( ( $true != vAPP($o,$o,f3,$true) )
| spl0_81 ),
inference(avatar_component_clause,[],[f4358]) ).
thf(f4174,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_19
| ~ spl0_47 ),
inference(forward_demodulation,[],[f134,f938]) ).
thf(f5076,plain,
( spl0_41
| ~ spl0_52
| spl0_81 ),
inference(avatar_contradiction_clause,[],[f5075]) ).
thf(f5075,plain,
( $false
| spl0_41
| ~ spl0_52
| spl0_81 ),
inference(trivial_inequality_removal,[],[f5064]) ).
thf(f5064,plain,
( ( $true = $false )
| spl0_41
| ~ spl0_52
| spl0_81 ),
inference(backward_demodulation,[],[f1505,f5049]) ).
thf(f5074,plain,
( spl0_41
| ~ spl0_51
| spl0_81 ),
inference(avatar_contradiction_clause,[],[f5073]) ).
thf(f5073,plain,
( $false
| spl0_41
| ~ spl0_51
| spl0_81 ),
inference(trivial_inequality_removal,[],[f5065]) ).
thf(f5065,plain,
( ( $true = $false )
| spl0_41
| ~ spl0_51
| spl0_81 ),
inference(backward_demodulation,[],[f1309,f5049]) ).
thf(f4984,plain,
( ~ spl0_65
| ~ spl0_28
| ~ spl0_51
| spl0_79 ),
inference(avatar_split_clause,[],[f4983,f4160,f1307,f270,f2428]) ).
thf(f4983,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_28
| ~ spl0_51
| spl0_79 ),
inference(forward_demodulation,[],[f4161,f4816]) ).
thf(f4816,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| ~ spl0_28
| ~ spl0_51 ),
inference(forward_demodulation,[],[f272,f1309]) ).
thf(f272,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f4981,plain,
( spl0_78
| ~ spl0_3
| ~ spl0_36
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f4980,f2614,f443,f19,f4103]) ).
thf(f4980,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_3
| ~ spl0_36
| ~ spl0_70 ),
inference(backward_demodulation,[],[f4919,f2616]) ).
thf(f4919,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_3
| ~ spl0_36 ),
inference(backward_demodulation,[],[f21,f445]) ).
thf(f445,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))) = $false )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f443]) ).
thf(f4978,plain,
( spl0_70
| ~ spl0_36
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f4925,f453,f443,f2614]) ).
thf(f4925,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_36
| ~ spl0_38 ),
inference(forward_demodulation,[],[f455,f445]) ).
thf(f4969,plain,
( spl0_13
| ~ spl0_39
| ~ spl0_42
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f4968]) ).
thf(f4968,plain,
( $false
| spl0_13
| ~ spl0_39
| ~ spl0_42
| ~ spl0_52 ),
inference(subsumption_resolution,[],[f4967,f623]) ).
thf(f4967,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_13
| ~ spl0_39
| ~ spl0_42
| ~ spl0_52 ),
inference(forward_demodulation,[],[f4950,f1505]) ).
thf(f4950,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| spl0_13
| ~ spl0_39
| ~ spl0_42 ),
inference(backward_demodulation,[],[f4930,f623]) ).
thf(f4958,plain,
( ~ spl0_27
| ~ spl0_42
| spl0_53
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[],[f4957]) ).
thf(f4957,plain,
( $false
| ~ spl0_27
| ~ spl0_42
| spl0_53
| ~ spl0_65 ),
inference(subsumption_resolution,[],[f4956,f1510]) ).
thf(f4956,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_27
| ~ spl0_42
| ~ spl0_65 ),
inference(forward_demodulation,[],[f4955,f2430]) ).
thf(f4955,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_27
| ~ spl0_42
| ~ spl0_65 ),
inference(forward_demodulation,[],[f4954,f2430]) ).
thf(f4954,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_27
| ~ spl0_42
| ~ spl0_65 ),
inference(forward_demodulation,[],[f4944,f2430]) ).
thf(f4944,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_27
| ~ spl0_42 ),
inference(backward_demodulation,[],[f261,f623]) ).
thf(f261,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f4924,plain,
( ~ spl0_3
| ~ spl0_36
| spl0_53
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[],[f4923]) ).
thf(f4923,plain,
( $false
| ~ spl0_3
| ~ spl0_36
| spl0_53
| ~ spl0_65 ),
inference(subsumption_resolution,[],[f4922,f1510]) ).
thf(f4922,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_3
| ~ spl0_36
| ~ spl0_65 ),
inference(forward_demodulation,[],[f4921,f2430]) ).
thf(f4921,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_3
| ~ spl0_36
| ~ spl0_65 ),
inference(forward_demodulation,[],[f4920,f2430]) ).
thf(f4920,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_3
| ~ spl0_36
| ~ spl0_65 ),
inference(forward_demodulation,[],[f4919,f2430]) ).
thf(f4879,plain,
( spl0_53
| ~ spl0_65
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f4878]) ).
thf(f4878,plain,
( $false
| spl0_53
| ~ spl0_65
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f4876,f1510]) ).
thf(f4876,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_65
| ~ spl0_78 ),
inference(backward_demodulation,[],[f4104,f2430]) ).
thf(f4872,plain,
( spl0_65
| ~ spl0_5
| ~ spl0_38
| ~ spl0_51
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f4806,f4160,f1307,f453,f70,f2428]) ).
thf(f4806,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_5
| ~ spl0_38
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f4805,f4162]) ).
thf(f4805,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_5
| ~ spl0_38
| ~ spl0_51 ),
inference(forward_demodulation,[],[f4804,f1309]) ).
thf(f4804,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_5
| ~ spl0_38 ),
inference(forward_demodulation,[],[f455,f72]) ).
thf(f4871,plain,
( spl0_65
| ~ spl0_5
| ~ spl0_36
| ~ spl0_51
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f4811,f4160,f1307,f443,f70,f2428]) ).
thf(f4811,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_5
| ~ spl0_36
| ~ spl0_51
| ~ spl0_79 ),
inference(backward_demodulation,[],[f4162,f4810]) ).
thf(f4810,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| ~ spl0_5
| ~ spl0_36
| ~ spl0_51 ),
inference(forward_demodulation,[],[f4809,f1309]) ).
thf(f4809,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_5
| ~ spl0_36 ),
inference(forward_demodulation,[],[f445,f72]) ).
thf(f4845,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_51
| spl0_75 ),
inference(avatar_contradiction_clause,[],[f4844]) ).
thf(f4844,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| ~ spl0_51
| spl0_75 ),
inference(subsumption_resolution,[],[f4843,f3953]) ).
thf(f4843,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_5
| ~ spl0_11
| ~ spl0_51 ),
inference(forward_demodulation,[],[f4842,f1309]) ).
thf(f4842,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[],[f99,f72]) ).
thf(f4622,plain,
( spl0_42
| spl0_75
| ~ spl0_13
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f4563,f599,f106,f3952,f622]) ).
thf(f4563,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_13
| ~ spl0_39 ),
inference(superposition,[],[f4026,f4]) ).
thf(f4026,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_13
| ~ spl0_39 ),
inference(forward_demodulation,[],[f108,f601]) ).
thf(f108,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))) = $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f4619,plain,
( ~ spl0_13
| ~ spl0_39
| spl0_42
| ~ spl0_44
| spl0_75 ),
inference(avatar_contradiction_clause,[],[f4618]) ).
thf(f4618,plain,
( $false
| ~ spl0_13
| ~ spl0_39
| spl0_42
| ~ spl0_44
| spl0_75 ),
inference(subsumption_resolution,[],[f4617,f624]) ).
thf(f4617,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_13
| ~ spl0_39
| spl0_42
| ~ spl0_44
| spl0_75 ),
inference(forward_demodulation,[],[f4616,f4590]) ).
thf(f4590,plain,
( ( $true = vAPP($o,$o,f2,$true) )
| ~ spl0_13
| ~ spl0_39
| ~ spl0_44
| spl0_75 ),
inference(subsumption_resolution,[],[f4573,f4589]) ).
thf(f4589,plain,
( ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_13
| ~ spl0_39
| ~ spl0_44
| spl0_75 ),
inference(subsumption_resolution,[],[f4569,f635]) ).
thf(f4569,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_13
| ~ spl0_39
| spl0_75 ),
inference(constrained_superposition,[],[f3953,f4026]) ).
thf(f4573,plain,
( ( $true = vAPP($o,$o,f2,$true) )
| ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_13
| ~ spl0_39
| spl0_75 ),
inference(binary_proxy_clausification,[],[f4572]) ).
thf(f4572,plain,
( ( vAPP($o,$o,f2,$true) != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_13
| ~ spl0_39
| spl0_75 ),
inference(trivial_inequality_removal,[],[f4571]) ).
thf(f4571,plain,
( ( $false != $false )
| ( vAPP($o,$o,f2,$true) != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_13
| ~ spl0_39
| spl0_75 ),
inference(constrained_superposition,[],[f3953,f4026]) ).
thf(f4616,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_13
| ~ spl0_39
| spl0_42
| spl0_75 ),
inference(subsumption_resolution,[],[f4574,f624]) ).
thf(f4574,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_13
| ~ spl0_39
| spl0_75 ),
inference(binary_proxy_clausification,[],[f4572]) ).
thf(f4519,plain,
( spl0_41
| ~ spl0_25
| spl0_3
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f4056,f599,f19,f250,f617]) ).
thf(f4056,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ( $false = vAPP($o,$o,f3,$true) )
| spl0_3
| ~ spl0_39 ),
inference(superposition,[],[f3752,f4]) ).
thf(f3752,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| spl0_3
| ~ spl0_39 ),
inference(forward_demodulation,[],[f20,f601]) ).
thf(f4517,plain,
( spl0_42
| ~ spl0_75 ),
inference(avatar_contradiction_clause,[],[f4516]) ).
thf(f4516,plain,
( $false
| spl0_42
| ~ spl0_75 ),
inference(subsumption_resolution,[],[f4515,f624]) ).
thf(f4515,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_75 ),
inference(duplicate_literal_removal,[],[f4510]) ).
thf(f4510,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_75 ),
inference(superposition,[],[f3954,f4]) ).
thf(f4480,plain,
( ~ spl0_44
| spl0_61 ),
inference(avatar_contradiction_clause,[],[f4479]) ).
thf(f4479,plain,
( $false
| ~ spl0_44
| spl0_61 ),
inference(subsumption_resolution,[],[f4478,f635]) ).
thf(f4478,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_44
| spl0_61 ),
inference(forward_demodulation,[],[f4469,f635]) ).
thf(f4469,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_44
| spl0_61 ),
inference(backward_demodulation,[],[f2165,f635]) ).
thf(f2165,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| spl0_61 ),
inference(avatar_component_clause,[],[f2164]) ).
thf(f4472,plain,
( ~ spl0_44
| spl0_59 ),
inference(avatar_contradiction_clause,[],[f4471]) ).
thf(f4471,plain,
( $false
| ~ spl0_44
| spl0_59 ),
inference(subsumption_resolution,[],[f4466,f635]) ).
thf(f4466,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_44
| spl0_59 ),
inference(backward_demodulation,[],[f2155,f635]) ).
thf(f2155,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| spl0_59 ),
inference(avatar_component_clause,[],[f2154]) ).
thf(f2154,plain,
( spl0_59
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
thf(f4449,plain,
( ~ spl0_1
| spl0_3
| spl0_12
| ~ spl0_39
| ~ spl0_41
| ~ spl0_47
| ~ spl0_51
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f4448]) ).
thf(f4448,plain,
( $false
| ~ spl0_1
| spl0_3
| spl0_12
| ~ spl0_39
| ~ spl0_41
| ~ spl0_47
| ~ spl0_51
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f4447,f4087]) ).
thf(f4087,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| spl0_3
| ~ spl0_39
| ~ spl0_47 ),
inference(backward_demodulation,[],[f3787,f4086]) ).
thf(f4086,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))) )
| spl0_3
| ~ spl0_39
| ~ spl0_47 ),
inference(subsumption_resolution,[],[f4064,f938]) ).
thf(f4064,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))) )
| spl0_3
| ~ spl0_39 ),
inference(superposition,[],[f3752,f4]) ).
thf(f3787,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_1
| ~ spl0_39 ),
inference(forward_demodulation,[],[f12,f601]) ).
thf(f4447,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| ~ spl0_1
| spl0_3
| spl0_12
| ~ spl0_39
| ~ spl0_41
| ~ spl0_47
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f4446,f938]) ).
thf(f4446,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_1
| spl0_3
| spl0_12
| ~ spl0_39
| ~ spl0_41
| ~ spl0_47
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f4445,f4087]) ).
thf(f4445,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_12
| ~ spl0_41
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f102,f4400]) ).
thf(f4400,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_41
| ~ spl0_51
| ~ spl0_79 ),
inference(forward_demodulation,[],[f4385,f1309]) ).
thf(f4385,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_41
| ~ spl0_79 ),
inference(backward_demodulation,[],[f4162,f619]) ).
thf(f102,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_12 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f4420,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_39
| ~ spl0_41
| ~ spl0_47
| ~ spl0_51
| spl0_53
| ~ spl0_60
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f4419]) ).
thf(f4419,plain,
( $false
| ~ spl0_1
| spl0_3
| ~ spl0_39
| ~ spl0_41
| ~ spl0_47
| ~ spl0_51
| spl0_53
| ~ spl0_60
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f4418,f1510]) ).
thf(f4418,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| spl0_3
| ~ spl0_39
| ~ spl0_41
| ~ spl0_47
| ~ spl0_51
| ~ spl0_60
| ~ spl0_79 ),
inference(forward_demodulation,[],[f4417,f938]) ).
thf(f4417,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_1
| spl0_3
| ~ spl0_39
| ~ spl0_41
| ~ spl0_47
| ~ spl0_51
| ~ spl0_60
| ~ spl0_79 ),
inference(forward_demodulation,[],[f4416,f4087]) ).
thf(f4416,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_41
| ~ spl0_51
| ~ spl0_60
| ~ spl0_79 ),
inference(forward_demodulation,[],[f2160,f4400]) ).
thf(f4367,plain,
( spl0_75
| ~ spl0_52
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f4324,f2164,f1504,f3952]) ).
thf(f4324,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_52
| ~ spl0_61 ),
inference(forward_demodulation,[],[f2166,f1505]) ).
thf(f4283,plain,
( spl0_5
| spl0_27
| ~ spl0_39
| ~ spl0_50 ),
inference(avatar_contradiction_clause,[],[f4282]) ).
thf(f4282,plain,
( $false
| spl0_5
| spl0_27
| ~ spl0_39
| ~ spl0_50 ),
inference(subsumption_resolution,[],[f4281,f260]) ).
thf(f4281,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_5
| ~ spl0_39
| ~ spl0_50 ),
inference(forward_demodulation,[],[f4280,f4266]) ).
thf(f4266,plain,
( ( $true = vAPP($o,$o,f3,$true) )
| spl0_5
| ~ spl0_39 ),
inference(subsumption_resolution,[],[f4259,f71]) ).
thf(f71,plain,
( ( x != $false )
| spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f4259,plain,
( ( $true = vAPP($o,$o,f3,$true) )
| ( x = $false )
| ~ spl0_39 ),
inference(superposition,[],[f601,f4]) ).
thf(f4280,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_5
| ~ spl0_39
| ~ spl0_50 ),
inference(forward_demodulation,[],[f4269,f4266]) ).
thf(f4269,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| spl0_5
| ~ spl0_39
| ~ spl0_50 ),
inference(backward_demodulation,[],[f1113,f4266]) ).
thf(f4246,plain,
( ~ spl0_13
| spl0_18
| ~ spl0_39
| spl0_65 ),
inference(avatar_contradiction_clause,[],[f4245]) ).
thf(f4245,plain,
( $false
| ~ spl0_13
| spl0_18
| ~ spl0_39
| spl0_65 ),
inference(subsumption_resolution,[],[f4243,f2429]) ).
thf(f4243,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_13
| spl0_18
| ~ spl0_39 ),
inference(trivial_inequality_removal,[],[f4242]) ).
thf(f4242,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_13
| spl0_18
| ~ spl0_39 ),
inference(superposition,[],[f4119,f4]) ).
thf(f4119,plain,
( ( $true != vAPP($o,$o,f1,$false) )
| ~ spl0_13
| spl0_18
| ~ spl0_39 ),
inference(forward_demodulation,[],[f3822,f4026]) ).
thf(f3822,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_18
| ~ spl0_39 ),
inference(forward_demodulation,[],[f129,f601]) ).
thf(f129,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))) != $true )
| spl0_18 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f4213,plain,
( spl0_48
| ~ spl0_49
| ~ spl0_52
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f4212]) ).
thf(f4212,plain,
( $false
| spl0_48
| ~ spl0_49
| ~ spl0_52
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f4211,f2616]) ).
thf(f4211,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| spl0_48
| ~ spl0_49
| ~ spl0_52 ),
inference(forward_demodulation,[],[f4197,f960]) ).
thf(f960,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f958]) ).
thf(f4197,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_48
| ~ spl0_52 ),
inference(backward_demodulation,[],[f945,f1505]) ).
thf(f945,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| spl0_48 ),
inference(avatar_component_clause,[],[f944]) ).
thf(f4210,plain,
( ~ spl0_43
| ~ spl0_49
| ~ spl0_52
| spl0_53
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f4209]) ).
thf(f4209,plain,
( $false
| ~ spl0_43
| ~ spl0_49
| ~ spl0_52
| spl0_53
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f4208,f1510]) ).
thf(f4208,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_43
| ~ spl0_49
| ~ spl0_52
| ~ spl0_70 ),
inference(forward_demodulation,[],[f4207,f2616]) ).
thf(f4207,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_43
| ~ spl0_49
| ~ spl0_52 ),
inference(forward_demodulation,[],[f4196,f960]) ).
thf(f4196,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_43
| ~ spl0_52 ),
inference(backward_demodulation,[],[f630,f1505]) ).
thf(f630,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f628]) ).
thf(f4195,plain,
( spl0_44
| spl0_52 ),
inference(avatar_contradiction_clause,[],[f4194]) ).
thf(f4194,plain,
( $false
| spl0_44
| spl0_52 ),
inference(subsumption_resolution,[],[f4193,f636]) ).
thf(f636,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_44 ),
inference(avatar_component_clause,[],[f634]) ).
thf(f4193,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| spl0_52 ),
inference(trivial_inequality_removal,[],[f4192]) ).
thf(f4192,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f2,$false) )
| spl0_52 ),
inference(superposition,[],[f1506,f4]) ).
thf(f1506,plain,
( ( $true != vAPP($o,$o,f2,$false) )
| spl0_52 ),
inference(avatar_component_clause,[],[f1504]) ).
thf(f4163,plain,
( spl0_79
| ~ spl0_78
| spl0_3
| ~ spl0_39
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f4158,f958,f599,f19,f4103,f4160]) ).
thf(f4158,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| spl0_3
| ~ spl0_39
| ~ spl0_49 ),
inference(forward_demodulation,[],[f4060,f960]) ).
thf(f4060,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| spl0_3
| ~ spl0_39 ),
inference(superposition,[],[f3752,f4]) ).
thf(f4135,plain,
( ~ spl0_53
| ~ spl0_47
| spl0_64 ),
inference(avatar_split_clause,[],[f3220,f2181,f936,f1508]) ).
thf(f3220,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_47
| spl0_64 ),
inference(backward_demodulation,[],[f2182,f938]) ).
thf(f2182,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_64 ),
inference(avatar_component_clause,[],[f2181]) ).
thf(f4113,plain,
( spl0_78
| ~ spl0_13
| ~ spl0_21
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f4112,f599,f142,f106,f4103]) ).
thf(f4112,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_13
| ~ spl0_21
| ~ spl0_39 ),
inference(forward_demodulation,[],[f4011,f4026]) ).
thf(f4011,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_21
| ~ spl0_39 ),
inference(forward_demodulation,[],[f144,f601]) ).
thf(f144,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))) = $false )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f142]) ).
thf(f4110,plain,
( spl0_78
| ~ spl0_31
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f4042,f958,f288,f4103]) ).
thf(f4042,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_31
| ~ spl0_49 ),
inference(forward_demodulation,[],[f290,f960]) ).
thf(f4109,plain,
( ~ spl0_53
| spl0_3
| spl0_36
| ~ spl0_39
| ~ spl0_49
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f4077,f2614,f958,f599,f443,f19,f1508]) ).
thf(f4077,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_3
| spl0_36
| ~ spl0_39
| ~ spl0_49
| ~ spl0_70 ),
inference(forward_demodulation,[],[f4076,f2616]) ).
thf(f4076,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_3
| spl0_36
| ~ spl0_39
| ~ spl0_49 ),
inference(forward_demodulation,[],[f4075,f960]) ).
thf(f4075,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| spl0_3
| spl0_36
| ~ spl0_39 ),
inference(subsumption_resolution,[],[f4058,f3740]) ).
thf(f3740,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| spl0_36
| ~ spl0_39 ),
inference(forward_demodulation,[],[f444,f601]) ).
thf(f4058,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| spl0_3
| ~ spl0_39 ),
inference(superposition,[],[f3752,f4]) ).
thf(f4097,plain,
( ~ spl0_53
| spl0_3
| spl0_38
| ~ spl0_39
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f4085,f958,f599,f453,f19,f1508]) ).
thf(f4085,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_3
| spl0_38
| ~ spl0_39
| ~ spl0_49 ),
inference(forward_demodulation,[],[f4084,f960]) ).
thf(f4084,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_3
| spl0_38
| ~ spl0_39 ),
inference(subsumption_resolution,[],[f4062,f3775]) ).
thf(f3775,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f454,f601]) ).
thf(f4062,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| spl0_3
| ~ spl0_39 ),
inference(superposition,[],[f3752,f4]) ).
thf(f4095,plain,
( ~ spl0_53
| spl0_3
| ~ spl0_39
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f4088,f936,f599,f19,f1508]) ).
thf(f4088,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_3
| ~ spl0_39
| ~ spl0_47 ),
inference(backward_demodulation,[],[f3752,f4086]) ).
thf(f4031,plain,
( ~ spl0_14
| ~ spl0_49
| ~ spl0_58
| spl0_69 ),
inference(avatar_contradiction_clause,[],[f4030]) ).
thf(f4030,plain,
( $false
| ~ spl0_14
| ~ spl0_49
| ~ spl0_58
| spl0_69 ),
inference(subsumption_resolution,[],[f3768,f4023]) ).
thf(f4023,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_14
| ~ spl0_49
| ~ spl0_58 ),
inference(forward_demodulation,[],[f4022,f1912]) ).
thf(f4022,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_14
| ~ spl0_49 ),
inference(forward_demodulation,[],[f112,f960]) ).
thf(f3768,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| ~ spl0_49
| spl0_69 ),
inference(forward_demodulation,[],[f2611,f960]) ).
thf(f2611,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_69 ),
inference(avatar_component_clause,[],[f2610]) ).
thf(f3997,plain,
( ~ spl0_4
| spl0_20
| ~ spl0_39
| ~ spl0_49
| spl0_53
| ~ spl0_58
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[],[f3996]) ).
thf(f3996,plain,
( $false
| ~ spl0_4
| spl0_20
| ~ spl0_39
| ~ spl0_49
| spl0_53
| ~ spl0_58
| ~ spl0_65 ),
inference(subsumption_resolution,[],[f3995,f1912]) ).
thf(f3995,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_4
| spl0_20
| ~ spl0_39
| ~ spl0_49
| spl0_53
| ~ spl0_58
| ~ spl0_65 ),
inference(forward_demodulation,[],[f3989,f2430]) ).
thf(f3989,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| spl0_20
| ~ spl0_39
| ~ spl0_49
| spl0_53
| ~ spl0_58 ),
inference(backward_demodulation,[],[f3840,f3986]) ).
thf(f3986,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_4
| ~ spl0_39
| ~ spl0_49
| spl0_53
| ~ spl0_58 ),
inference(subsumption_resolution,[],[f3985,f1510]) ).
thf(f3985,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_4
| ~ spl0_39
| ~ spl0_49
| ~ spl0_58 ),
inference(forward_demodulation,[],[f3883,f1912]) ).
thf(f3883,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_4
| ~ spl0_39
| ~ spl0_49 ),
inference(forward_demodulation,[],[f3845,f960]) ).
thf(f3845,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(superposition,[],[f3746,f4]) ).
thf(f3746,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(forward_demodulation,[],[f25,f601]) ).
thf(f3840,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_20
| ~ spl0_39 ),
inference(forward_demodulation,[],[f138,f601]) ).
thf(f3969,plain,
( spl0_73
| spl0_58
| ~ spl0_4
| spl0_18
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f3968,f599,f128,f23,f1910,f3919]) ).
thf(f3968,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_4
| spl0_18
| ~ spl0_39 ),
inference(subsumption_resolution,[],[f3860,f3822]) ).
thf(f3860,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(binary_proxy_clausification,[],[f3849]) ).
thf(f3849,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(constrained_superposition,[],[f3746,f3746]) ).
thf(f3964,plain,
( spl0_58
| ~ spl0_4
| ~ spl0_39
| ~ spl0_47
| spl0_53 ),
inference(avatar_split_clause,[],[f3928,f1508,f936,f599,f23,f1910]) ).
thf(f3928,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_4
| ~ spl0_39
| ~ spl0_47
| spl0_53 ),
inference(backward_demodulation,[],[f3857,f3904]) ).
thf(f3904,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| ~ spl0_39
| ~ spl0_47
| spl0_53 ),
inference(subsumption_resolution,[],[f3903,f1510]) ).
thf(f3903,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_demodulation,[],[f3850,f938]) ).
thf(f3850,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(superposition,[],[f3746,f4]) ).
thf(f3857,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(trivial_inequality_removal,[],[f3854]) ).
thf(f3854,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(superposition,[],[f3746,f4]) ).
thf(f3963,plain,
( ~ spl0_4
| spl0_21
| ~ spl0_39
| ~ spl0_47
| spl0_53 ),
inference(avatar_contradiction_clause,[],[f3962]) ).
thf(f3962,plain,
( $false
| ~ spl0_4
| spl0_21
| ~ spl0_39
| ~ spl0_47
| spl0_53 ),
inference(subsumption_resolution,[],[f3904,f3821]) ).
thf(f3821,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| spl0_21
| ~ spl0_39 ),
inference(forward_demodulation,[],[f143,f601]) ).
thf(f3955,plain,
( spl0_75
| spl0_60
| ~ spl0_4
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f3844,f599,f23,f2158,f3952]) ).
thf(f3844,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_4
| ~ spl0_39 ),
inference(superposition,[],[f3746,f4]) ).
thf(f3926,plain,
( spl0_73
| spl0_74
| ~ spl0_4
| ~ spl0_39
| spl0_53 ),
inference(avatar_split_clause,[],[f3910,f1508,f599,f23,f3923,f3919]) ).
thf(f3910,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_4
| ~ spl0_39
| spl0_53 ),
inference(subsumption_resolution,[],[f3858,f1510]) ).
thf(f3858,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(binary_proxy_clausification,[],[f3852]) ).
thf(f3852,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_4
| ~ spl0_39 ),
inference(constrained_superposition,[],[f3746,f3746]) ).
thf(f3838,plain,
( ~ spl0_4
| ~ spl0_20
| ~ spl0_39
| spl0_53 ),
inference(avatar_contradiction_clause,[],[f3837]) ).
thf(f3837,plain,
( $false
| ~ spl0_4
| ~ spl0_20
| ~ spl0_39
| spl0_53 ),
inference(subsumption_resolution,[],[f3836,f1510]) ).
thf(f3836,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_20
| ~ spl0_39 ),
inference(backward_demodulation,[],[f3746,f3834]) ).
thf(f3834,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_20
| ~ spl0_39 ),
inference(forward_demodulation,[],[f139,f601]) ).
thf(f3827,plain,
( ~ spl0_4
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47
| spl0_53 ),
inference(avatar_contradiction_clause,[],[f3826]) ).
thf(f3826,plain,
( $false
| ~ spl0_4
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47
| spl0_53 ),
inference(subsumption_resolution,[],[f3825,f1510]) ).
thf(f3825,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_demodulation,[],[f3824,f938]) ).
thf(f3824,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_4
| ~ spl0_22
| ~ spl0_39 ),
inference(backward_demodulation,[],[f3746,f3823]) ).
thf(f3823,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_22
| ~ spl0_39 ),
inference(forward_demodulation,[],[f149,f601]) ).
thf(f3819,plain,
( ~ spl0_8
| spl0_2
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f3781,f599,f14,f83]) ).
thf(f3781,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_2
| ~ spl0_39 ),
inference(forward_demodulation,[],[f15,f601]) ).
thf(f3808,plain,
( ~ spl0_65
| spl0_70 ),
inference(avatar_contradiction_clause,[],[f3807]) ).
thf(f3807,plain,
( $false
| ~ spl0_65
| spl0_70 ),
inference(subsumption_resolution,[],[f3803,f2430]) ).
thf(f3803,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_65
| spl0_70 ),
inference(backward_demodulation,[],[f2615,f2430]) ).
thf(f2615,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| spl0_70 ),
inference(avatar_component_clause,[],[f2614]) ).
thf(f3795,plain,
( ~ spl0_15
| ~ spl0_22
| ~ spl0_49
| spl0_68
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f3794]) ).
thf(f3794,plain,
( $false
| ~ spl0_15
| ~ spl0_22
| ~ spl0_49
| spl0_68
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f3603,f3772]) ).
thf(f3772,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| ~ spl0_49
| spl0_68
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3771,f2616]) ).
thf(f3771,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_49
| spl0_68 ),
inference(forward_demodulation,[],[f2557,f960]) ).
thf(f2557,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| spl0_68 ),
inference(avatar_component_clause,[],[f2556]) ).
thf(f3603,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_15
| ~ spl0_22 ),
inference(backward_demodulation,[],[f149,f117]) ).
thf(f117,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))) = $false )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f115]) ).
thf(f3791,plain,
( spl0_58
| ~ spl0_47
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f3306,f2548,f936,f1910]) ).
thf(f3306,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_47
| ~ spl0_67 ),
inference(forward_demodulation,[],[f2550,f938]) ).
thf(f2550,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f2548]) ).
thf(f3788,plain,
( ~ spl0_62
| ~ spl0_49
| spl0_71 ),
inference(avatar_split_clause,[],[f3765,f2645,f958,f2168]) ).
thf(f3765,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_49
| spl0_71 ),
inference(forward_demodulation,[],[f2646,f960]) ).
thf(f3755,plain,
( spl0_3
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| ~ spl0_49 ),
inference(avatar_contradiction_clause,[],[f3754]) ).
thf(f3754,plain,
( $false
| spl0_3
| ~ spl0_31
| ~ spl0_38
| ~ spl0_39
| ~ spl0_49 ),
inference(subsumption_resolution,[],[f3753,f3057]) ).
thf(f3057,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_31
| ~ spl0_49 ),
inference(backward_demodulation,[],[f290,f960]) ).
thf(f3753,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_3
| ~ spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f3752,f3733]) ).
thf(f3733,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f455,f601]) ).
thf(f3722,plain,
( ~ spl0_36
| ~ spl0_39
| ~ spl0_41
| spl0_42
| ~ spl0_51 ),
inference(avatar_contradiction_clause,[],[f3721]) ).
thf(f3721,plain,
( $false
| ~ spl0_36
| ~ spl0_39
| ~ spl0_41
| spl0_42
| ~ spl0_51 ),
inference(subsumption_resolution,[],[f3720,f624]) ).
thf(f3720,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_36
| ~ spl0_39
| ~ spl0_41
| ~ spl0_51 ),
inference(forward_demodulation,[],[f3710,f1309]) ).
thf(f3710,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_36
| ~ spl0_39
| ~ spl0_41 ),
inference(backward_demodulation,[],[f3664,f619]) ).
thf(f3664,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| ~ spl0_36
| ~ spl0_39 ),
inference(backward_demodulation,[],[f445,f601]) ).
thf(f3692,plain,
( ~ spl0_11
| ~ spl0_39
| ~ spl0_42
| spl0_44 ),
inference(avatar_contradiction_clause,[],[f3691]) ).
thf(f3691,plain,
( $false
| ~ spl0_11
| ~ spl0_39
| ~ spl0_42
| spl0_44 ),
inference(subsumption_resolution,[],[f3690,f636]) ).
thf(f3690,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_11
| ~ spl0_39
| ~ spl0_42 ),
inference(forward_demodulation,[],[f3689,f623]) ).
thf(f3689,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_11
| ~ spl0_39 ),
inference(forward_demodulation,[],[f99,f601]) ).
thf(f3672,plain,
( ~ spl0_15
| ~ spl0_39
| ~ spl0_42
| ~ spl0_59
| spl0_65 ),
inference(avatar_contradiction_clause,[],[f3671]) ).
thf(f3671,plain,
( $false
| ~ spl0_15
| ~ spl0_39
| ~ spl0_42
| ~ spl0_59
| spl0_65 ),
inference(subsumption_resolution,[],[f3670,f2429]) ).
thf(f3670,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_15
| ~ spl0_39
| ~ spl0_42
| ~ spl0_59 ),
inference(forward_demodulation,[],[f3669,f2156]) ).
thf(f2156,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f2154]) ).
thf(f3669,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_15
| ~ spl0_39
| ~ spl0_42 ),
inference(forward_demodulation,[],[f3661,f623]) ).
thf(f3661,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_15
| ~ spl0_39 ),
inference(backward_demodulation,[],[f117,f601]) ).
thf(f3617,plain,
( spl0_7
| spl0_39 ),
inference(avatar_contradiction_clause,[],[f3616]) ).
thf(f3616,plain,
( $false
| spl0_7
| spl0_39 ),
inference(subsumption_resolution,[],[f3614,f80]) ).
thf(f3614,plain,
( ( vAPP($o,$o,f3,x) = $false )
| spl0_39 ),
inference(trivial_inequality_removal,[],[f3613]) ).
thf(f3613,plain,
( ( $true != $true )
| ( vAPP($o,$o,f3,x) = $false )
| spl0_39 ),
inference(superposition,[],[f600,f4]) ).
thf(f600,plain,
( ( vAPP($o,$o,f3,x) != $true )
| spl0_39 ),
inference(avatar_component_clause,[],[f599]) ).
thf(f3540,plain,
( ~ spl0_45
| ~ spl0_51 ),
inference(avatar_contradiction_clause,[],[f3539]) ).
thf(f3539,plain,
( $false
| ~ spl0_45
| ~ spl0_51 ),
inference(trivial_inequality_removal,[],[f3538]) ).
thf(f3538,plain,
( ( $true = $false )
| ~ spl0_45
| ~ spl0_51 ),
inference(backward_demodulation,[],[f1309,f643]) ).
thf(f643,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f641]) ).
thf(f641,plain,
( spl0_45
<=> ( $false = vAPP($o,$o,f3,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
thf(f3532,plain,
( spl0_70
| ~ spl0_44
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f3531,f2679,f634,f2614]) ).
thf(f3531,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_44
| ~ spl0_72 ),
inference(forward_demodulation,[],[f2681,f635]) ).
thf(f3495,plain,
( ~ spl0_49
| spl0_65
| spl0_70 ),
inference(avatar_contradiction_clause,[],[f3494]) ).
thf(f3494,plain,
( $false
| ~ spl0_49
| spl0_65
| spl0_70 ),
inference(subsumption_resolution,[],[f3493,f2429]) ).
thf(f3493,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_49
| spl0_70 ),
inference(subsumption_resolution,[],[f3491,f960]) ).
thf(f3491,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f1,$false) )
| spl0_70 ),
inference(superposition,[],[f2615,f4]) ).
thf(f3455,plain,
( ~ spl0_29
| ~ spl0_49
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f3454]) ).
thf(f3454,plain,
( $false
| ~ spl0_29
| ~ spl0_49
| ~ spl0_68 ),
inference(trivial_inequality_removal,[],[f3453]) ).
thf(f3453,plain,
( ( $true = $false )
| ~ spl0_29
| ~ spl0_49
| ~ spl0_68 ),
inference(backward_demodulation,[],[f3059,f3452]) ).
thf(f3452,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_29
| ~ spl0_49 ),
inference(forward_demodulation,[],[f276,f960]) ).
thf(f3059,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_49
| ~ spl0_68 ),
inference(backward_demodulation,[],[f2558,f960]) ).
thf(f3410,plain,
( spl0_51
| ~ spl0_5
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f3409,f599,f70,f1307]) ).
thf(f3409,plain,
( ( $true = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_39 ),
inference(forward_demodulation,[],[f601,f72]) ).
thf(f3408,plain,
( ~ spl0_5
| spl0_9
| ~ spl0_24
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f3407]) ).
thf(f3407,plain,
( $false
| ~ spl0_5
| spl0_9
| ~ spl0_24
| ~ spl0_36 ),
inference(subsumption_resolution,[],[f3406,f3379]) ).
thf(f3379,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| spl0_9 ),
inference(backward_demodulation,[],[f89,f72]) ).
thf(f89,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f3,x)) != $false )
| spl0_9 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f88,plain,
( spl0_9
<=> ( vAPP($o,$o,f2,vAPP($o,$o,f3,x)) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f3406,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_demodulation,[],[f3405,f248]) ).
thf(f248,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f246,plain,
( spl0_24
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f3405,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_5
| ~ spl0_36 ),
inference(forward_demodulation,[],[f445,f72]) ).
thf(f3404,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_21
| spl0_53 ),
inference(avatar_contradiction_clause,[],[f3403]) ).
thf(f3403,plain,
( $false
| ~ spl0_5
| ~ spl0_15
| ~ spl0_21
| spl0_53 ),
inference(subsumption_resolution,[],[f3401,f1510]) ).
thf(f3401,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_5
| ~ spl0_15
| ~ spl0_21 ),
inference(backward_demodulation,[],[f3392,f3400]) ).
thf(f3400,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f117,f72]) ).
thf(f3392,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_demodulation,[],[f144,f72]) ).
thf(f3395,plain,
( ~ spl0_5
| ~ spl0_21
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f3394]) ).
thf(f3394,plain,
( $false
| ~ spl0_5
| ~ spl0_21
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f3393]) ).
thf(f3393,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_21
| ~ spl0_22 ),
inference(backward_demodulation,[],[f3390,f3392]) ).
thf(f3390,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_demodulation,[],[f149,f72]) ).
thf(f3369,plain,
( ~ spl0_12
| ~ spl0_60 ),
inference(avatar_contradiction_clause,[],[f3368]) ).
thf(f3368,plain,
( $false
| ~ spl0_12
| ~ spl0_60 ),
inference(trivial_inequality_removal,[],[f3367]) ).
thf(f3367,plain,
( ( $true = $false )
| ~ spl0_12
| ~ spl0_60 ),
inference(forward_demodulation,[],[f103,f2160]) ).
thf(f3365,plain,
( ~ spl0_29
| ~ spl0_49
| spl0_53
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f3364]) ).
thf(f3364,plain,
( $false
| ~ spl0_29
| ~ spl0_49
| spl0_53
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f3363,f1510]) ).
thf(f3363,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_29
| ~ spl0_49
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3362,f2616]) ).
thf(f3362,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_29
| ~ spl0_49 ),
inference(forward_demodulation,[],[f276,f960]) ).
thf(f3336,plain,
( ~ spl0_13
| ~ spl0_15
| spl0_65 ),
inference(avatar_contradiction_clause,[],[f3335]) ).
thf(f3335,plain,
( $false
| ~ spl0_13
| ~ spl0_15
| spl0_65 ),
inference(subsumption_resolution,[],[f3334,f2429]) ).
thf(f3334,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_13
| ~ spl0_15 ),
inference(backward_demodulation,[],[f117,f108]) ).
thf(f3324,plain,
( ~ spl0_11
| ~ spl0_15
| ~ spl0_44
| spl0_65 ),
inference(avatar_contradiction_clause,[],[f3323]) ).
thf(f3323,plain,
( $false
| ~ spl0_11
| ~ spl0_15
| ~ spl0_44
| spl0_65 ),
inference(subsumption_resolution,[],[f3322,f2429]) ).
thf(f3322,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_11
| ~ spl0_15
| ~ spl0_44 ),
inference(forward_demodulation,[],[f3321,f635]) ).
thf(f3321,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_11
| ~ spl0_15 ),
inference(forward_demodulation,[],[f117,f99]) ).
thf(f3266,plain,
( ~ spl0_18
| ~ spl0_22
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f3265]) ).
thf(f3265,plain,
( $false
| ~ spl0_18
| ~ spl0_22
| ~ spl0_47 ),
inference(trivial_inequality_removal,[],[f3264]) ).
thf(f3264,plain,
( ( $true = $false )
| ~ spl0_18
| ~ spl0_22
| ~ spl0_47 ),
inference(forward_demodulation,[],[f3263,f938]) ).
thf(f3263,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f149,f130]) ).
thf(f3246,plain,
( spl0_19
| ~ spl0_47
| ~ spl0_49
| ~ spl0_69 ),
inference(avatar_contradiction_clause,[],[f3245]) ).
thf(f3245,plain,
( $false
| spl0_19
| ~ spl0_47
| ~ spl0_49
| ~ spl0_69 ),
inference(subsumption_resolution,[],[f3244,f3056]) ).
thf(f3056,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_49
| ~ spl0_69 ),
inference(backward_demodulation,[],[f2612,f960]) ).
thf(f3244,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_19
| ~ spl0_47 ),
inference(forward_demodulation,[],[f133,f938]) ).
thf(f133,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_19 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f3189,plain,
( spl0_23
| ~ spl0_2
| ~ spl0_9
| ~ spl0_31
| ~ spl0_44
| ~ spl0_49
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f3188,f2610,f958,f634,f288,f88,f14,f151]) ).
thf(f3188,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_31
| ~ spl0_44
| ~ spl0_49
| ~ spl0_69 ),
inference(forward_demodulation,[],[f3187,f3056]) ).
thf(f3187,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_31
| ~ spl0_44
| ~ spl0_49 ),
inference(forward_demodulation,[],[f3186,f3057]) ).
thf(f3186,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_44 ),
inference(forward_demodulation,[],[f3185,f635]) ).
thf(f3185,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_44 ),
inference(forward_demodulation,[],[f3179,f635]) ).
thf(f3179,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_2
| ~ spl0_9 ),
inference(backward_demodulation,[],[f16,f90]) ).
thf(f90,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f3,x)) = $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f3157,plain,
( spl0_65
| ~ spl0_46
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f3069,f958,f932,f2428]) ).
thf(f3069,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_46
| ~ spl0_49 ),
inference(forward_demodulation,[],[f934,f960]) ).
thf(f3156,plain,
( ~ spl0_65
| ~ spl0_7
| ~ spl0_24
| spl0_37
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f3072,f634,f448,f246,f79,f2428]) ).
thf(f3072,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_7
| ~ spl0_24
| spl0_37
| ~ spl0_44 ),
inference(backward_demodulation,[],[f2213,f635]) ).
thf(f2213,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_24
| spl0_37 ),
inference(forward_demodulation,[],[f2212,f248]) ).
thf(f2212,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_7
| spl0_37 ),
inference(forward_demodulation,[],[f449,f81]) ).
thf(f81,plain,
( ( vAPP($o,$o,f3,x) = $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f449,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x))))) != $false )
| spl0_37 ),
inference(avatar_component_clause,[],[f448]) ).
thf(f3064,plain,
( ~ spl0_31
| ~ spl0_49
| spl0_53
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[],[f3063]) ).
thf(f3063,plain,
( $false
| ~ spl0_31
| ~ spl0_49
| spl0_53
| ~ spl0_65 ),
inference(subsumption_resolution,[],[f3062,f1510]) ).
thf(f3062,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_31
| ~ spl0_49
| ~ spl0_65 ),
inference(forward_demodulation,[],[f3057,f2430]) ).
thf(f3043,plain,
( spl0_53
| ~ spl0_57
| ~ spl0_61
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[],[f3042]) ).
thf(f3042,plain,
( $false
| spl0_53
| ~ spl0_57
| ~ spl0_61
| ~ spl0_65 ),
inference(subsumption_resolution,[],[f3041,f1510]) ).
thf(f3041,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_57
| ~ spl0_61
| ~ spl0_65 ),
inference(forward_demodulation,[],[f3038,f2430]) ).
thf(f3038,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_57
| ~ spl0_61 ),
inference(backward_demodulation,[],[f1907,f2166]) ).
thf(f1907,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1905]) ).
thf(f1905,plain,
( spl0_57
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
thf(f3031,plain,
( spl0_44
| ~ spl0_49
| ~ spl0_7
| ~ spl0_24
| spl0_37 ),
inference(avatar_split_clause,[],[f2725,f448,f246,f79,f958,f634]) ).
thf(f2725,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_7
| ~ spl0_24
| spl0_37 ),
inference(superposition,[],[f2213,f4]) ).
thf(f3027,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_31
| spl0_37 ),
inference(avatar_contradiction_clause,[],[f3026]) ).
thf(f3026,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_31
| spl0_37 ),
inference(trivial_inequality_removal,[],[f3025]) ).
thf(f3025,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_31
| spl0_37 ),
inference(backward_demodulation,[],[f2403,f290]) ).
thf(f2403,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_37 ),
inference(subsumption_resolution,[],[f2388,f2213]) ).
thf(f2388,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24 ),
inference(superposition,[],[f2085,f4]) ).
thf(f2085,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24 ),
inference(backward_demodulation,[],[f1928,f248]) ).
thf(f1928,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_1
| ~ spl0_7 ),
inference(backward_demodulation,[],[f12,f81]) ).
thf(f3010,plain,
( spl0_31
| ~ spl0_33
| ~ spl0_47
| spl0_49 ),
inference(avatar_contradiction_clause,[],[f3009]) ).
thf(f3009,plain,
( $false
| spl0_31
| ~ spl0_33
| ~ spl0_47
| spl0_49 ),
inference(trivial_inequality_removal,[],[f3004]) ).
thf(f3004,plain,
( ( $true = $false )
| spl0_31
| ~ spl0_33
| ~ spl0_47
| spl0_49 ),
inference(backward_demodulation,[],[f2953,f2985]) ).
thf(f2985,plain,
( ! [X0: $o] : ( $false = X0 )
| spl0_31
| ~ spl0_33
| ~ spl0_47
| spl0_49 ),
inference(subsumption_resolution,[],[f2984,f959]) ).
thf(f2984,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = X0 ) )
| spl0_31
| ~ spl0_33
| ~ spl0_47
| spl0_49 ),
inference(forward_demodulation,[],[f2983,f2953]) ).
thf(f2983,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) ) )
| spl0_31
| ~ spl0_33
| spl0_49 ),
inference(subsumption_resolution,[],[f2941,f2704]) ).
thf(f2704,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f1,X0) )
| ( $false = X0 ) )
| spl0_49 ),
inference(superposition,[],[f959,f4]) ).
thf(f2941,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,X0) ) )
| spl0_31
| ~ spl0_33 ),
inference(binary_proxy_clausification,[],[f2939]) ).
thf(f2939,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) != vAPP($o,$o,f1,X0) ) )
| spl0_31
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f2937]) ).
thf(f2937,plain,
( ! [X0: $o] :
( ( $false != $false )
| ( $false = X0 )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) != vAPP($o,$o,f1,X0) ) )
| spl0_31
| ~ spl0_33 ),
inference(constrained_superposition,[],[f289,f2892]) ).
thf(f2892,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,X0)) )
| ( $false = X0 ) )
| ~ spl0_33 ),
inference(superposition,[],[f303,f4]) ).
thf(f2953,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| spl0_31
| ~ spl0_33
| ~ spl0_47 ),
inference(subsumption_resolution,[],[f2943,f2945]) ).
thf(f2945,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_31
| ~ spl0_47 ),
inference(trivial_inequality_removal,[],[f2935]) ).
thf(f2935,plain,
( ( $false != $false )
| ( $true != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_31
| ~ spl0_47 ),
inference(constrained_superposition,[],[f289,f938]) ).
thf(f2943,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ( $true = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_31
| ~ spl0_33 ),
inference(binary_proxy_clausification,[],[f2942]) ).
thf(f2942,plain,
( ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_31
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f2936]) ).
thf(f2936,plain,
( ( $false != $false )
| ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_31
| ~ spl0_33 ),
inference(constrained_superposition,[],[f289,f303]) ).
thf(f2977,plain,
( spl0_31
| ~ spl0_33
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f2976]) ).
thf(f2976,plain,
( $false
| spl0_31
| ~ spl0_33
| ~ spl0_47 ),
inference(subsumption_resolution,[],[f2959,f2953]) ).
thf(f2959,plain,
( ( $true != vAPP($o,$o,f1,$true) )
| spl0_31
| ~ spl0_33
| ~ spl0_47 ),
inference(backward_demodulation,[],[f2945,f2953]) ).
thf(f2952,plain,
( spl0_46
| spl0_31
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f2946,f936,f288,f932]) ).
thf(f2946,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_31
| ~ spl0_47 ),
inference(trivial_inequality_removal,[],[f2933]) ).
thf(f2933,plain,
( ( $false != $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_31
| ~ spl0_47 ),
inference(superposition,[],[f289,f2883]) ).
thf(f2883,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f0,X0) )
| ( $false = X0 ) )
| ~ spl0_47 ),
inference(superposition,[],[f938,f4]) ).
thf(f2847,plain,
( spl0_54
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f2834,f124,f79,f1892]) ).
thf(f1892,plain,
( spl0_54
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
thf(f124,plain,
( spl0_17
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f2834,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f126,f81]) ).
thf(f126,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) = $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f2846,plain,
( ~ spl0_66
| ~ spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f2843,f115,f79,f2544]) ).
thf(f2843,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_7
| spl0_15 ),
inference(forward_demodulation,[],[f116,f81]) ).
thf(f2803,plain,
( spl0_49
| ~ spl0_47
| spl0_33 ),
inference(avatar_split_clause,[],[f2708,f301,f936,f958]) ).
thf(f2708,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,$true) )
| spl0_33 ),
inference(superposition,[],[f302,f4]) ).
thf(f302,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_33 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f2799,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_33
| spl0_69
| ~ spl0_72 ),
inference(avatar_contradiction_clause,[],[f2798]) ).
thf(f2798,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_33
| spl0_69
| ~ spl0_72 ),
inference(trivial_inequality_removal,[],[f2797]) ).
thf(f2797,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_33
| spl0_69
| ~ spl0_72 ),
inference(forward_demodulation,[],[f2796,f2743]) ).
thf(f2743,plain,
( ! [X0: $o] : ( $false = X0 )
| spl0_33
| spl0_69 ),
inference(subsumption_resolution,[],[f2742,f2707]) ).
thf(f2707,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,X0)) )
| ( $false = X0 ) )
| spl0_33 ),
inference(superposition,[],[f302,f4]) ).
thf(f2742,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,X0)) )
| ( $false = X0 ) )
| spl0_69 ),
inference(duplicate_literal_removal,[],[f2741]) ).
thf(f2741,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,X0)) )
| ( $false = X0 )
| ( $false = X0 ) )
| spl0_69 ),
inference(binary_proxy_clausification,[],[f2727]) ).
thf(f2727,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,X0)) != X0 )
| ( $false = X0 ) )
| spl0_69 ),
inference(superposition,[],[f2611,f4]) ).
thf(f2796,plain,
( ( $true = vAPP($o,$o,f1,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_33
| spl0_69
| ~ spl0_72 ),
inference(trivial_inequality_removal,[],[f2795]) ).
thf(f2795,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f1,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_33
| spl0_69
| ~ spl0_72 ),
inference(forward_demodulation,[],[f2736,f2743]) ).
thf(f2736,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ( $true = vAPP($o,$o,f1,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_69
| ~ spl0_72 ),
inference(binary_proxy_clausification,[],[f2735]) ).
thf(f2735,plain,
( ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_69
| ~ spl0_72 ),
inference(trivial_inequality_removal,[],[f2732]) ).
thf(f2732,plain,
( ( $true != $true )
| ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_69
| ~ spl0_72 ),
inference(constrained_superposition,[],[f2611,f2687]) ).
thf(f2687,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_72 ),
inference(backward_demodulation,[],[f2085,f2681]) ).
thf(f2774,plain,
( ~ spl0_23
| spl0_33
| spl0_69 ),
inference(avatar_contradiction_clause,[],[f2773]) ).
thf(f2773,plain,
( $false
| ~ spl0_23
| spl0_33
| spl0_69 ),
inference(trivial_inequality_removal,[],[f2767]) ).
thf(f2767,plain,
( ( $true = $false )
| ~ spl0_23
| spl0_33
| spl0_69 ),
inference(backward_demodulation,[],[f153,f2743]) ).
thf(f2685,plain,
( spl0_72
| ~ spl0_7
| ~ spl0_24
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f2684,f453,f246,f79,f2679]) ).
thf(f2684,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_7
| ~ spl0_24
| ~ spl0_38 ),
inference(forward_demodulation,[],[f2683,f248]) ).
thf(f2683,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) )
| ~ spl0_7
| ~ spl0_38 ),
inference(forward_demodulation,[],[f455,f81]) ).
thf(f2682,plain,
( spl0_72
| spl0_69
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f2390,f246,f79,f10,f2610,f2679]) ).
thf(f2390,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24 ),
inference(superposition,[],[f2085,f4]) ).
thf(f2673,plain,
( ~ spl0_23
| spl0_47
| ~ spl0_69
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f2672]) ).
thf(f2672,plain,
( $false
| ~ spl0_23
| spl0_47
| ~ spl0_69
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f2671,f937]) ).
thf(f2671,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_23
| ~ spl0_69
| ~ spl0_71 ),
inference(forward_demodulation,[],[f2670,f153]) ).
thf(f2670,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_69
| ~ spl0_71 ),
inference(backward_demodulation,[],[f2647,f2612]) ).
thf(f2665,plain,
( spl0_66
| ~ spl0_7
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f2664,f115,f79,f2544]) ).
thf(f2664,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_7
| ~ spl0_15 ),
inference(forward_demodulation,[],[f117,f81]) ).
thf(f2659,plain,
( ~ spl0_23
| spl0_47
| ~ spl0_67 ),
inference(avatar_contradiction_clause,[],[f2658]) ).
thf(f2658,plain,
( $false
| ~ spl0_23
| spl0_47
| ~ spl0_67 ),
inference(subsumption_resolution,[],[f2657,f937]) ).
thf(f2657,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_23
| ~ spl0_67 ),
inference(forward_demodulation,[],[f2656,f153]) ).
thf(f2656,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_23
| ~ spl0_67 ),
inference(backward_demodulation,[],[f2550,f153]) ).
thf(f2648,plain,
( spl0_61
| spl0_71
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f1726,f79,f23,f2645,f2164]) ).
thf(f1726,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f1602,f4]) ).
thf(f1602,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f25,f81]) ).
thf(f2640,plain,
( ~ spl0_70
| ~ spl0_7
| ~ spl0_24
| spl0_38
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f2639,f634,f453,f246,f79,f2614]) ).
thf(f2639,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_7
| ~ spl0_24
| spl0_38
| ~ spl0_44 ),
inference(forward_demodulation,[],[f2638,f635]) ).
thf(f2638,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_7
| ~ spl0_24
| spl0_38 ),
inference(forward_demodulation,[],[f2637,f248]) ).
thf(f2637,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) )
| ~ spl0_7
| spl0_38 ),
inference(forward_demodulation,[],[f454,f81]) ).
thf(f2590,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_38
| ~ spl0_44
| spl0_55
| ~ spl0_59 ),
inference(avatar_contradiction_clause,[],[f2589]) ).
thf(f2589,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_38
| ~ spl0_44
| spl0_55
| ~ spl0_59 ),
inference(subsumption_resolution,[],[f2583,f2565]) ).
thf(f2565,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_38 ),
inference(forward_demodulation,[],[f2085,f2442]) ).
thf(f2442,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_7
| ~ spl0_24
| ~ spl0_38 ),
inference(forward_demodulation,[],[f2441,f248]) ).
thf(f2441,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) )
| ~ spl0_7
| ~ spl0_38 ),
inference(forward_demodulation,[],[f455,f81]) ).
thf(f2583,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_44
| spl0_55
| ~ spl0_59 ),
inference(backward_demodulation,[],[f2574,f635]) ).
thf(f2574,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| spl0_55
| ~ spl0_59 ),
inference(backward_demodulation,[],[f1897,f2156]) ).
thf(f2564,plain,
( spl0_23
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_38
| spl0_65 ),
inference(avatar_split_clause,[],[f2563,f2428,f453,f246,f79,f10,f151]) ).
thf(f2563,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_38
| spl0_65 ),
inference(subsumption_resolution,[],[f2562,f2429]) ).
thf(f2562,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_38 ),
inference(forward_demodulation,[],[f2392,f2442]) ).
thf(f2392,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24 ),
inference(superposition,[],[f2085,f4]) ).
thf(f2551,plain,
( spl0_66
| spl0_67
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f1728,f79,f23,f2548,f2544]) ).
thf(f1728,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f1602,f4]) ).
thf(f2458,plain,
( ~ spl0_23
| spl0_47
| ~ spl0_64 ),
inference(avatar_contradiction_clause,[],[f2457]) ).
thf(f2457,plain,
( $false
| ~ spl0_23
| spl0_47
| ~ spl0_64 ),
inference(subsumption_resolution,[],[f2456,f937]) ).
thf(f2456,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_23
| ~ spl0_64 ),
inference(backward_demodulation,[],[f2183,f153]) ).
thf(f2183,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f2181]) ).
thf(f2419,plain,
( ~ spl0_48
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f2397,f1508,f246,f79,f10,f944]) ).
thf(f2397,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_53 ),
inference(trivial_inequality_removal,[],[f2396]) ).
thf(f2396,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_53 ),
inference(constrained_superposition,[],[f1509,f2085]) ).
thf(f2417,plain,
( spl0_48
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f2416,f936,f246,f79,f10,f944]) ).
thf(f2416,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_47 ),
inference(trivial_inequality_removal,[],[f2415]) ).
thf(f2415,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_47 ),
inference(forward_demodulation,[],[f2392,f938]) ).
thf(f2355,plain,
( spl0_44
| ~ spl0_7
| ~ spl0_24
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f2216,f443,f246,f79,f634]) ).
thf(f2216,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_7
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_demodulation,[],[f2215,f248]) ).
thf(f2215,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_7
| ~ spl0_36 ),
inference(forward_demodulation,[],[f445,f81]) ).
thf(f2305,plain,
( spl0_53
| ~ spl0_47
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f2304,f2181,f936,f1508]) ).
thf(f2304,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_47
| ~ spl0_64 ),
inference(forward_demodulation,[],[f2183,f938]) ).
thf(f2283,plain,
( ~ spl0_53
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_43
| ~ spl0_44
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f2274,f936,f634,f628,f246,f79,f10,f1508]) ).
thf(f2274,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| spl0_43
| ~ spl0_44
| ~ spl0_47 ),
inference(backward_demodulation,[],[f2198,f2272]) ).
thf(f2272,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_44
| ~ spl0_47 ),
inference(trivial_inequality_removal,[],[f2271]) ).
thf(f2271,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_44
| ~ spl0_47 ),
inference(forward_demodulation,[],[f2259,f938]) ).
thf(f2259,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_44 ),
inference(superposition,[],[f2202,f4]) ).
thf(f2202,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_44 ),
inference(backward_demodulation,[],[f2085,f635]) ).
thf(f2198,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_43
| ~ spl0_44 ),
inference(backward_demodulation,[],[f629,f635]) ).
thf(f2211,plain,
( spl0_31
| ~ spl0_44
| ~ spl0_49
| ~ spl0_57 ),
inference(avatar_contradiction_clause,[],[f2210]) ).
thf(f2210,plain,
( $false
| spl0_31
| ~ spl0_44
| ~ spl0_49
| ~ spl0_57 ),
inference(subsumption_resolution,[],[f2209,f1969]) ).
thf(f1969,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_31
| ~ spl0_49 ),
inference(forward_demodulation,[],[f289,f960]) ).
thf(f2209,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_44
| ~ spl0_57 ),
inference(forward_demodulation,[],[f2208,f635]) ).
thf(f2208,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_44
| ~ spl0_57 ),
inference(forward_demodulation,[],[f2201,f635]) ).
thf(f2201,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_44
| ~ spl0_57 ),
inference(backward_demodulation,[],[f1907,f635]) ).
thf(f2197,plain,
( spl0_19
| ~ spl0_47
| ~ spl0_54
| ~ spl0_57 ),
inference(avatar_contradiction_clause,[],[f2196]) ).
thf(f2196,plain,
( $false
| spl0_19
| ~ spl0_47
| ~ spl0_54
| ~ spl0_57 ),
inference(subsumption_resolution,[],[f2193,f2189]) ).
thf(f2189,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_54
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1894,f1907]) ).
thf(f1894,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1892]) ).
thf(f2193,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_19
| ~ spl0_47 ),
inference(backward_demodulation,[],[f133,f938]) ).
thf(f2184,plain,
( spl0_57
| spl0_64
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f1733,f79,f23,f2181,f1905]) ).
thf(f1733,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f1602,f4]) ).
thf(f2139,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| ~ spl0_49
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f2138]) ).
thf(f2138,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| ~ spl0_49
| ~ spl0_53 ),
inference(trivial_inequality_removal,[],[f2137]) ).
thf(f2137,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| ~ spl0_49
| ~ spl0_53 ),
inference(forward_demodulation,[],[f2136,f1509]) ).
thf(f2136,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| ~ spl0_49
| ~ spl0_53 ),
inference(forward_demodulation,[],[f2127,f2123]) ).
thf(f2123,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| ~ spl0_49
| ~ spl0_53 ),
inference(trivial_inequality_removal,[],[f2122]) ).
thf(f2122,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| ~ spl0_49
| ~ spl0_53 ),
inference(forward_demodulation,[],[f2121,f1509]) ).
thf(f2121,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| ~ spl0_49 ),
inference(forward_demodulation,[],[f2103,f960]) ).
thf(f2103,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37 ),
inference(superposition,[],[f2089,f4]) ).
thf(f2089,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37 ),
inference(forward_demodulation,[],[f2085,f1317]) ).
thf(f1317,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37 ),
inference(backward_demodulation,[],[f973,f248]) ).
thf(f973,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_7
| ~ spl0_37 ),
inference(forward_demodulation,[],[f450,f81]) ).
thf(f2127,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| ~ spl0_49
| ~ spl0_53 ),
inference(backward_demodulation,[],[f2089,f2123]) ).
thf(f2016,plain,
( spl0_55
| ~ spl0_7
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1971,f147,f79,f1896]) ).
thf(f1971,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_7
| ~ spl0_22 ),
inference(forward_demodulation,[],[f149,f81]) ).
thf(f1974,plain,
( ~ spl0_7
| ~ spl0_22
| ~ spl0_57 ),
inference(avatar_contradiction_clause,[],[f1973]) ).
thf(f1973,plain,
( $false
| ~ spl0_7
| ~ spl0_22
| ~ spl0_57 ),
inference(trivial_inequality_removal,[],[f1972]) ).
thf(f1972,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_22
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1971,f1907]) ).
thf(f1950,plain,
( spl0_14
| ~ spl0_19
| ~ spl0_47
| ~ spl0_49 ),
inference(avatar_contradiction_clause,[],[f1949]) ).
thf(f1949,plain,
( $false
| spl0_14
| ~ spl0_19
| ~ spl0_47
| ~ spl0_49 ),
inference(subsumption_resolution,[],[f1948,f1880]) ).
thf(f1880,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_19
| ~ spl0_47 ),
inference(forward_demodulation,[],[f134,f938]) ).
thf(f1948,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_14
| ~ spl0_19
| ~ spl0_47
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1947,f938]) ).
thf(f1947,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_14
| ~ spl0_19
| ~ spl0_47
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1887,f1880]) ).
thf(f1887,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_14
| ~ spl0_49 ),
inference(forward_demodulation,[],[f111,f960]) ).
thf(f111,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_14 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f1943,plain,
( spl0_53
| ~ spl0_33
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f1877,f958,f301,f1508]) ).
thf(f1877,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_33
| ~ spl0_49 ),
inference(forward_demodulation,[],[f303,f960]) ).
thf(f1917,plain,
( spl0_57
| spl0_53
| ~ spl0_4
| ~ spl0_7
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f1916,f936,f79,f23,f1508,f1905]) ).
thf(f1916,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1733,f938]) ).
thf(f1883,plain,
( ~ spl0_19
| ~ spl0_47
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f1882]) ).
thf(f1882,plain,
( $false
| ~ spl0_19
| ~ spl0_47
| ~ spl0_53 ),
inference(trivial_inequality_removal,[],[f1881]) ).
thf(f1881,plain,
( ( $true = $false )
| ~ spl0_19
| ~ spl0_47
| ~ spl0_53 ),
inference(forward_demodulation,[],[f1880,f1509]) ).
thf(f1804,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_17
| spl0_22
| spl0_53 ),
inference(avatar_contradiction_clause,[],[f1803]) ).
thf(f1803,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| spl0_17
| spl0_22
| spl0_53 ),
inference(subsumption_resolution,[],[f1802,f1692]) ).
thf(f1692,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_7
| spl0_17 ),
inference(forward_demodulation,[],[f125,f81]) ).
thf(f125,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) != $true )
| spl0_17 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f1802,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_4
| ~ spl0_7
| spl0_22
| spl0_53 ),
inference(subsumption_resolution,[],[f1801,f1688]) ).
thf(f1688,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_7
| spl0_22 ),
inference(forward_demodulation,[],[f148,f81]) ).
thf(f148,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))) != $true )
| spl0_22 ),
inference(avatar_component_clause,[],[f147]) ).
thf(f1801,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_4
| ~ spl0_7
| spl0_53 ),
inference(subsumption_resolution,[],[f1757,f1510]) ).
thf(f1757,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1737]) ).
thf(f1737,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_4
| ~ spl0_7 ),
inference(constrained_superposition,[],[f1602,f1602]) ).
thf(f1783,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_15
| ~ spl0_23
| spl0_47 ),
inference(avatar_contradiction_clause,[],[f1782]) ).
thf(f1782,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| spl0_15
| ~ spl0_23
| spl0_47 ),
inference(subsumption_resolution,[],[f1781,f937]) ).
thf(f1781,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| ~ spl0_7
| spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1780,f153]) ).
thf(f1780,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_4
| ~ spl0_7
| spl0_15
| ~ spl0_23 ),
inference(subsumption_resolution,[],[f1729,f1683]) ).
thf(f1683,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_7
| spl0_15 ),
inference(forward_demodulation,[],[f116,f81]) ).
thf(f1729,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_23 ),
inference(superposition,[],[f1602,f1295]) ).
thf(f1295,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f0,X0) )
| ( $false = X0 ) )
| ~ spl0_23 ),
inference(duplicate_literal_removal,[],[f1293]) ).
thf(f1293,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f0,X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl0_23 ),
inference(binary_proxy_clausification,[],[f1290]) ).
thf(f1290,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f0,X0) = X0 )
| ( $false = X0 ) )
| ~ spl0_23 ),
inference(superposition,[],[f153,f4]) ).
thf(f1695,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1694]) ).
thf(f1694,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f1693]) ).
thf(f1693,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f955,f1602]) ).
thf(f955,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f16,f81]) ).
thf(f1619,plain,
( ~ spl0_43
| spl0_3
| ~ spl0_7
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f1612,f246,f79,f19,f628]) ).
thf(f1612,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_3
| ~ spl0_7
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1611,f248]) ).
thf(f1611,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f20,f81]) ).
thf(f1541,plain,
( spl0_53
| ~ spl0_7
| ~ spl0_24
| ~ spl0_29
| ~ spl0_37
| ~ spl0_48
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f1540,f958,f944,f448,f274,f246,f79,f1508]) ).
thf(f1540,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_7
| ~ spl0_24
| ~ spl0_29
| ~ spl0_37
| ~ spl0_48
| ~ spl0_49 ),
inference(backward_demodulation,[],[f1526,f1381]) ).
thf(f1381,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| ~ spl0_48 ),
inference(forward_demodulation,[],[f946,f1317]) ).
thf(f1526,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_29
| ~ spl0_49 ),
inference(backward_demodulation,[],[f276,f960]) ).
thf(f1537,plain,
( ~ spl0_44
| ~ spl0_7
| ~ spl0_24
| spl0_36 ),
inference(avatar_split_clause,[],[f1316,f443,f246,f79,f634]) ).
thf(f1316,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_7
| ~ spl0_24
| spl0_36 ),
inference(backward_demodulation,[],[f689,f248]) ).
thf(f689,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_7
| spl0_36 ),
inference(forward_demodulation,[],[f444,f81]) ).
thf(f1535,plain,
( ~ spl0_53
| spl0_33
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f1528,f958,f301,f1508]) ).
thf(f1528,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_33
| ~ spl0_49 ),
inference(backward_demodulation,[],[f302,f960]) ).
thf(f1502,plain,
( spl0_49
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| spl0_44 ),
inference(avatar_split_clause,[],[f1501,f634,f448,f246,f79,f958]) ).
thf(f1501,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37
| spl0_44 ),
inference(subsumption_resolution,[],[f1466,f636]) ).
thf(f1466,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_7
| ~ spl0_24
| ~ spl0_37 ),
inference(superposition,[],[f1317,f4]) ).
thf(f1378,plain,
( ~ spl0_14
| ~ spl0_33
| ~ spl0_49 ),
inference(avatar_contradiction_clause,[],[f1377]) ).
thf(f1377,plain,
( $false
| ~ spl0_14
| ~ spl0_33
| ~ spl0_49 ),
inference(trivial_inequality_removal,[],[f1376]) ).
thf(f1376,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_33
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1375,f1372]) ).
thf(f1372,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_33
| ~ spl0_49 ),
inference(backward_demodulation,[],[f303,f960]) ).
thf(f1375,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_14
| ~ spl0_33
| ~ spl0_49 ),
inference(backward_demodulation,[],[f1278,f1372]) ).
thf(f1278,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_14
| ~ spl0_33 ),
inference(forward_demodulation,[],[f112,f303]) ).
thf(f1370,plain,
( ~ spl0_49
| ~ spl0_2
| ~ spl0_7
| ~ spl0_20
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f1361,f301,f137,f79,f14,f958]) ).
thf(f1361,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_20
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f1356]) ).
thf(f1356,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f1,$true) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_20
| ~ spl0_33 ),
inference(constrained_superposition,[],[f1048,f303]) ).
thf(f1048,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f955,f949]) ).
thf(f949,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f139,f81]) ).
thf(f1367,plain,
( spl0_49
| ~ spl0_33
| spl0_47 ),
inference(avatar_split_clause,[],[f1366,f936,f301,f958]) ).
thf(f1366,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_33
| spl0_47 ),
inference(subsumption_resolution,[],[f1351,f937]) ).
thf(f1351,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_33 ),
inference(superposition,[],[f303,f4]) ).
thf(f1320,plain,
( ~ spl0_7
| ~ spl0_11
| spl0_15
| ~ spl0_24
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1319]) ).
thf(f1319,plain,
( $false
| ~ spl0_7
| ~ spl0_11
| spl0_15
| ~ spl0_24
| ~ spl0_37 ),
inference(subsumption_resolution,[],[f1317,f1277]) ).
thf(f1277,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_11
| spl0_15 ),
inference(forward_demodulation,[],[f1276,f1261]) ).
thf(f1261,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f99,f81]) ).
thf(f1276,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_7
| spl0_15 ),
inference(forward_demodulation,[],[f116,f81]) ).
thf(f1315,plain,
( spl0_24
| ~ spl0_7
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1314,f438,f79,f246]) ).
thf(f438,plain,
( spl0_35
<=> ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
thf(f1314,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_7
| ~ spl0_35 ),
inference(forward_demodulation,[],[f440,f81]) ).
thf(f440,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x))) = $false )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f438]) ).
thf(f1305,plain,
( spl0_24
| ~ spl0_41
| spl0_45 ),
inference(avatar_contradiction_clause,[],[f1304]) ).
thf(f1304,plain,
( $false
| spl0_24
| ~ spl0_41
| spl0_45 ),
inference(subsumption_resolution,[],[f1303,f642]) ).
thf(f642,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| spl0_45 ),
inference(avatar_component_clause,[],[f641]) ).
thf(f1303,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| spl0_24
| ~ spl0_41 ),
inference(subsumption_resolution,[],[f1297,f619]) ).
thf(f1297,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f3,$false) )
| spl0_24 ),
inference(superposition,[],[f247,f4]) ).
thf(f247,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| spl0_24 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f1265,plain,
( ~ spl0_7
| ~ spl0_15
| ~ spl0_37
| spl0_38
| ~ spl0_44 ),
inference(avatar_contradiction_clause,[],[f1264]) ).
thf(f1264,plain,
( $false
| ~ spl0_7
| ~ spl0_15
| ~ spl0_37
| spl0_38
| ~ spl0_44 ),
inference(subsumption_resolution,[],[f1250,f1252]) ).
thf(f1252,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_7
| ~ spl0_37
| spl0_38 ),
inference(forward_demodulation,[],[f1251,f973]) ).
thf(f1251,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) )
| ~ spl0_7
| spl0_38 ),
inference(forward_demodulation,[],[f454,f81]) ).
thf(f1250,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_7
| ~ spl0_15
| ~ spl0_44 ),
inference(forward_demodulation,[],[f1249,f635]) ).
thf(f1249,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_15
| ~ spl0_44 ),
inference(forward_demodulation,[],[f1239,f635]) ).
thf(f1239,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_7
| ~ spl0_15
| ~ spl0_44 ),
inference(backward_demodulation,[],[f1182,f635]) ).
thf(f1182,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_7
| ~ spl0_15 ),
inference(forward_demodulation,[],[f117,f81]) ).
thf(f1225,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_45 ),
inference(avatar_contradiction_clause,[],[f1224]) ).
thf(f1224,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| spl0_45 ),
inference(subsumption_resolution,[],[f1223,f642]) ).
thf(f1223,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7 ),
inference(backward_demodulation,[],[f81,f72]) ).
thf(f1126,plain,
( ~ spl0_7
| spl0_34
| ~ spl0_45 ),
inference(avatar_contradiction_clause,[],[f1125]) ).
thf(f1125,plain,
( $false
| ~ spl0_7
| spl0_34
| ~ spl0_45 ),
inference(subsumption_resolution,[],[f1118,f643]) ).
thf(f1118,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_7
| spl0_34 ),
inference(backward_demodulation,[],[f434,f81]) ).
thf(f434,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f3,x)) != $false )
| spl0_34 ),
inference(avatar_component_clause,[],[f433]) ).
thf(f433,plain,
( spl0_34
<=> ( vAPP($o,$o,f3,vAPP($o,$o,f3,x)) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
thf(f1114,plain,
( spl0_5
| spl0_50
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f416,f19,f1111,f70]) ).
thf(f416,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ( x = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f1109,plain,
( spl0_5
| spl0_41
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f746,f79,f617,f70]) ).
thf(f746,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ( x = $false )
| ~ spl0_7 ),
inference(superposition,[],[f81,f4]) ).
thf(f1108,plain,
( ~ spl0_5
| spl0_34
| ~ spl0_45 ),
inference(avatar_contradiction_clause,[],[f1107]) ).
thf(f1107,plain,
( $false
| ~ spl0_5
| spl0_34
| ~ spl0_45 ),
inference(subsumption_resolution,[],[f1106,f643]) ).
thf(f1106,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_5
| spl0_34
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1105,f643]) ).
thf(f1105,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| spl0_34 ),
inference(forward_demodulation,[],[f434,f72]) ).
thf(f983,plain,
( ~ spl0_23
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f982]) ).
thf(f982,plain,
( $false
| ~ spl0_23
| ~ spl0_47 ),
inference(trivial_inequality_removal,[],[f981]) ).
thf(f981,plain,
( ( $true = $false )
| ~ spl0_23
| ~ spl0_47 ),
inference(forward_demodulation,[],[f153,f938]) ).
thf(f971,plain,
( spl0_23
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f966,f132,f119,f151]) ).
thf(f119,plain,
( spl0_16
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f966,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f121,f134]) ).
thf(f121,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f961,plain,
( spl0_49
| spl0_33
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f851,f288,f301,f958]) ).
thf(f851,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_31 ),
inference(superposition,[],[f290,f4]) ).
thf(f939,plain,
( spl0_46
| spl0_47
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f853,f288,f936,f932]) ).
thf(f853,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_31 ),
inference(superposition,[],[f290,f4]) ).
thf(f930,plain,
( ~ spl0_7
| spl0_11
| ~ spl0_13
| spl0_42
| spl0_44 ),
inference(avatar_contradiction_clause,[],[f929]) ).
thf(f929,plain,
( $false
| ~ spl0_7
| spl0_11
| ~ spl0_13
| spl0_42
| spl0_44 ),
inference(subsumption_resolution,[],[f928,f624]) ).
thf(f928,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_7
| spl0_11
| ~ spl0_13
| spl0_42
| spl0_44 ),
inference(forward_demodulation,[],[f927,f914]) ).
thf(f914,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_7
| spl0_11
| ~ spl0_13
| spl0_42 ),
inference(subsumption_resolution,[],[f891,f893]) ).
thf(f893,plain,
( ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_13
| spl0_42 ),
inference(trivial_inequality_removal,[],[f888]) ).
thf(f888,plain,
( ( $false != $false )
| ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_13
| spl0_42 ),
inference(constrained_superposition,[],[f624,f820]) ).
thf(f820,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f108,f81]) ).
thf(f891,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| spl0_11
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f890]) ).
thf(f890,plain,
( ( vAPP($o,$o,f2,$false) != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| spl0_11
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f889]) ).
thf(f889,plain,
( ( $false != $false )
| ( vAPP($o,$o,f2,$false) != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| spl0_11
| ~ spl0_13 ),
inference(constrained_superposition,[],[f735,f820]) ).
thf(f735,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| spl0_11 ),
inference(forward_demodulation,[],[f98,f81]) ).
thf(f98,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))) != $false )
| spl0_11 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f927,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| spl0_11
| ~ spl0_13
| spl0_44 ),
inference(subsumption_resolution,[],[f892,f636]) ).
thf(f892,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| spl0_11
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f890]) ).
thf(f908,plain,
( ~ spl0_7
| spl0_11
| ~ spl0_13
| spl0_44 ),
inference(avatar_contradiction_clause,[],[f907]) ).
thf(f907,plain,
( $false
| ~ spl0_7
| spl0_11
| ~ spl0_13
| spl0_44 ),
inference(subsumption_resolution,[],[f906,f735]) ).
thf(f906,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_13
| spl0_44 ),
inference(subsumption_resolution,[],[f899,f636]) ).
thf(f899,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_13 ),
inference(duplicate_literal_removal,[],[f898]) ).
thf(f898,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ( $false = vAPP($o,$o,f2,$false) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f881]) ).
thf(f881,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ( vAPP($o,$o,f2,$false) != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_13 ),
inference(constrained_superposition,[],[f820,f820]) ).
thf(f728,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f727]) ).
thf(f727,plain,
( $false
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f726]) ).
thf(f726,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f725,f486]) ).
thf(f486,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(backward_demodulation,[],[f478,f410]) ).
thf(f410,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f149,f117]) ).
thf(f478,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f139,f117]) ).
thf(f725,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f724,f511]) ).
thf(f511,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_15
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f134,f486]) ).
thf(f724,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_14
| ~ spl0_33 ),
inference(backward_demodulation,[],[f112,f303]) ).
thf(f701,plain,
( ~ spl0_44
| ~ spl0_7
| spl0_36
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f691,f641,f443,f79,f634]) ).
thf(f691,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_7
| spl0_36
| ~ spl0_45 ),
inference(forward_demodulation,[],[f690,f643]) ).
thf(f690,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_7
| spl0_36
| ~ spl0_45 ),
inference(forward_demodulation,[],[f689,f643]) ).
thf(f700,plain,
( spl0_44
| ~ spl0_7
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f699,f106,f97,f79,f634]) ).
thf(f699,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_7
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f694,f697]) ).
thf(f697,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f99,f81]) ).
thf(f694,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f108,f81]) ).
thf(f677,plain,
( ~ spl0_7
| spl0_11
| ~ spl0_44 ),
inference(avatar_contradiction_clause,[],[f676]) ).
thf(f676,plain,
( $false
| ~ spl0_7
| spl0_11
| ~ spl0_44 ),
inference(subsumption_resolution,[],[f668,f635]) ).
thf(f668,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_7
| spl0_11
| ~ spl0_44 ),
inference(backward_demodulation,[],[f654,f635]) ).
thf(f654,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| spl0_11 ),
inference(backward_demodulation,[],[f98,f81]) ).
thf(f675,plain,
( ~ spl0_7
| spl0_13
| ~ spl0_44 ),
inference(avatar_contradiction_clause,[],[f674]) ).
thf(f674,plain,
( $false
| ~ spl0_7
| spl0_13
| ~ spl0_44 ),
inference(subsumption_resolution,[],[f673,f635]) ).
thf(f673,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_7
| spl0_13
| ~ spl0_44 ),
inference(forward_demodulation,[],[f667,f635]) ).
thf(f667,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| spl0_13
| ~ spl0_44 ),
inference(backward_demodulation,[],[f655,f635]) ).
thf(f655,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_7
| spl0_13 ),
inference(backward_demodulation,[],[f107,f81]) ).
thf(f665,plain,
( spl0_44
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f664,f88,f79,f634]) ).
thf(f664,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f90,f81]) ).
thf(f652,plain,
( ~ spl0_45
| ~ spl0_34
| spl0_35 ),
inference(avatar_split_clause,[],[f651,f438,f433,f641]) ).
thf(f651,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_34
| spl0_35 ),
inference(forward_demodulation,[],[f439,f435]) ).
thf(f435,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f3,x)) = $false )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f433]) ).
thf(f439,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x))) != $false )
| spl0_35 ),
inference(avatar_component_clause,[],[f438]) ).
thf(f620,plain,
( spl0_7
| spl0_41
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f568,f433,f617,f79]) ).
thf(f568,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ( vAPP($o,$o,f3,x) = $false )
| ~ spl0_34 ),
inference(superposition,[],[f435,f4]) ).
thf(f485,plain,
( spl0_19
| ~ spl0_2
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f484,f137,f115,f14,f132]) ).
thf(f484,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_2
| ~ spl0_15
| ~ spl0_20 ),
inference(subsumption_resolution,[],[f382,f478]) ).
thf(f382,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_2
| ~ spl0_15 ),
inference(constrained_superposition,[],[f376,f376]) ).
thf(f376,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_2
| ~ spl0_15 ),
inference(forward_demodulation,[],[f16,f117]) ).
thf(f456,plain,
( spl0_38
| spl0_33
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f422,f19,f301,f453]) ).
thf(f422,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f451,plain,
( spl0_37
| spl0_31
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f421,f19,f288,f448]) ).
thf(f421,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x))))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f446,plain,
( spl0_36
| spl0_29
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f420,f19,f274,f443]) ).
thf(f420,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f436,plain,
( spl0_34
| spl0_25
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f418,f19,f250,f433]) ).
thf(f418,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ( vAPP($o,$o,f3,vAPP($o,$o,f3,x)) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f409,plain,
( ~ spl0_15
| spl0_20
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f408]) ).
thf(f408,plain,
( $false
| ~ spl0_15
| spl0_20
| spl0_22 ),
inference(subsumption_resolution,[],[f403,f398]) ).
thf(f398,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_15
| spl0_22 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f397,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_15
| spl0_22 ),
inference(superposition,[],[f375,f4]) ).
thf(f375,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| ~ spl0_15
| spl0_22 ),
inference(forward_demodulation,[],[f148,f117]) ).
thf(f403,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_15
| spl0_20
| spl0_22 ),
inference(backward_demodulation,[],[f374,f398]) ).
thf(f374,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_15
| spl0_20 ),
inference(forward_demodulation,[],[f138,f117]) ).
thf(f407,plain,
( ~ spl0_2
| ~ spl0_15
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f406]) ).
thf(f406,plain,
( $false
| ~ spl0_2
| ~ spl0_15
| spl0_22 ),
inference(trivial_inequality_removal,[],[f405]) ).
thf(f405,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_15
| spl0_22 ),
inference(forward_demodulation,[],[f404,f398]) ).
thf(f404,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_15
| spl0_22 ),
inference(forward_demodulation,[],[f401,f398]) ).
thf(f401,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_2
| ~ spl0_15
| spl0_22 ),
inference(backward_demodulation,[],[f376,f398]) ).
thf(f372,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f371]) ).
thf(f371,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f370,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f369,f368]) ).
thf(f368,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f308,f359]) ).
thf(f359,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f117,f72]) ).
thf(f308,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f25,f72]) ).
thf(f369,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f177,f359]) ).
thf(f177,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f16,f72]) ).
thf(f304,plain,
( spl0_32
| spl0_33
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f235,f70,f19,f301,f297]) ).
thf(f235,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f197,f4]) ).
thf(f197,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f21,f72]) ).
thf(f162,plain,
( ~ spl0_17
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f161]) ).
thf(f161,plain,
( $false
| ~ spl0_17
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f160]) ).
thf(f160,plain,
( ( $true = $false )
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f126,f139]) ).
thf(f159,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f158]) ).
thf(f158,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f157,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f12,f21]) ).
thf(f156,plain,
( spl0_20
| spl0_23
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f64,f14,f151,f137]) ).
thf(f64,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f154,plain,
( spl0_17
| spl0_22
| spl0_23
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f65,f14,f151,f147,f124]) ).
thf(f65,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))) = $true )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) = $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f63]) ).
thf(f63,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f16,f16]) ).
thf(f145,plain,
( spl0_21
| spl0_19
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f62,f14,f132,f142]) ).
thf(f62,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f135,plain,
( spl0_17
| spl0_18
| spl0_19
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f67,f14,f132,f128,f124]) ).
thf(f67,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))) = $true )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) = $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f61]) ).
thf(f61,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))))) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f16,f16]) ).
thf(f122,plain,
( spl0_15
| spl0_16
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f60,f14,f119,f115]) ).
thf(f60,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f113,plain,
( spl0_13
| spl0_14
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f59,f14,f110,f106]) ).
thf(f59,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f104,plain,
( spl0_11
| spl0_12
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f58,f14,f101,f97]) ).
thf(f58,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f95,plain,
( spl0_9
| spl0_10
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f57,f14,f92,f88]) ).
thf(f57,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,x)) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f26,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f23,f19]) ).
thf(f8,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) = $false )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))) = $false ) ),
inference(binary_proxy_clausification,[],[f6]) ).
thf(f6,plain,
vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))),
inference(flattening,[],[f2]) ).
thf(f2,negated_conjecture,
vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kaminski4) ).
thf(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f7,f14,f10]) ).
thf(f7,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,x)))))))) = $true )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,x)))))))) = $true ) ),
inference(binary_proxy_clausification,[],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO500^1.004 : TPTP v8.2.0. Released v4.1.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 10:03:08 EDT 2024
% 0.22/0.36 % CPUTime :
% 0.22/0.37 % (16593)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (16596)WARNING: value z3 for option sas not known
% 0.22/0.38 % (16597)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % Exception at run slice level
% 0.22/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.38 % (16594)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (16595)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (16598)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)
% 0.22/0.38 % (16599)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)
% 0.22/0.38 % Exception at run slice level
% 0.22/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.38 % (16596)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)
% 0.22/0.38 % Exception at run slice level
% 0.22/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.39 % (16600)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)
% 0.22/0.39 % (16600)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.40 % (16601)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.40 % (16601)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.40 % Exception at run slice level
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.40 % (16602)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)
% 0.22/0.40 % (16602)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.40 % (16603)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)
% 0.22/0.42 % (16604)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)
% 1.48/0.58 % (16603)First to succeed.
% 1.48/0.59 % (16603)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16593"
% 1.48/0.59 % (16603)Refutation found. Thanks to Tanya!
% 1.48/0.59 % SZS status Theorem for theBenchmark
% 1.48/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.48/0.60 % (16603)------------------------------
% 1.48/0.60 % (16603)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.48/0.60 % (16603)Termination reason: Refutation
% 1.48/0.60
% 1.48/0.60 % (16603)Memory used [KB]: 2534
% 1.48/0.60 % (16603)Time elapsed: 0.190 s
% 1.48/0.60 % (16603)Instructions burned: 480 (million)
% 1.48/0.60 % (16593)Success in time 0.215 s
%------------------------------------------------------------------------------