%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV157^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:41:33 EDT 2024
% Result : Theorem 0.15s 0.52s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 61
% Syntax : Number of formulae : 390 ( 34 unt; 39 typ; 0 def)
% Number of atoms : 4043 ( 326 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 13821 ( 463 ~; 752 |; 740 &;8811 @)
% ( 21 <=>;1110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 1105 (1105 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 54 con; 0-2 aty)
% (1924 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2245 (1989 ^ 255 !; 0 ?;2245 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a ).
thf(func_def_24,type,
sK5: a > a > $o ).
thf(func_def_25,type,
sK6: a > a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a ).
thf(func_def_33,type,
sK14: a > a > $o ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a > a > $o ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: ( a > a > $o ) > a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a ).
thf(func_def_50,type,
sK31: a ).
thf(func_def_51,type,
sK32: a ).
thf(func_def_52,type,
sK33: a ).
thf(func_def_53,type,
sK34: a ).
thf(func_def_54,type,
sK35: a ).
thf(func_def_55,type,
sK36: a ).
thf(func_def_56,type,
sK37: a ).
thf(f1250,plain,
$false,
inference(avatar_sat_refutation,[],[f34,f123,f142,f177,f183,f191,f201,f244,f334,f374,f505,f587,f680,f699,f900,f935,f1029,f1185,f1201,f1235,f1241,f1249]) ).
thf(f1249,plain,
( ~ spl0_7
| ~ spl0_25
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1248]) ).
thf(f1248,plain,
( $false
| ~ spl0_7
| ~ spl0_25
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f1247]) ).
thf(f1247,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_25
| ~ spl0_27 ),
inference(boolean_simplification,[],[f1246]) ).
thf(f1246,plain,
( ( $true = ~ $true )
| ~ spl0_7
| ~ spl0_25
| ~ spl0_27 ),
inference(boolean_simplification,[],[f1244]) ).
thf(f1244,plain,
( ( ( ~ ( ( sK5 @ sK37 @ sK36 )
| $true ) )
= $true )
| ~ spl0_7
| ~ spl0_25
| ~ spl0_27 ),
inference(backward_demodulation,[],[f1223,f1231]) ).
thf(f1231,plain,
( ( ( sK3 @ sK37 @ sK36 )
= $true )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f1230]) ).
thf(f1230,plain,
( spl0_27
<=> ( ( sK3 @ sK37 @ sK36 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
thf(f1223,plain,
( ( ( ~ ( ( sK5 @ sK37 @ sK36 )
| ( sK3 @ sK37 @ sK36 ) ) )
= $true )
| ~ spl0_7
| ~ spl0_25 ),
inference(boolean_simplification,[],[f1219]) ).
thf(f1219,plain,
( ( ( ( ( sK5 @ sK37 @ sK36 )
| ( sK3 @ sK37 @ sK36 ) )
=> $false )
= $true )
| ~ spl0_7
| ~ spl0_25 ),
inference(superposition,[],[f996,f1215]) ).
thf(f1215,plain,
( ( $false
= ( sK20 @ sK37 @ sK36 ) )
| ~ spl0_25 ),
inference(boolean_simplification,[],[f1214]) ).
thf(f1214,plain,
( ( ( $true
=> ( sK20 @ sK37 @ sK36 ) )
= $false )
| ~ spl0_25 ),
inference(backward_demodulation,[],[f1211,f1213]) ).
thf(f1213,plain,
( ( $true
= ( ( sK3 @ sK37 @ sK36 )
| ( sK5 @ sK37 @ sK36 ) ) )
| ~ spl0_25 ),
inference(binary_proxy_clausification,[],[f1211]) ).
thf(f1211,plain,
( ( ( ( ( sK3 @ sK37 @ sK36 )
| ( sK5 @ sK37 @ sK36 ) )
=> ( sK20 @ sK37 @ sK36 ) )
= $false )
| ~ spl0_25 ),
inference(beta_eta_normalization,[],[f1210]) ).
thf(f1210,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK36 )
| ( sK5 @ Y0 @ sK36 ) )
=> ( sK20 @ Y0 @ sK36 ) )
@ sK37 ) )
| ~ spl0_25 ),
inference(sigma_clausification,[],[f1207]) ).
thf(f1207,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK36 )
| ( sK5 @ Y0 @ sK36 ) )
=> ( sK20 @ Y0 @ sK36 ) ) )
= $false )
| ~ spl0_25 ),
inference(beta_eta_normalization,[],[f1205]) ).
thf(f1205,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) )
@ sK36 ) )
| ~ spl0_25 ),
inference(sigma_clausification,[],[f1181]) ).
thf(f1181,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1180]) ).
thf(f1180,plain,
( spl0_25
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f996,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK5 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) )
=> ( sK20 @ X1 @ X2 ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f995]) ).
thf(f995,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK20 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f986]) ).
thf(f986,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK20 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f985]) ).
thf(f985,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f981]) ).
thf(f981,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f980]) ).
thf(f980,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f973,f979]) ).
thf(f979,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y0 @ Y1 )
& ( sK20 @ Y1 @ Y2 ) )
=> ( sK20 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f973]) ).
thf(f973,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y0 @ Y1 )
& ( sK20 @ Y1 @ Y2 ) )
=> ( sK20 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f961]) ).
thf(f961,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y0 @ Y1 )
& ( sK20 @ Y1 @ Y2 ) )
=> ( sK20 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) )
=> ( sK20 @ sK17 @ sK19 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f960]) ).
thf(f960,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK19 ) )
@ sK20 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f959]) ).
thf(f959,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK19 ) ) )
= $false )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f958]) ).
thf(f958,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK19 ) ) ) ) )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f949,f957]) ).
thf(f957,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK17 @ sK18 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK18 @ sK19 ) ) ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f949]) ).
thf(f949,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK17 @ sK18 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK18 @ sK19 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK19 ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f948]) ).
thf(f948,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK17 @ sK18 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK18 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK17 @ Y0 ) ) ) )
@ sK19 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f945]) ).
thf(f945,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK17 @ sK18 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK18 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK17 @ Y0 ) ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f944]) ).
thf(f944,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK17 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK17 @ Y1 ) ) ) ) )
@ sK18 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f941]) ).
thf(f941,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK17 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK17 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f940]) ).
thf(f940,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) )
@ sK17 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f197]) ).
thf(f197,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f196,plain,
( spl0_7
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f1241,plain,
( ~ spl0_7
| ~ spl0_25
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f1240]) ).
thf(f1240,plain,
( $false
| ~ spl0_7
| ~ spl0_25
| ~ spl0_28 ),
inference(trivial_inequality_removal,[],[f1239]) ).
thf(f1239,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_25
| ~ spl0_28 ),
inference(boolean_simplification,[],[f1238]) ).
thf(f1238,plain,
( ( $true = ~ $true )
| ~ spl0_7
| ~ spl0_25
| ~ spl0_28 ),
inference(boolean_simplification,[],[f1236]) ).
thf(f1236,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK37 @ sK36 ) ) ) )
| ~ spl0_7
| ~ spl0_25
| ~ spl0_28 ),
inference(backward_demodulation,[],[f1223,f1234]) ).
thf(f1234,plain,
( ( $true
= ( sK5 @ sK37 @ sK36 ) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1233]) ).
thf(f1233,plain,
( spl0_28
<=> ( $true
= ( sK5 @ sK37 @ sK36 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
thf(f1235,plain,
( spl0_27
| spl0_28
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1226,f1180,f1233,f1230]) ).
thf(f1226,plain,
( ( ( sK3 @ sK37 @ sK36 )
= $true )
| ( $true
= ( sK5 @ sK37 @ sK36 ) )
| ~ spl0_25 ),
inference(binary_proxy_clausification,[],[f1213]) ).
thf(f1201,plain,
( ~ spl0_7
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1200]) ).
thf(f1200,plain,
( $false
| ~ spl0_7
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f1196]) ).
thf(f1196,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_26 ),
inference(superposition,[],[f1194,f1089]) ).
thf(f1089,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK20 @ X1 @ X2 )
& ( sK20 @ X2 @ Y0 ) )
=> ( sK20 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1088]) ).
thf(f1088,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ X1 @ Y0 )
& ( sK20 @ Y0 @ Y1 ) )
=> ( sK20 @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_7 ),
inference(pi_clausification,[],[f1084]) ).
thf(f1084,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ X1 @ Y0 )
& ( sK20 @ Y0 @ Y1 ) )
=> ( sK20 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1083]) ).
thf(f1083,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y0 @ Y1 )
& ( sK20 @ Y1 @ Y2 ) )
=> ( sK20 @ Y0 @ Y2 ) ) ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f979]) ).
thf(f1194,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK20 @ sK34 @ sK33 )
& ( sK20 @ sK33 @ Y0 ) )
=> ( sK20 @ sK34 @ Y0 ) ) ) )
| ~ spl0_26 ),
inference(beta_eta_normalization,[],[f1193]) ).
thf(f1193,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ Y0 @ sK33 )
& ( sK20 @ sK33 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) )
@ sK34 )
= $false )
| ~ spl0_26 ),
inference(sigma_clausification,[],[f1192]) ).
thf(f1192,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ Y0 @ sK33 )
& ( sK20 @ sK33 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_26 ),
inference(beta_eta_normalization,[],[f1188]) ).
thf(f1188,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) )
@ sK33 )
= $false )
| ~ spl0_26 ),
inference(sigma_clausification,[],[f1184]) ).
thf(f1184,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1183]) ).
thf(f1183,plain,
( spl0_26
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f1185,plain,
( spl0_25
| spl0_26
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f1176,f500,f1183,f1180]) ).
thf(f500,plain,
( spl0_13
<=> ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f1176,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1173]) ).
thf(f1173,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_13 ),
inference(not_proxy_clausification,[],[f501]) ).
thf(f501,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f500]) ).
thf(f1029,plain,
( ~ spl0_7
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f1028]) ).
thf(f1028,plain,
( $false
| ~ spl0_7
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f1027]) ).
thf(f1027,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_15 ),
inference(boolean_simplification,[],[f1026]) ).
thf(f1026,plain,
( ( $true = ~ $true )
| ~ spl0_7
| ~ spl0_15 ),
inference(backward_demodulation,[],[f1010,f951]) ).
thf(f951,plain,
( ( $true
= ( ( sK5 @ sK32 @ sK31 )
| ( sK3 @ sK32 @ sK31 ) ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f947]) ).
thf(f947,plain,
( ( ( ( ( sK5 @ sK32 @ sK31 )
| ( sK3 @ sK32 @ sK31 ) )
=> ( sK20 @ sK32 @ sK31 ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f946]) ).
thf(f946,plain,
( ( ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK31 )
| ( sK3 @ Y0 @ sK31 ) )
=> ( sK20 @ Y0 @ sK31 ) )
@ sK32 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f943]) ).
thf(f943,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK31 )
| ( sK3 @ Y0 @ sK31 ) )
=> ( sK20 @ Y0 @ sK31 ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f942]) ).
thf(f942,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) )
@ sK31 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f583]) ).
thf(f583,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f582]) ).
thf(f582,plain,
( spl0_15
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f1010,plain,
( ( ( ~ ( ( sK5 @ sK32 @ sK31 )
| ( sK3 @ sK32 @ sK31 ) ) )
= $true )
| ~ spl0_7
| ~ spl0_15 ),
inference(boolean_simplification,[],[f1003]) ).
thf(f1003,plain,
( ( $true
= ( ( ( sK5 @ sK32 @ sK31 )
| ( sK3 @ sK32 @ sK31 ) )
=> $false ) )
| ~ spl0_7
| ~ spl0_15 ),
inference(superposition,[],[f996,f950]) ).
thf(f950,plain,
( ( ( sK20 @ sK32 @ sK31 )
= $false )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f947]) ).
thf(f935,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f934]) ).
thf(f934,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f933]) ).
thf(f933,plain,
( ( $true = $false )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(boolean_simplification,[],[f932]) ).
thf(f932,plain,
( ( $true = ~ $true )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(boolean_simplification,[],[f931]) ).
thf(f931,plain,
( ( $true
= ( ~ ( ( sK5 @ sK29 @ sK30 )
| $true ) ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f927,f916]) ).
thf(f916,plain,
( ( $true
= ( sK3 @ sK29 @ sK30 ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f914]) ).
thf(f914,plain,
( ( ( ( sK3 @ sK29 @ sK30 )
=> ( sK14 @ sK29 @ sK30 ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f913]) ).
thf(f913,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK29 @ Y0 )
=> ( sK14 @ sK29 @ Y0 ) )
@ sK30 ) )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f909]) ).
thf(f909,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK29 @ Y0 )
=> ( sK14 @ sK29 @ Y0 ) ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f906]) ).
thf(f906,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) )
@ sK29 ) )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f698]) ).
thf(f698,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f697]) ).
thf(f697,plain,
( spl0_20
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f927,plain,
( ( $true
= ( ~ ( ( sK5 @ sK29 @ sK30 )
| ( sK3 @ sK29 @ sK30 ) ) ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(boolean_simplification,[],[f924]) ).
thf(f924,plain,
( ( $true
= ( ( ( sK5 @ sK29 @ sK30 )
| ( sK3 @ sK29 @ sK30 ) )
=> $false ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(superposition,[],[f752,f915]) ).
thf(f915,plain,
( ( ( sK14 @ sK29 @ sK30 )
= $false )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f914]) ).
thf(f752,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK5 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
=> ( sK14 @ X2 @ X1 ) )
= $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f751]) ).
thf(f751,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(pi_clausification,[],[f744]) ).
thf(f744,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f743]) ).
thf(f743,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(pi_clausification,[],[f732]) ).
thf(f732,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(boolean_simplification,[],[f731]) ).
thf(f731,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& $true )
= $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(backward_demodulation,[],[f719,f729]) ).
thf(f729,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f719]) ).
thf(f719,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f715]) ).
thf(f715,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK14 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_8
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f714]) ).
thf(f714,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ sK14 )
= $false )
| ~ spl0_8
| ~ spl0_9 ),
inference(sigma_clausification,[],[f706]) ).
thf(f706,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
= $false )
| ~ spl0_8
| ~ spl0_9 ),
inference(boolean_simplification,[],[f705]) ).
thf(f705,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
= $false )
| ~ spl0_8
| ~ spl0_9 ),
inference(boolean_simplification,[],[f704]) ).
thf(f704,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
= $false )
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f703,f240]) ).
thf(f240,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f239,plain,
( spl0_9
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f703,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f702]) ).
thf(f702,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
@ sK13 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f689]) ).
thf(f689,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f688]) ).
thf(f688,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK12 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f200]) ).
thf(f200,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f199,plain,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f900,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f899]) ).
thf(f899,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f898]) ).
thf(f898,plain,
( ( $true = $false )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_19 ),
inference(forward_demodulation,[],[f891,f745]) ).
thf(f745,plain,
( ( ( sK14 @ sK27 @ sK26 )
= $false )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f734]) ).
thf(f734,plain,
( ( ( ( ( sK14 @ sK25 @ sK26 )
& ( sK14 @ sK27 @ sK25 ) )
=> ( sK14 @ sK27 @ sK26 ) )
= $false )
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f733]) ).
thf(f733,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK14 @ sK25 @ sK26 )
& ( sK14 @ Y0 @ sK25 ) )
=> ( sK14 @ Y0 @ sK26 ) )
@ sK27 ) )
| ~ spl0_19 ),
inference(sigma_clausification,[],[f717]) ).
thf(f717,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ sK25 @ sK26 )
& ( sK14 @ Y0 @ sK25 ) )
=> ( sK14 @ Y0 @ sK26 ) ) ) )
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f716]) ).
thf(f716,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ sK25 @ Y0 )
& ( sK14 @ Y1 @ sK25 ) )
=> ( sK14 @ Y1 @ Y0 ) ) )
@ sK26 )
= $false )
| ~ spl0_19 ),
inference(sigma_clausification,[],[f711]) ).
thf(f711,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ sK25 @ Y0 )
& ( sK14 @ Y1 @ sK25 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f707]) ).
thf(f707,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y2 @ Y1 ) ) ) )
@ sK25 )
= $false )
| ~ spl0_19 ),
inference(sigma_clausification,[],[f695]) ).
thf(f695,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f694]) ).
thf(f694,plain,
( spl0_19
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f891,plain,
( ( ( sK14 @ sK27 @ sK26 )
= $true )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_19 ),
inference(boolean_simplification,[],[f890]) ).
thf(f890,plain,
( ( $true
= ( $true
=> ( sK14 @ sK27 @ sK26 ) ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_19 ),
inference(superposition,[],[f834,f767]) ).
thf(f767,plain,
( ( $true
= ( sK14 @ sK25 @ sK26 ) )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f746]) ).
thf(f746,plain,
( ( $true
= ( ( sK14 @ sK25 @ sK26 )
& ( sK14 @ sK27 @ sK25 ) ) )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f734]) ).
thf(f834,plain,
( ! [X0: a] :
( ( ( sK14 @ sK25 @ X0 )
=> ( sK14 @ sK27 @ X0 ) )
= $true )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_19 ),
inference(boolean_simplification,[],[f823]) ).
thf(f823,plain,
( ! [X0: a] :
( ( ( $true
& ( sK14 @ sK25 @ X0 ) )
=> ( sK14 @ sK27 @ X0 ) )
= $true )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_19 ),
inference(superposition,[],[f809,f769]) ).
thf(f769,plain,
( ( $true
= ( sK14 @ sK27 @ sK25 ) )
| ~ spl0_19 ),
inference(boolean_simplification,[],[f768]) ).
thf(f768,plain,
( ( $true
= ( $true
& ( sK14 @ sK27 @ sK25 ) ) )
| ~ spl0_19 ),
inference(backward_demodulation,[],[f746,f767]) ).
thf(f809,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK14 @ X3 @ X2 )
& ( sK14 @ X2 @ X1 ) )
=> ( sK14 @ X3 @ X1 ) )
= $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f808]) ).
thf(f808,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK14 @ Y0 @ X2 )
& ( sK14 @ X2 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) )
@ X3 ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(pi_clausification,[],[f805]) ).
thf(f805,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ Y0 @ X2 )
& ( sK14 @ X2 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) ) ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f804]) ).
thf(f804,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 @ Y0 )
& ( sK14 @ Y0 @ X1 ) )
=> ( sK14 @ Y1 @ X1 ) ) )
@ X2 ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(pi_clausification,[],[f793]) ).
thf(f793,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 @ Y0 )
& ( sK14 @ Y0 @ X1 ) )
=> ( sK14 @ Y1 @ X1 ) ) ) ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f792]) ).
thf(f792,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(pi_clausification,[],[f729]) ).
thf(f699,plain,
( spl0_19
| spl0_20
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f690,f368,f697,f694]) ).
thf(f368,plain,
( spl0_11
<=> ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f690,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f683]) ).
thf(f683,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_11 ),
inference(not_proxy_clausification,[],[f369]) ).
thf(f369,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f368]) ).
thf(f680,plain,
( ~ spl0_7
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f679]) ).
thf(f679,plain,
( $false
| ~ spl0_7
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f678]) ).
thf(f678,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_16 ),
inference(forward_demodulation,[],[f662,f599]) ).
thf(f599,plain,
( ( ( sK20 @ sK21 @ sK22 )
= $false )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f598]) ).
thf(f598,plain,
( ( ( ( ( sK20 @ sK23 @ sK22 )
& ( sK20 @ sK21 @ sK23 ) )
=> ( sK20 @ sK21 @ sK22 ) )
= $false )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f597]) ).
thf(f597,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK20 @ Y0 @ sK22 )
& ( sK20 @ sK21 @ Y0 ) )
=> ( sK20 @ sK21 @ sK22 ) )
@ sK23 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f596]) ).
thf(f596,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK20 @ Y0 @ sK22 )
& ( sK20 @ sK21 @ Y0 ) )
=> ( sK20 @ sK21 @ sK22 ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f595]) ).
thf(f595,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ sK21 @ Y1 ) )
=> ( sK20 @ sK21 @ Y0 ) ) )
@ sK22 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f594]) ).
thf(f594,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ sK21 @ Y1 ) )
=> ( sK20 @ sK21 @ Y0 ) ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f590]) ).
thf(f590,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
@ sK21 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f586]) ).
thf(f586,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f585]) ).
thf(f585,plain,
( spl0_16
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f662,plain,
( ( ( sK20 @ sK21 @ sK22 )
= $true )
| ~ spl0_7
| ~ spl0_16 ),
inference(boolean_simplification,[],[f659]) ).
thf(f659,plain,
( ( $true
= ( $true
=> ( sK20 @ sK21 @ sK22 ) ) )
| ~ spl0_7
| ~ spl0_16 ),
inference(superposition,[],[f630,f622]) ).
thf(f622,plain,
( ( $true
= ( sK20 @ sK21 @ sK24 ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f619]) ).
thf(f619,plain,
( ( ( ( sK20 @ sK24 @ sK22 )
& ( sK20 @ sK21 @ sK24 ) )
= $true )
| ~ spl0_16 ),
inference(not_proxy_clausification,[],[f608]) ).
thf(f608,plain,
( ( ( ~ ( ( sK20 @ sK24 @ sK22 )
& ( sK20 @ sK21 @ sK24 ) ) )
= $false )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f607]) ).
thf(f607,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK20 @ Y0 @ sK22 )
& ( sK20 @ sK21 @ Y0 ) )
@ sK24 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f604]) ).
thf(f604,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK20 @ Y0 @ sK22 )
& ( sK20 @ sK21 @ Y0 ) ) )
= $false )
| ~ spl0_16 ),
inference(boolean_simplification,[],[f602]) ).
thf(f602,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK20 @ Y0 @ sK22 )
& ( sK20 @ sK21 @ Y0 ) )
=> $false ) )
= $false )
| ~ spl0_16 ),
inference(backward_demodulation,[],[f596,f599]) ).
thf(f630,plain,
( ! [X0: a] :
( $true
= ( ( sK20 @ X0 @ sK24 )
=> ( sK20 @ X0 @ sK22 ) ) )
| ~ spl0_7
| ~ spl0_16 ),
inference(boolean_simplification,[],[f627]) ).
thf(f627,plain,
( ! [X0: a] :
( ( ( ( sK20 @ X0 @ sK24 )
& $true )
=> ( sK20 @ X0 @ sK22 ) )
= $true )
| ~ spl0_7
| ~ spl0_16 ),
inference(superposition,[],[f429,f625]) ).
thf(f625,plain,
( ( $true
= ( sK20 @ sK24 @ sK22 ) )
| ~ spl0_16 ),
inference(boolean_simplification,[],[f624]) ).
thf(f624,plain,
( ( $true
= ( ( sK20 @ sK24 @ sK22 )
& $true ) )
| ~ spl0_16 ),
inference(backward_demodulation,[],[f619,f622]) ).
thf(f429,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK20 @ X1 @ X2 )
& ( sK20 @ X2 @ X3 ) )
=> ( sK20 @ X1 @ X3 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f428]) ).
thf(f428,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK20 @ X1 @ X2 )
& ( sK20 @ X2 @ Y0 ) )
=> ( sK20 @ X1 @ Y0 ) )
@ X3 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f424]) ).
thf(f424,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK20 @ X1 @ X2 )
& ( sK20 @ X2 @ Y0 ) )
=> ( sK20 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f423]) ).
thf(f423,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ X1 @ Y0 )
& ( sK20 @ Y0 @ Y1 ) )
=> ( sK20 @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_7 ),
inference(pi_clausification,[],[f411]) ).
thf(f411,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ X1 @ Y0 )
& ( sK20 @ Y0 @ Y1 ) )
=> ( sK20 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f410]) ).
thf(f410,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y0 @ Y1 )
& ( sK20 @ Y1 @ Y2 ) )
=> ( sK20 @ Y0 @ Y2 ) ) ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f402]) ).
thf(f402,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y0 @ Y1 )
& ( sK20 @ Y1 @ Y2 ) )
=> ( sK20 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f401]) ).
thf(f401,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y0 @ Y1 )
& ( sK20 @ Y1 @ Y2 ) )
=> ( sK20 @ Y0 @ Y2 ) ) ) ) )
& $true )
= $true )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f392,f399]) ).
thf(f399,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f392]) ).
thf(f392,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y0 @ Y1 )
& ( sK20 @ Y1 @ Y2 ) )
=> ( sK20 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f390]) ).
thf(f390,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y0 @ Y1 )
& ( sK20 @ Y1 @ Y2 ) )
=> ( sK20 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) )
=> ( sK20 @ sK17 @ sK19 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f389]) ).
thf(f389,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK19 ) )
@ sK20 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f383]) ).
thf(f383,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK19 ) ) )
= $false )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f382]) ).
thf(f382,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK17 @ sK18 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK18 @ sK19 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK19 ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f381]) ).
thf(f381,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK17 @ sK18 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK18 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK17 @ Y0 ) ) ) )
@ sK19 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f380]) ).
thf(f380,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK17 @ sK18 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK18 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK17 @ Y0 ) ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f379]) ).
thf(f379,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK17 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK17 @ Y1 ) ) ) ) )
@ sK18 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f378]) ).
thf(f378,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK17 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK17 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f377]) ).
thf(f377,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) )
@ sK17 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f197]) ).
thf(f587,plain,
( spl0_15
| spl0_16
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f578,f503,f196,f585,f582]) ).
thf(f503,plain,
( spl0_14
<=> ( $false
= ( sK20 @ sK18 @ sK19 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f578,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_7
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f575]) ).
thf(f575,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_7
| ~ spl0_14 ),
inference(not_proxy_clausification,[],[f516]) ).
thf(f516,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_7
| ~ spl0_14 ),
inference(boolean_simplification,[],[f511]) ).
thf(f511,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_7
| ~ spl0_14 ),
inference(superposition,[],[f404,f504]) ).
thf(f504,plain,
( ( $false
= ( sK20 @ sK18 @ sK19 ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f503]) ).
thf(f404,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK18 @ sK19 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f403]) ).
thf(f403,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK18 @ sK19 ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[],[f398]) ).
thf(f398,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK18 @ sK19 ) ) ) )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f397]) ).
thf(f397,plain,
( ( $true
= ( $true
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK18 @ sK19 ) ) ) ) )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f384,f396]) ).
thf(f396,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK17 @ sK18 ) ) )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f384]) ).
thf(f384,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK17 @ sK18 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK18 @ sK19 ) ) ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f382]) ).
thf(f505,plain,
( spl0_13
| spl0_14
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f490,f196,f503,f500]) ).
thf(f490,plain,
( ( $false
= ( sK20 @ sK18 @ sK19 ) )
| ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f489]) ).
thf(f489,plain,
( ( $false
= ( sK20 @ sK18 @ sK19 ) )
| ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) )
=> $false ) )
| ~ spl0_7 ),
inference(superposition,[],[f454,f473]) ).
thf(f473,plain,
( ! [X0: a] :
( ( ( sK20 @ sK17 @ X0 )
= $false )
| ( ( sK20 @ X0 @ sK19 )
= $false ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f464]) ).
thf(f464,plain,
( ! [X0: a] :
( $false
= ( ( sK20 @ sK17 @ X0 )
& ( sK20 @ X0 @ sK19 ) ) )
| ~ spl0_7 ),
inference(not_proxy_clausification,[],[f444]) ).
thf(f444,plain,
( ! [X0: a] :
( ( ~ ( ( sK20 @ sK17 @ X0 )
& ( sK20 @ X0 @ sK19 ) ) )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f437]) ).
thf(f437,plain,
( ! [X0: a] :
( $true
= ( ( ( sK20 @ sK17 @ X0 )
& ( sK20 @ X0 @ sK19 ) )
=> $false ) )
| ~ spl0_7 ),
inference(superposition,[],[f429,f394]) ).
thf(f394,plain,
( ( $false
= ( sK20 @ sK17 @ sK19 ) )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f393]) ).
thf(f393,plain,
( ( ( $true
=> ( sK20 @ sK17 @ sK19 ) )
= $false )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f390,f392]) ).
thf(f454,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y0 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK17 @ sK18 ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f453]) ).
thf(f453,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK17 @ sK18 ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[],[f396]) ).
thf(f374,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f365,f239,f199,f368]) ).
thf(f365,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(boolean_simplification,[],[f363]) ).
thf(f363,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f355,f217]) ).
thf(f217,plain,
( ( ( sK14 @ sK12 @ sK13 )
= $false )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f216]) ).
thf(f216,plain,
( ( ( $true
=> ( sK14 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f213,f215]) ).
thf(f215,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f213]) ).
thf(f213,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK14 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f212]) ).
thf(f212,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ sK14 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f211]) ).
thf(f211,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
= $false )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f210]) ).
thf(f210,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f207,f209]) ).
thf(f209,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f207]) ).
thf(f207,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f206]) ).
thf(f206,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
@ sK13 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f205]) ).
thf(f205,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f204]) ).
thf(f204,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK12 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f200]) ).
thf(f355,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK12 @ sK13 ) )
= $true )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f354]) ).
thf(f354,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ X1 )
= $true )
| ~ spl0_9 ),
inference(pi_clausification,[],[f240]) ).
thf(f334,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f333]) ).
thf(f333,plain,
( $false
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f332]) ).
thf(f332,plain,
( ( $true = $false )
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f318,f287]) ).
thf(f287,plain,
( ( $false
= ( sK14 @ sK16 @ sK15 ) )
| ~ spl0_8
| ~ spl0_10 ),
inference(boolean_simplification,[],[f286]) ).
thf(f286,plain,
( ( $false
= ( $true
=> ( sK14 @ sK16 @ sK15 ) ) )
| ~ spl0_8
| ~ spl0_10 ),
inference(backward_demodulation,[],[f283,f285]) ).
thf(f285,plain,
( ( ( sK5 @ sK16 @ sK15 )
= $true )
| ~ spl0_8
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f283]) ).
thf(f283,plain,
( ( $false
= ( ( sK5 @ sK16 @ sK15 )
=> ( sK14 @ sK16 @ sK15 ) ) )
| ~ spl0_8
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f282]) ).
thf(f282,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK5 @ Y0 @ sK15 )
=> ( sK14 @ Y0 @ sK15 ) )
@ sK16 ) )
| ~ spl0_8
| ~ spl0_10 ),
inference(sigma_clausification,[],[f279]) ).
thf(f279,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 @ sK15 )
=> ( sK14 @ Y0 @ sK15 ) ) )
= $false )
| ~ spl0_8
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f277]) ).
thf(f277,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) )
@ sK15 ) )
| ~ spl0_8
| ~ spl0_10 ),
inference(sigma_clausification,[],[f274]) ).
thf(f274,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_8
| ~ spl0_10 ),
inference(not_proxy_clausification,[],[f271]) ).
thf(f271,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_8
| ~ spl0_10 ),
inference(boolean_simplification,[],[f270]) ).
thf(f270,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& $true ) ) )
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f269,f221]) ).
thf(f221,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f220]) ).
thf(f220,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f215,f219]) ).
thf(f219,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f215]) ).
thf(f269,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) ) ) ) )
= $true )
| ~ spl0_8
| ~ spl0_10 ),
inference(boolean_simplification,[],[f266]) ).
thf(f266,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y2 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y2 @ Y0 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f257,f217]) ).
thf(f257,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK12 @ sK13 ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f256]) ).
thf(f256,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ X1 )
= $true )
| ~ spl0_10 ),
inference(pi_clausification,[],[f243]) ).
thf(f243,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f242,plain,
( spl0_10
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f318,plain,
( ( $true
= ( sK14 @ sK16 @ sK15 ) )
| ~ spl0_8
| ~ spl0_10 ),
inference(boolean_simplification,[],[f317]) ).
thf(f317,plain,
( ( $true
= ( $true
=> ( sK14 @ sK16 @ sK15 ) ) )
| ~ spl0_8
| ~ spl0_10 ),
inference(boolean_simplification,[],[f316]) ).
thf(f316,plain,
( ( ( ( $true
| ( sK3 @ sK16 @ sK15 ) )
=> ( sK14 @ sK16 @ sK15 ) )
= $true )
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f302,f285]) ).
thf(f302,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK5 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
=> ( sK14 @ X2 @ X1 ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f301]) ).
thf(f301,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_8 ),
inference(pi_clausification,[],[f297]) ).
thf(f297,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f296]) ).
thf(f296,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[],[f219]) ).
thf(f244,plain,
( spl0_9
| spl0_10
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f237,f199,f242,f239]) ).
thf(f237,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f209]) ).
thf(f201,plain,
( spl0_7
| spl0_8
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f194,f29,f199,f196]) ).
thf(f29,plain,
( spl0_1
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f194,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f30]) ).
thf(f30,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f191,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f190]) ).
thf(f190,plain,
( $false
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f189,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[],[f188]) ).
thf(f188,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[],[f186]) ).
thf(f186,plain,
( ( $true
= ( ~ ( ( sK3 @ sK10 @ sK11 )
| $true ) ) )
| ~ spl0_4
| ~ spl0_6 ),
inference(backward_demodulation,[],[f169,f176]) ).
thf(f176,plain,
( ( $true
= ( sK5 @ sK10 @ sK11 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f175,plain,
( spl0_6
<=> ( $true
= ( sK5 @ sK10 @ sK11 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f169,plain,
( ( $true
= ( ~ ( ( sK3 @ sK10 @ sK11 )
| ( sK5 @ sK10 @ sK11 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f163]) ).
thf(f163,plain,
( ( $true
= ( ( ( sK3 @ sK10 @ sK11 )
| ( sK5 @ sK10 @ sK11 ) )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[],[f55,f159]) ).
thf(f159,plain,
( ( ( sK6 @ sK10 @ sK11 )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f158]) ).
thf(f158,plain,
( ( ( $true
=> ( sK6 @ sK10 @ sK11 ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f155,f157]) ).
thf(f157,plain,
( ( ( ( sK5 @ sK10 @ sK11 )
| ( sK3 @ sK10 @ sK11 ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f155]) ).
thf(f155,plain,
( ( ( ( ( sK5 @ sK10 @ sK11 )
| ( sK3 @ sK10 @ sK11 ) )
=> ( sK6 @ sK10 @ sK11 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f154]) ).
thf(f154,plain,
( ( ( ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK6 @ sK10 @ Y0 ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f151]) ).
thf(f151,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK6 @ sK10 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f149]) ).
thf(f149,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f122]) ).
thf(f122,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f121]) ).
thf(f121,plain,
( spl0_4
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f55,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK3 @ X1 @ X2 )
| ( sK5 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f54]) ).
thf(f54,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f53]) ).
thf(f53,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f52]) ).
thf(f52,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f51]) ).
thf(f51,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f50]) ).
thf(f50,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(backward_demodulation,[],[f38,f49]) ).
thf(f49,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f38]) ).
thf(f38,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f26]) ).
thf(f26,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK4 @ sK2 ) ) ),
inference(beta_eta_normalization,[],[f25]) ).
thf(f25,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f19]) ).
thf(f19,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK4 @ sK2 ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK4 @ sK2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
| ( sK3 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK2 ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
| ( sK3 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ sK2 ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ sK2 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a,X2: a > a > $o,X3: a] :
( ~ ( ( ! [X4: a,X5: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a,X9: a] :
( ( ( X6 @ X7 @ X9 )
& ( X6 @ X9 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
& ! [X10: a,X11: a] :
( ( X2 @ X11 @ X10 )
=> ( X6 @ X11 @ X10 ) ) )
=> ( X6 @ X5 @ X4 ) )
| ! [X12: a > a > $o] :
( ( ! [X13: a,X14: a,X15: a] :
( ( ( X12 @ X14 @ X15 )
& ( X12 @ X13 @ X14 ) )
=> ( X12 @ X13 @ X15 ) )
& ! [X16: a,X17: a] :
( ( X0 @ X16 @ X17 )
=> ( X12 @ X16 @ X17 ) ) )
=> ( X12 @ X5 @ X4 ) ) )
=> ! [X18: a > a > $o] :
( ( ! [X19: a,X20: a,X21: a] :
( ( ( X18 @ X20 @ X21 )
& ( X18 @ X19 @ X20 ) )
=> ( X18 @ X19 @ X21 ) )
& ! [X22: a,X23: a] :
( ( ( X2 @ X22 @ X23 )
| ( X0 @ X22 @ X23 ) )
=> ( X18 @ X22 @ X23 ) ) )
=> ( X18 @ X5 @ X4 ) ) )
& ! [X24: a,X25: a,X26: a] :
( ( ! [X27: a > a > $o] :
( ( ! [X28: a,X29: a] :
( ( ( X2 @ X28 @ X29 )
| ( X0 @ X28 @ X29 ) )
=> ( X27 @ X28 @ X29 ) )
& ! [X30: a,X31: a,X32: a] :
( ( ( X27 @ X32 @ X30 )
& ( X27 @ X30 @ X31 ) )
=> ( X27 @ X32 @ X31 ) ) )
=> ( X27 @ X25 @ X24 ) )
& ! [X33: a > a > $o] :
( ( ! [X34: a,X35: a,X36: a] :
( ( ( X33 @ X36 @ X34 )
& ( X33 @ X35 @ X36 ) )
=> ( X33 @ X35 @ X34 ) )
& ! [X37: a,X38: a] :
( ( ( X0 @ X37 @ X38 )
| ( X2 @ X37 @ X38 ) )
=> ( X33 @ X37 @ X38 ) ) )
=> ( X33 @ X26 @ X25 ) ) )
=> ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a] :
( ( ( X2 @ X41 @ X40 )
| ( X0 @ X41 @ X40 ) )
=> ( X39 @ X41 @ X40 ) )
& ! [X42: a,X43: a,X44: a] :
( ( ( X39 @ X43 @ X42 )
& ( X39 @ X44 @ X43 ) )
=> ( X39 @ X44 @ X42 ) ) )
=> ( X39 @ X26 @ X24 ) ) ) )
=> ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a,X48: a] :
( ( ( X45 @ X46 @ X47 )
& ( X45 @ X48 @ X46 ) )
=> ( X45 @ X48 @ X47 ) )
& ! [X49: a,X50: a] :
( ( ( X2 @ X50 @ X49 )
| ( X0 @ X50 @ X49 ) )
=> ( X45 @ X50 @ X49 ) ) )
=> ( X45 @ X1 @ X3 ) ) )
| ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a] :
( ( ( X0 @ X53 @ X52 )
| ( X2 @ X53 @ X52 ) )
=> ( X51 @ X53 @ X52 ) )
& ! [X54: a,X55: a,X56: a] :
( ( ( X51 @ X55 @ X54 )
& ( X51 @ X56 @ X55 ) )
=> ( X51 @ X56 @ X54 ) ) )
=> ( X51 @ X1 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X2: a,X1: a > a > $o,X3: a] :
( ~ ( ( ! [X6: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X7: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ! [X7: a,X6: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X10: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) )
& ! [X4: a > a > $o] :
( ( ! [X10: a,X8: a,X9: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X10: a,X9: a,X8: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X7 ) ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X6: a,X7: a,X5: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
| ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X2: a,X1: a > a > $o,X3: a] :
( ~ ( ( ! [X6: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X7: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ! [X7: a,X6: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X10: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) )
& ! [X4: a > a > $o] :
( ( ! [X10: a,X8: a,X9: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X10: a,X9: a,X8: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X7 ) ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X6: a,X7: a,X5: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
| ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Dy95EzKudm/Vampire---4.8_11174',cTHM250G_pme) ).
thf(f183,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f182]) ).
thf(f182,plain,
( $false
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f181]) ).
thf(f181,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[],[f180]) ).
thf(f180,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[],[f178]) ).
thf(f178,plain,
( ( $true
= ( ~ ( $true
| ( sK5 @ sK10 @ sK11 ) ) ) )
| ~ spl0_4
| ~ spl0_5 ),
inference(backward_demodulation,[],[f169,f173]) ).
thf(f173,plain,
( ( $true
= ( sK3 @ sK10 @ sK11 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f172,plain,
( spl0_5
<=> ( $true
= ( sK3 @ sK10 @ sK11 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f177,plain,
( spl0_5
| spl0_6
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f170,f121,f175,f172]) ).
thf(f170,plain,
( ( $true
= ( sK3 @ sK10 @ sK11 ) )
| ( $true
= ( sK5 @ sK10 @ sK11 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f157]) ).
thf(f142,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f141]) ).
thf(f141,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f137]) ).
thf(f137,plain,
( ( $true = $false )
| ~ spl0_3 ),
inference(superposition,[],[f134,f85]) ).
thf(f85,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ X2 @ X3 ) )
=> ( sK6 @ X1 @ X3 ) )
= $true ),
inference(beta_eta_normalization,[],[f84]) ).
thf(f84,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ X2 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f83]) ).
thf(f83,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ X2 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f82]) ).
thf(f82,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f75]) ).
thf(f75,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ X1 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f74]) ).
thf(f74,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f49]) ).
thf(f134,plain,
( ( ( ( ( sK6 @ sK7 @ sK9 )
& ( sK6 @ sK9 @ sK8 ) )
=> ( sK6 @ sK7 @ sK8 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f133]) ).
thf(f133,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK7 @ Y0 )
& ( sK6 @ Y0 @ sK8 ) )
=> ( sK6 @ sK7 @ sK8 ) )
@ sK9 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f132]) ).
thf(f132,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK7 @ Y0 )
& ( sK6 @ Y0 @ sK8 ) )
=> ( sK6 @ sK7 @ sK8 ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f131]) ).
thf(f131,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK7 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ sK7 @ Y0 ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f128]) ).
thf(f128,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK7 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ sK7 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f126]) ).
thf(f126,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
@ sK7 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f119]) ).
thf(f119,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f118,plain,
( spl0_3
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f123,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f114,f32,f121,f118]) ).
thf(f32,plain,
( spl0_2
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f114,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f104]) ).
thf(f104,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f47]) ).
thf(f47,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f46]) ).
thf(f46,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[],[f44,f37]) ).
thf(f37,plain,
( ( sK6 @ sK4 @ sK2 )
= $false ),
inference(binary_proxy_clausification,[],[f26]) ).
thf(f44,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK4 @ sK2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f43]) ).
thf(f43,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f33]) ).
thf(f33,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f34,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f27,f32,f29]) ).
thf(f27,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f22]) ).
thf(f22,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( $false
= ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) ) ) ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( $false
= ( $false
| ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) ) ) ),
inference(backward_demodulation,[],[f17,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV157^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.30 % Computer : n020.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 11:57:01 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 This is a TH0_THM_NEQ_NAR problem
% 0.10/0.31 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.Dy95EzKudm/Vampire---4.8_11174
% 0.15/0.33 % (11289)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.33 % (11285)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on Vampire---4 for (2999ds/27Mi)
% 0.15/0.33 % (11288)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.33 % (11284)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.15/0.33 % (11283)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.33 % (11290)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.33 % (11287)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.33 % (11284)Instruction limit reached!
% 0.15/0.33 % (11284)------------------------------
% 0.15/0.33 % (11284)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (11284)Termination reason: Unknown
% 0.15/0.33 % (11284)Termination phase: Naming
% 0.15/0.33
% 0.15/0.33 % (11284)Memory used [KB]: 1023
% 0.15/0.33 % (11284)Time elapsed: 0.003 s
% 0.15/0.33 % (11284)Instructions burned: 4 (million)
% 0.15/0.33 % (11284)------------------------------
% 0.15/0.33 % (11284)------------------------------
% 0.15/0.33 % (11287)Instruction limit reached!
% 0.15/0.33 % (11287)------------------------------
% 0.15/0.33 % (11287)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (11287)Termination reason: Unknown
% 0.15/0.33 % (11287)Termination phase: shuffling
% 0.15/0.33
% 0.15/0.33 % (11287)Memory used [KB]: 1023
% 0.15/0.33 % (11287)Time elapsed: 0.002 s
% 0.15/0.33 % (11287)Instructions burned: 2 (million)
% 0.15/0.33 % (11287)------------------------------
% 0.15/0.33 % (11287)------------------------------
% 0.15/0.33 % (11290)Instruction limit reached!
% 0.15/0.33 % (11290)------------------------------
% 0.15/0.33 % (11290)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (11290)Termination reason: Unknown
% 0.15/0.33 % (11290)Termination phase: Naming
% 0.15/0.33
% 0.15/0.33 % (11290)Memory used [KB]: 1023
% 0.15/0.33 % (11290)Time elapsed: 0.003 s
% 0.15/0.33 % (11290)Instructions burned: 3 (million)
% 0.15/0.33 % (11290)------------------------------
% 0.15/0.33 % (11290)------------------------------
% 0.15/0.33 % (11286)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.33 % (11286)Instruction limit reached!
% 0.15/0.33 % (11286)------------------------------
% 0.15/0.33 % (11286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (11286)Termination reason: Unknown
% 0.15/0.33 % (11286)Termination phase: Naming
% 0.15/0.33
% 0.15/0.33 % (11286)Memory used [KB]: 1023
% 0.15/0.33 % (11286)Time elapsed: 0.003 s
% 0.15/0.33 % (11286)Instructions burned: 3 (million)
% 0.15/0.33 % (11286)------------------------------
% 0.15/0.33 % (11286)------------------------------
% 0.15/0.33 % (11289)Instruction limit reached!
% 0.15/0.33 % (11289)------------------------------
% 0.15/0.33 % (11289)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (11289)Termination reason: Unknown
% 0.15/0.33 % (11289)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (11289)Memory used [KB]: 5628
% 0.15/0.33 % (11289)Time elapsed: 0.010 s
% 0.15/0.33 % (11289)Instructions burned: 18 (million)
% 0.15/0.33 % (11289)------------------------------
% 0.15/0.33 % (11289)------------------------------
% 0.15/0.34 % (11285)Instruction limit reached!
% 0.15/0.34 % (11285)------------------------------
% 0.15/0.34 % (11285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (11285)Termination reason: Unknown
% 0.15/0.34 % (11285)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (11285)Memory used [KB]: 5756
% 0.15/0.34 % (11285)Time elapsed: 0.015 s
% 0.15/0.34 % (11285)Instructions burned: 27 (million)
% 0.15/0.34 % (11285)------------------------------
% 0.15/0.34 % (11285)------------------------------
% 0.15/0.34 % (11291)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (2999ds/37Mi)
% 0.15/0.34 % (11292)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.15/0.34 % (11293)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.34 % (11293)Instruction limit reached!
% 0.15/0.34 % (11293)------------------------------
% 0.15/0.34 % (11293)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (11293)Termination reason: Unknown
% 0.15/0.34 % (11293)Termination phase: Naming
% 0.15/0.34
% 0.15/0.34 % (11293)Memory used [KB]: 1023
% 0.15/0.34 % (11293)Time elapsed: 0.003 s
% 0.15/0.34 % (11293)Instructions burned: 4 (million)
% 0.15/0.34 % (11293)------------------------------
% 0.15/0.34 % (11293)------------------------------
% 0.15/0.34 % (11294)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.15/0.35 % (11292)Instruction limit reached!
% 0.15/0.35 % (11292)------------------------------
% 0.15/0.35 % (11292)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (11292)Termination reason: Unknown
% 0.15/0.35 % (11292)Termination phase: Saturation
% 0.15/0.35
% 0.15/0.35 % (11292)Memory used [KB]: 5756
% 0.15/0.35 % (11292)Time elapsed: 0.009 s
% 0.15/0.35 % (11292)Instructions burned: 15 (million)
% 0.15/0.35 % (11292)------------------------------
% 0.15/0.35 % (11292)------------------------------
% 0.15/0.35 % (11295)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.15/0.35 % (11296)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.15/0.35 % (11295)Instruction limit reached!
% 0.15/0.35 % (11295)------------------------------
% 0.15/0.35 % (11295)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (11295)Termination reason: Unknown
% 0.15/0.35 % (11295)Termination phase: Property scanning
% 0.15/0.35
% 0.15/0.35 % (11295)Memory used [KB]: 1151
% 0.15/0.35 % (11295)Time elapsed: 0.005 s
% 0.15/0.35 % (11295)Instructions burned: 9 (million)
% 0.15/0.35 % (11295)------------------------------
% 0.15/0.35 % (11295)------------------------------
% 0.15/0.36 % (11291)Instruction limit reached!
% 0.15/0.36 % (11291)------------------------------
% 0.15/0.36 % (11291)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (11291)Termination reason: Unknown
% 0.15/0.36 % (11291)Termination phase: Saturation
% 0.15/0.36
% 0.15/0.36 % (11291)Memory used [KB]: 5628
% 0.15/0.36 % (11291)Time elapsed: 0.017 s
% 0.15/0.36 % (11291)Instructions burned: 39 (million)
% 0.15/0.36 % (11291)------------------------------
% 0.15/0.36 % (11291)------------------------------
% 0.15/0.36 % (11297)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.36 % (11297)Instruction limit reached!
% 0.15/0.36 % (11297)------------------------------
% 0.15/0.36 % (11297)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (11297)Termination reason: Unknown
% 0.15/0.36 % (11297)Termination phase: Naming
% 0.15/0.36
% 0.15/0.36 % (11297)Memory used [KB]: 1023
% 0.15/0.36 % (11297)Time elapsed: 0.003 s
% 0.15/0.36 % (11297)Instructions burned: 4 (million)
% 0.15/0.36 % (11297)------------------------------
% 0.15/0.36 % (11297)------------------------------
% 0.15/0.36 % (11296)Instruction limit reached!
% 0.15/0.36 % (11296)------------------------------
% 0.15/0.36 % (11296)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (11296)Termination reason: Unknown
% 0.15/0.36 % (11296)Termination phase: Property scanning
% 0.15/0.36
% 0.15/0.36 % (11296)Memory used [KB]: 1151
% 0.15/0.36 % (11296)Time elapsed: 0.009 s
% 0.15/0.36 % (11296)Instructions burned: 18 (million)
% 0.15/0.36 % (11296)------------------------------
% 0.15/0.36 % (11296)------------------------------
% 0.15/0.36 % (11298)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.36 % (11298)Instruction limit reached!
% 0.15/0.36 % (11298)------------------------------
% 0.15/0.36 % (11298)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (11298)Termination reason: Unknown
% 0.15/0.36 % (11298)Termination phase: Naming
% 0.15/0.36
% 0.15/0.36 % (11298)Memory used [KB]: 1023
% 0.15/0.36 % (11298)Time elapsed: 0.003 s
% 0.15/0.36 % (11298)Instructions burned: 4 (million)
% 0.15/0.36 % (11298)------------------------------
% 0.15/0.36 % (11298)------------------------------
% 0.15/0.37 % (11299)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.15/0.37 % (11300)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.37 % (11300)Instruction limit reached!
% 0.15/0.37 % (11300)------------------------------
% 0.15/0.37 % (11300)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (11300)Termination reason: Unknown
% 0.15/0.37 % (11300)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (11300)Memory used [KB]: 1023
% 0.15/0.37 % (11300)Time elapsed: 0.003 s
% 0.15/0.37 % (11300)Instructions burned: 4 (million)
% 0.15/0.37 % (11300)------------------------------
% 0.15/0.37 % (11300)------------------------------
% 0.15/0.37 % (11299)Instruction limit reached!
% 0.15/0.37 % (11299)------------------------------
% 0.15/0.37 % (11299)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (11299)Termination reason: Unknown
% 0.15/0.37 % (11299)Termination phase: Property scanning
% 0.15/0.37
% 0.15/0.37 % (11299)Memory used [KB]: 1151
% 0.15/0.37 % (11299)Time elapsed: 0.005 s
% 0.15/0.37 % (11299)Instructions burned: 8 (million)
% 0.15/0.37 % (11299)------------------------------
% 0.15/0.37 % (11299)------------------------------
% 0.15/0.37 % (11301)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.15/0.37 % (11302)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.37 % (11301)Instruction limit reached!
% 0.15/0.37 % (11301)------------------------------
% 0.15/0.37 % (11301)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (11301)Termination reason: Unknown
% 0.15/0.37 % (11301)Termination phase: Preprocessing 3
% 0.15/0.37
% 0.15/0.37 % (11301)Memory used [KB]: 1023
% 0.15/0.37 % (11301)Time elapsed: 0.003 s
% 0.15/0.37 % (11301)Instructions burned: 4 (million)
% 0.15/0.37 % (11301)------------------------------
% 0.15/0.37 % (11301)------------------------------
% 0.15/0.38 % (11303)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.15/0.38 % (11302)Instruction limit reached!
% 0.15/0.38 % (11302)------------------------------
% 0.15/0.38 % (11302)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (11302)Termination reason: Unknown
% 0.15/0.38 % (11302)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (11302)Memory used [KB]: 5628
% 0.15/0.38 % (11302)Time elapsed: 0.010 s
% 0.15/0.38 % (11302)Instructions burned: 19 (million)
% 0.15/0.38 % (11302)------------------------------
% 0.15/0.38 % (11302)------------------------------
% 0.15/0.38 % (11304)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.15/0.38 % (11305)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on Vampire---4 for (2999ds/902Mi)
% 0.15/0.39 % (11304)Instruction limit reached!
% 0.15/0.39 % (11304)------------------------------
% 0.15/0.39 % (11304)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (11304)Termination reason: Unknown
% 0.15/0.39 % (11304)Termination phase: Preprocessing 3
% 0.15/0.39
% 0.15/0.39 % (11304)Memory used [KB]: 1023
% 0.15/0.39 % (11304)Time elapsed: 0.004 s
% 0.15/0.39 % (11304)Instructions burned: 6 (million)
% 0.15/0.39 % (11304)------------------------------
% 0.15/0.39 % (11304)------------------------------
% 0.15/0.39 % (11306)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (2999ds/21Mi)
% 0.15/0.39 % (11307)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.15/0.40 % (11307)Instruction limit reached!
% 0.15/0.40 % (11307)------------------------------
% 0.15/0.40 % (11307)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (11307)Termination reason: Unknown
% 0.15/0.40 % (11307)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (11307)Memory used [KB]: 1023
% 0.15/0.40 % (11307)Time elapsed: 0.004 s
% 0.15/0.40 % (11307)Instructions burned: 7 (million)
% 0.15/0.40 % (11307)------------------------------
% 0.15/0.40 % (11307)------------------------------
% 0.15/0.40 % (11306)Instruction limit reached!
% 0.15/0.40 % (11306)------------------------------
% 0.15/0.40 % (11306)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (11306)Termination reason: Unknown
% 0.15/0.40 % (11306)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (11306)Memory used [KB]: 5756
% 0.15/0.40 % (11306)Time elapsed: 0.012 s
% 0.15/0.40 % (11306)Instructions burned: 22 (million)
% 0.15/0.40 % (11306)------------------------------
% 0.15/0.40 % (11306)------------------------------
% 0.15/0.40 % (11308)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.15/0.40 % (11308)Instruction limit reached!
% 0.15/0.40 % (11308)------------------------------
% 0.15/0.40 % (11308)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (11308)Termination reason: Unknown
% 0.15/0.40 % (11308)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (11308)Memory used [KB]: 1023
% 0.15/0.40 % (11308)Time elapsed: 0.004 s
% 0.15/0.40 % (11308)Instructions burned: 6 (million)
% 0.15/0.40 % (11308)------------------------------
% 0.15/0.40 % (11308)------------------------------
% 0.15/0.41 % (11283)Instruction limit reached!
% 0.15/0.41 % (11283)------------------------------
% 0.15/0.41 % (11283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (11283)Termination reason: Unknown
% 0.15/0.41 % (11283)Termination phase: Saturation
% 0.15/0.41
% 0.15/0.41 % (11283)Memory used [KB]: 6268
% 0.15/0.41 % (11283)Time elapsed: 0.083 s
% 0.15/0.41 % (11283)Instructions burned: 183 (million)
% 0.15/0.41 % (11283)------------------------------
% 0.15/0.41 % (11283)------------------------------
% 0.15/0.41 % (11309)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.15/0.41 % (11310)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on Vampire---4 for (2999ds/779Mi)
% 0.15/0.41 % (11311)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (2999ds/19Mi)
% 0.15/0.42 % (11312)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2999ds/879Mi)
% 0.15/0.42 % (11311)Instruction limit reached!
% 0.15/0.42 % (11311)------------------------------
% 0.15/0.42 % (11311)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (11311)Termination reason: Unknown
% 0.15/0.42 % (11311)Termination phase: Saturation
% 0.15/0.42
% 0.15/0.42 % (11311)Memory used [KB]: 5500
% 0.15/0.42 % (11311)Time elapsed: 0.009 s
% 0.15/0.42 % (11311)Instructions burned: 20 (million)
% 0.15/0.42 % (11311)------------------------------
% 0.15/0.42 % (11311)------------------------------
% 0.15/0.43 % (11313)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.15/0.44 % (11313)Instruction limit reached!
% 0.15/0.44 % (11313)------------------------------
% 0.15/0.44 % (11313)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.44 % (11313)Termination reason: Unknown
% 0.15/0.44 % (11313)Termination phase: Saturation
% 0.15/0.44
% 0.15/0.44 % (11313)Memory used [KB]: 5756
% 0.15/0.44 % (11313)Time elapsed: 0.011 s
% 0.15/0.44 % (11313)Instructions burned: 18 (million)
% 0.15/0.44 % (11313)------------------------------
% 0.15/0.44 % (11313)------------------------------
% 0.15/0.46 % (11314)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.15/0.46 % (11314)Instruction limit reached!
% 0.15/0.46 % (11314)------------------------------
% 0.15/0.46 % (11314)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.46 % (11314)Termination reason: Unknown
% 0.15/0.46 % (11314)Termination phase: Preprocessing 2
% 0.15/0.46
% 0.15/0.46 % (11314)Memory used [KB]: 1023
% 0.15/0.46 % (11314)Time elapsed: 0.003 s
% 0.15/0.46 % (11314)Instructions burned: 3 (million)
% 0.15/0.46 % (11314)------------------------------
% 0.15/0.46 % (11314)------------------------------
% 0.15/0.46 % (11288)Instruction limit reached!
% 0.15/0.46 % (11288)------------------------------
% 0.15/0.46 % (11288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.46 % (11288)Termination reason: Unknown
% 0.15/0.46 % (11288)Termination phase: Saturation
% 0.15/0.46
% 0.15/0.46 % (11288)Memory used [KB]: 6396
% 0.15/0.46 % (11288)Time elapsed: 0.137 s
% 0.15/0.46 % (11288)Instructions burned: 275 (million)
% 0.15/0.46 % (11288)------------------------------
% 0.15/0.46 % (11288)------------------------------
% 0.15/0.47 % (11315)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2998ds/30Mi)
% 0.15/0.47 % (11316)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2998ds/127Mi)
% 0.15/0.49 % (11315)Instruction limit reached!
% 0.15/0.49 % (11315)------------------------------
% 0.15/0.49 % (11315)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.49 % (11315)Termination reason: Unknown
% 0.15/0.49 % (11315)Termination phase: Saturation
% 0.15/0.49
% 0.15/0.49 % (11315)Memory used [KB]: 5756
% 0.15/0.49 % (11315)Time elapsed: 0.016 s
% 0.15/0.49 % (11315)Instructions burned: 30 (million)
% 0.15/0.49 % (11315)------------------------------
% 0.15/0.49 % (11315)------------------------------
% 0.15/0.49 % (11294)First to succeed.
% 0.15/0.50 % (11317)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on Vampire---4 for (2998ds/100Mi)
% 0.15/0.52 % (11294)Refutation found. Thanks to Tanya!
% 0.15/0.52 % SZS status Theorem for Vampire---4
% 0.15/0.52 % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.52 % (11294)------------------------------
% 0.15/0.52 % (11294)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.52 % (11294)Termination reason: Refutation
% 0.15/0.52
% 0.15/0.52 % (11294)Memory used [KB]: 7036
% 0.15/0.52 % (11294)Time elapsed: 0.175 s
% 0.15/0.52 % (11294)Instructions burned: 299 (million)
% 0.15/0.52 % (11294)------------------------------
% 0.15/0.52 % (11294)------------------------------
% 0.15/0.52 % (11282)Success in time 0.203 s
% 0.15/0.52 % Vampire---4.8 exiting
%------------------------------------------------------------------------------