TSTP Solution File: SEV040^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV040^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 16:01:34 EDT 2024
% Result : Theorem 0.18s 0.54s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 24
% Syntax : Number of formulae : 393 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 4583 ( 662 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 10609 ( 658 ~; 622 |; 941 &;6243 @)
% ( 23 <=>; 715 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 448 ( 448 >; 0 *; 0 +; 0 <<)
% Number of symbols : 97 ( 93 usr; 69 con; 0-2 aty)
% (1407 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1727 (1522 ^ 205 !; 0 ?;1727 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: a > a > $o ).
thf(func_def_19,type,
sK3: a > a > $o ).
thf(func_def_20,type,
sK4: a > a > $o ).
thf(func_def_21,type,
sK5: a > a > $o ).
thf(func_def_22,type,
sK6: a > a > $o ).
thf(func_def_23,type,
sK7: a > a > $o ).
thf(func_def_24,type,
sK8: a > a > $o ).
thf(func_def_25,type,
sK9: a > a > $o ).
thf(func_def_26,type,
sK10: a > a > $o ).
thf(func_def_27,type,
sK11: a > a > $o ).
thf(func_def_28,type,
sK12: a ).
thf(func_def_29,type,
sK13: a ).
thf(func_def_30,type,
sK14: a ).
thf(func_def_31,type,
sK15: a ).
thf(func_def_32,type,
sK16: a ).
thf(func_def_33,type,
sK17: a ).
thf(func_def_34,type,
sK18: a ).
thf(func_def_35,type,
sK19: a ).
thf(func_def_36,type,
sK20: a ).
thf(func_def_37,type,
sK21: a ).
thf(func_def_38,type,
sK22: a ).
thf(func_def_39,type,
sK23: a ).
thf(func_def_40,type,
sK24: a ).
thf(func_def_41,type,
sK25: a ).
thf(func_def_42,type,
sK26: a ).
thf(func_def_43,type,
sK27: a ).
thf(func_def_44,type,
sK28: a ).
thf(func_def_45,type,
sK29: a ).
thf(func_def_46,type,
sK30: a ).
thf(func_def_47,type,
sK31: a > a > $o ).
thf(func_def_48,type,
sK32: a > a > $o ).
thf(func_def_49,type,
sK33: a ).
thf(func_def_50,type,
sK34: a ).
thf(func_def_51,type,
sK35: a ).
thf(func_def_52,type,
sK36: a ).
thf(func_def_53,type,
sK37: a ).
thf(func_def_54,type,
sK38: a ).
thf(func_def_55,type,
sK39: a ).
thf(func_def_56,type,
sK40: a ).
thf(func_def_57,type,
sK41: a ).
thf(func_def_58,type,
sK42: a ).
thf(func_def_59,type,
sK43: a > a > $o ).
thf(func_def_60,type,
sK44: a > a > $o ).
thf(func_def_61,type,
sK45: a ).
thf(func_def_62,type,
sK46: a > a > $o ).
thf(func_def_63,type,
sK47: a ).
thf(func_def_64,type,
sK48: a ).
thf(func_def_65,type,
sK49: a ).
thf(func_def_66,type,
sK50: a > a > $o ).
thf(func_def_67,type,
sK51: a ).
thf(func_def_68,type,
sK52: a > a > $o ).
thf(func_def_69,type,
sK53: a > a > $o ).
thf(func_def_70,type,
sK54: a ).
thf(func_def_71,type,
sK55: a > a > $o ).
thf(func_def_72,type,
sK56: a ).
thf(func_def_73,type,
sK57: a ).
thf(func_def_74,type,
sK58: a > a > $o ).
thf(func_def_75,type,
sK59: a > a > $o ).
thf(func_def_76,type,
sK60: a ).
thf(func_def_77,type,
sK61: a > a > $o ).
thf(func_def_78,type,
sK62: a ).
thf(func_def_79,type,
sK63: a ).
thf(func_def_80,type,
sK64: a > a > $o ).
thf(func_def_81,type,
sK65: a > a > $o ).
thf(func_def_82,type,
sK66: a > a > $o ).
thf(func_def_83,type,
sK67: a ).
thf(func_def_84,type,
sK68: a > a > $o ).
thf(func_def_85,type,
sK69: a ).
thf(func_def_86,type,
sK70: a ).
thf(f1973,plain,
$false,
inference(avatar_sat_refutation,[],[f17,f157,f190,f217,f229,f313,f322,f332,f381,f615,f741,f849,f935,f942,f946,f1156,f1187,f1197,f1318,f1399,f1405,f1413,f1628,f1815,f1965,f1972]) ).
thf(f1972,plain,
( ~ spl0_2
| ~ spl0_48
| ~ spl0_56 ),
inference(avatar_contradiction_clause,[],[f1971]) ).
thf(f1971,plain,
( $false
| ~ spl0_2
| ~ spl0_48
| ~ spl0_56 ),
inference(trivial_inequality_removal,[],[f1970]) ).
thf(f1970,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_48
| ~ spl0_56 ),
inference(boolean_simplification,[],[f1969]) ).
thf(f1969,plain,
( ( $true
= ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_48
| ~ spl0_56 ),
inference(forward_demodulation,[],[f1640,f1193]) ).
thf(f1193,plain,
( ( $false
= ( sK31 = sK32 ) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1192]) ).
thf(f1192,plain,
( spl0_56
<=> ( $false
= ( sK31 = sK32 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
thf(f1640,plain,
( ( ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_48 ),
inference(binary_proxy_clausification,[],[f1634]) ).
thf(f1634,plain,
( ( $false
!= ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_48 ),
inference(boolean_simplification,[],[f1633]) ).
thf(f1633,plain,
( ( ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
!= ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_48 ),
inference(forward_demodulation,[],[f908,f1152]) ).
thf(f1152,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 ) ) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1151]) ).
thf(f1151,plain,
( spl0_48
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
thf(f908,plain,
( ( ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) )
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f907]) ).
thf(f907,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y1 @ Y2 )
=> ( sK31 @ Y2 @ Y1 ) ) ) )
& ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y3 @ Y2 )
& ( sK31 @ Y1 @ Y3 ) )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) )
@ sK32 )
!= ( ^ [Y0: a > a > $o] :
( ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y2 @ Y1 )
=> ( sK31 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y3 @ Y2 ) )
=> ( sK31 @ Y3 @ Y1 ) ) ) ) ) )
@ sK32 ) )
| ~ spl0_2 ),
inference(negative_extensionality,[],[f906]) ).
thf(f906,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y2 @ Y1 )
=> ( sK31 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y3 @ Y2 ) )
=> ( sK31 @ Y3 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y1 @ Y2 )
=> ( sK31 @ Y2 @ Y1 ) ) ) )
& ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y3 @ Y2 )
& ( sK31 @ Y1 @ Y3 ) )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f905]) ).
thf(f905,plain,
( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
@ sK31 )
!= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y2 ) ) ) ) ) )
@ sK31 ) )
| ~ spl0_2 ),
inference(negative_extensionality,[],[f904]) ).
thf(f904,plain,
( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y2 ) ) ) ) ) ) )
!= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[],[f16]) ).
thf(f16,plain,
( ( $false
= ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y2 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f15,plain,
( spl0_2
<=> ( $false
= ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y2 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f1965,plain,
( ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(avatar_contradiction_clause,[],[f1964]) ).
thf(f1964,plain,
( $false
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(trivial_inequality_removal,[],[f1963]) ).
thf(f1963,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(forward_demodulation,[],[f1955,f1922]) ).
thf(f1922,plain,
( ( $false
= ( sK31 @ sK70 @ sK67 ) )
| ~ spl0_76 ),
inference(boolean_simplification,[],[f1921]) ).
thf(f1921,plain,
( ( $false
= ( $true
=> ( sK31 @ sK70 @ sK67 ) ) )
| ~ spl0_76 ),
inference(backward_demodulation,[],[f1917,f1920]) ).
thf(f1920,plain,
( ( ( sK31 @ sK67 @ sK70 )
= $true )
| ~ spl0_76 ),
inference(binary_proxy_clausification,[],[f1917]) ).
thf(f1917,plain,
( ( $false
= ( ( sK31 @ sK67 @ sK70 )
=> ( sK31 @ sK70 @ sK67 ) ) )
| ~ spl0_76 ),
inference(beta_eta_normalization,[],[f1916]) ).
thf(f1916,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK31 @ sK67 @ Y0 )
=> ( sK31 @ Y0 @ sK67 ) )
@ sK70 ) )
| ~ spl0_76 ),
inference(sigma_clausification,[],[f1855]) ).
thf(f1855,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK31 @ sK67 @ Y0 )
=> ( sK31 @ Y0 @ sK67 ) ) ) )
| ~ spl0_76 ),
inference(beta_eta_normalization,[],[f1854]) ).
thf(f1854,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) )
@ sK67 )
= $false )
| ~ spl0_76 ),
inference(sigma_clausification,[],[f1814]) ).
thf(f1814,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1813]) ).
thf(f1813,plain,
( spl0_76
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
thf(f1955,plain,
( ( $true
= ( sK31 @ sK70 @ sK67 ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(boolean_simplification,[],[f1954]) ).
thf(f1954,plain,
( ( ( $true
=> ( sK31 @ sK70 @ sK67 ) )
= $true )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(superposition,[],[f1948,f1920]) ).
thf(f1948,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK31 @ X2 @ X1 )
=> ( sK31 @ X1 @ X2 ) ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(beta_eta_normalization,[],[f1947]) ).
thf(f1947,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK31 @ Y0 @ X1 )
=> ( sK31 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(pi_clausification,[],[f1936]) ).
thf(f1936,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK31 @ Y0 @ X1 )
=> ( sK31 @ X1 @ Y0 ) ) ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(beta_eta_normalization,[],[f1935]) ).
thf(f1935,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(pi_clausification,[],[f1856]) ).
thf(f1856,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(binary_proxy_clausification,[],[f1845]) ).
thf(f1845,plain,
( ( $false
!= ( ( sK31 = sK64 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(boolean_simplification,[],[f1844]) ).
thf(f1844,plain,
( ( ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
!= ( ( sK31 = sK64 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(boolean_simplification,[],[f1843]) ).
thf(f1843,plain,
( ( ( ( sK31 = sK64 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
!= ( $false
& ( sK31 = sK64 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48
| ~ spl0_76 ),
inference(forward_demodulation,[],[f1654,f1814]) ).
thf(f1654,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK64 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
!= ( ( sK31 = sK64 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48 ),
inference(beta_eta_normalization,[],[f1653]) ).
thf(f1653,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y2 @ Y1 )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) )
@ sK64 )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y1 @ Y2 )
=> ( sK31 @ Y2 @ Y1 ) ) ) )
& ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y3 @ Y2 )
& ( sK31 @ Y1 @ Y3 ) )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) )
@ sK64 ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48 ),
inference(negative_extensionality,[],[f1649]) ).
thf(f1649,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y2 @ Y1 )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y1 @ Y2 )
=> ( sK31 @ Y2 @ Y1 ) ) ) )
& ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y3 @ Y2 )
& ( sK31 @ Y1 @ Y3 ) )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48 ),
inference(boolean_simplification,[],[f1646]) ).
thf(f1646,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y2 @ Y1 )
=> ( sK31 @ Y1 @ Y2 ) ) ) )
& $true ) )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y1 @ Y2 )
=> ( sK31 @ Y2 @ Y1 ) ) ) )
& ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y3 @ Y2 )
& ( sK31 @ Y1 @ Y3 ) )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48 ),
inference(backward_demodulation,[],[f906,f1644]) ).
thf(f1644,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48 ),
inference(boolean_simplification,[],[f1641]) ).
thf(f1641,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_40
| ~ spl0_48 ),
inference(backward_demodulation,[],[f941,f1640]) ).
thf(f941,plain,
( ( ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f940]) ).
thf(f940,plain,
( spl0_40
<=> ( ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
thf(f1815,plain,
( spl0_76
| spl0_56
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f1811,f1151,f1192,f1813]) ).
thf(f1811,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( sK31 = sK32 ) )
| ~ spl0_48 ),
inference(binary_proxy_clausification,[],[f1152]) ).
thf(f1628,plain,
( ~ spl0_2
| ~ spl0_49 ),
inference(avatar_contradiction_clause,[],[f1627]) ).
thf(f1627,plain,
( $false
| ~ spl0_2
| ~ spl0_49 ),
inference(trivial_inequality_removal,[],[f1626]) ).
thf(f1626,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1625,f1450]) ).
thf(f1450,plain,
( ( ( sK31 @ sK54 @ sK56 )
= $false )
| ~ spl0_49 ),
inference(binary_proxy_clausification,[],[f1447]) ).
thf(f1447,plain,
( ( $false
= ( ( ( sK31 @ sK57 @ sK56 )
& ( sK31 @ sK54 @ sK57 ) )
=> ( sK31 @ sK54 @ sK56 ) ) )
| ~ spl0_49 ),
inference(beta_eta_normalization,[],[f1446]) ).
thf(f1446,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK31 @ Y0 @ sK56 )
& ( sK31 @ sK54 @ Y0 ) )
=> ( sK31 @ sK54 @ sK56 ) )
@ sK57 ) )
| ~ spl0_49 ),
inference(sigma_clausification,[],[f1433]) ).
thf(f1433,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK31 @ Y0 @ sK56 )
& ( sK31 @ sK54 @ Y0 ) )
=> ( sK31 @ sK54 @ sK56 ) ) ) )
| ~ spl0_49 ),
inference(beta_eta_normalization,[],[f1432]) ).
thf(f1432,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ sK54 @ Y1 ) )
=> ( sK31 @ sK54 @ Y0 ) ) )
@ sK56 ) )
| ~ spl0_49 ),
inference(sigma_clausification,[],[f1429]) ).
thf(f1429,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ sK54 @ Y1 ) )
=> ( sK31 @ sK54 @ Y0 ) ) ) ) )
| ~ spl0_49 ),
inference(beta_eta_normalization,[],[f1428]) ).
thf(f1428,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
@ sK54 ) )
| ~ spl0_49 ),
inference(sigma_clausification,[],[f1155]) ).
thf(f1155,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f1154]) ).
thf(f1154,plain,
( spl0_49
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
thf(f1625,plain,
( ( ( sK31 @ sK54 @ sK56 )
= $true )
| ~ spl0_2
| ~ spl0_49 ),
inference(boolean_simplification,[],[f1624]) ).
thf(f1624,plain,
( ( $true
= ( $true
=> ( sK31 @ sK54 @ sK56 ) ) )
| ~ spl0_2
| ~ spl0_49 ),
inference(superposition,[],[f1556,f1451]) ).
thf(f1451,plain,
( ( $true
= ( ( sK31 @ sK57 @ sK56 )
& ( sK31 @ sK54 @ sK57 ) ) )
| ~ spl0_49 ),
inference(binary_proxy_clausification,[],[f1447]) ).
thf(f1556,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK31 @ X2 @ X1 )
& ( sK31 @ X3 @ X2 ) )
=> ( sK31 @ X3 @ X1 ) ) )
| ~ spl0_2
| ~ spl0_49 ),
inference(beta_eta_normalization,[],[f1555]) ).
thf(f1555,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK31 @ X2 @ X1 )
& ( sK31 @ Y0 @ X2 ) )
=> ( sK31 @ Y0 @ X1 ) )
@ X3 )
= $true )
| ~ spl0_2
| ~ spl0_49 ),
inference(pi_clausification,[],[f1551]) ).
thf(f1551,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK31 @ X2 @ X1 )
& ( sK31 @ Y0 @ X2 ) )
=> ( sK31 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_2
| ~ spl0_49 ),
inference(beta_eta_normalization,[],[f1550]) ).
thf(f1550,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK31 @ Y0 @ X1 )
& ( sK31 @ Y1 @ Y0 ) )
=> ( sK31 @ Y1 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_2
| ~ spl0_49 ),
inference(pi_clausification,[],[f1545]) ).
thf(f1545,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK31 @ Y0 @ X1 )
& ( sK31 @ Y1 @ Y0 ) )
=> ( sK31 @ Y1 @ X1 ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_49 ),
inference(beta_eta_normalization,[],[f1544]) ).
thf(f1544,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_2
| ~ spl0_49 ),
inference(pi_clausification,[],[f1434]) ).
thf(f1434,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_49 ),
inference(binary_proxy_clausification,[],[f1419]) ).
thf(f1419,plain,
( ( $false
!= ( ( sK31 = sK50 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_49 ),
inference(boolean_simplification,[],[f1416]) ).
thf(f1416,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK50 )
& $false )
!= ( ( sK31 = sK50 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_49 ),
inference(backward_demodulation,[],[f1327,f1155]) ).
thf(f1327,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK50 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
!= ( ( sK31 = sK50 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1326]) ).
thf(f1326,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y2 @ Y1 )
=> ( sK31 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y3 @ Y2 ) )
=> ( sK31 @ Y3 @ Y1 ) ) ) ) ) )
@ sK50 )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y1 @ Y2 )
=> ( sK31 @ Y2 @ Y1 ) ) ) )
& ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y3 @ Y2 )
& ( sK31 @ Y1 @ Y3 ) )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) )
@ sK50 ) )
| ~ spl0_2 ),
inference(negative_extensionality,[],[f906]) ).
thf(f1413,plain,
( ~ spl0_39
| ~ spl0_48 ),
inference(avatar_contradiction_clause,[],[f1412]) ).
thf(f1412,plain,
( $false
| ~ spl0_39
| ~ spl0_48 ),
inference(trivial_inequality_removal,[],[f1411]) ).
thf(f1411,plain,
( ( $false = $true )
| ~ spl0_39
| ~ spl0_48 ),
inference(boolean_simplification,[],[f1410]) ).
thf(f1410,plain,
( ( ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_39
| ~ spl0_48 ),
inference(forward_demodulation,[],[f938,f1152]) ).
thf(f938,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f937]) ).
thf(f937,plain,
( spl0_39
<=> ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
thf(f1405,plain,
( ~ spl0_39
| ~ spl0_56 ),
inference(avatar_contradiction_clause,[],[f1404]) ).
thf(f1404,plain,
( $false
| ~ spl0_39
| ~ spl0_56 ),
inference(trivial_inequality_removal,[],[f1403]) ).
thf(f1403,plain,
( ( $false = $true )
| ~ spl0_39
| ~ spl0_56 ),
inference(boolean_simplification,[],[f1402]) ).
thf(f1402,plain,
( ( ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_39
| ~ spl0_56 ),
inference(boolean_simplification,[],[f1401]) ).
thf(f1401,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_39
| ~ spl0_56 ),
inference(backward_demodulation,[],[f938,f1193]) ).
thf(f1399,plain,
( ~ spl0_2
| ~ spl0_57 ),
inference(avatar_contradiction_clause,[],[f1398]) ).
thf(f1398,plain,
( $false
| ~ spl0_2
| ~ spl0_57 ),
inference(trivial_inequality_removal,[],[f1397]) ).
thf(f1397,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1389,f1344]) ).
thf(f1344,plain,
( ( $false
= ( sK31 @ sK49 @ sK51 ) )
| ~ spl0_57 ),
inference(boolean_simplification,[],[f1343]) ).
thf(f1343,plain,
( ( $false
= ( $true
=> ( sK31 @ sK49 @ sK51 ) ) )
| ~ spl0_57 ),
inference(backward_demodulation,[],[f1332,f1342]) ).
thf(f1342,plain,
( ( ( sK31 @ sK51 @ sK49 )
= $true )
| ~ spl0_57 ),
inference(binary_proxy_clausification,[],[f1332]) ).
thf(f1332,plain,
( ( ( ( sK31 @ sK51 @ sK49 )
=> ( sK31 @ sK49 @ sK51 ) )
= $false )
| ~ spl0_57 ),
inference(beta_eta_normalization,[],[f1331]) ).
thf(f1331,plain,
( ( ( ^ [Y0: a] :
( ( sK31 @ Y0 @ sK49 )
=> ( sK31 @ sK49 @ Y0 ) )
@ sK51 )
= $false )
| ~ spl0_57 ),
inference(sigma_clausification,[],[f1325]) ).
thf(f1325,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK31 @ Y0 @ sK49 )
=> ( sK31 @ sK49 @ Y0 ) ) ) )
| ~ spl0_57 ),
inference(beta_eta_normalization,[],[f1324]) ).
thf(f1324,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) )
@ sK49 )
= $false )
| ~ spl0_57 ),
inference(sigma_clausification,[],[f1196]) ).
thf(f1196,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1195]) ).
thf(f1195,plain,
( spl0_57
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
thf(f1389,plain,
( ( $true
= ( sK31 @ sK49 @ sK51 ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(boolean_simplification,[],[f1387]) ).
thf(f1387,plain,
( ( $true
= ( $true
=> ( sK31 @ sK49 @ sK51 ) ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(superposition,[],[f1381,f1342]) ).
thf(f1381,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK31 @ X1 @ X2 )
=> ( sK31 @ X2 @ X1 ) ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(beta_eta_normalization,[],[f1380]) ).
thf(f1380,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK31 @ X1 @ Y0 )
=> ( sK31 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_2
| ~ spl0_57 ),
inference(pi_clausification,[],[f1378]) ).
thf(f1378,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK31 @ X1 @ Y0 )
=> ( sK31 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_2
| ~ spl0_57 ),
inference(beta_eta_normalization,[],[f1377]) ).
thf(f1377,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(pi_clausification,[],[f1354]) ).
thf(f1354,plain,
( ( $false
!= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(boolean_simplification,[],[f1353]) ).
thf(f1353,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(backward_demodulation,[],[f1339,f1350]) ).
thf(f1350,plain,
( ( ( sK31 = sK50 )
= $true )
| ~ spl0_2
| ~ spl0_57 ),
inference(binary_proxy_clausification,[],[f1339]) ).
thf(f1339,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK50 ) ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(boolean_simplification,[],[f1335]) ).
thf(f1335,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK50 )
& $true ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(backward_demodulation,[],[f1330,f1333]) ).
thf(f1333,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_57 ),
inference(binary_proxy_clausification,[],[f1330]) ).
thf(f1330,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK50 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(boolean_simplification,[],[f1329]) ).
thf(f1329,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK50 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
!= ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(boolean_simplification,[],[f1328]) ).
thf(f1328,plain,
( ( ( ( sK31 = sK50 )
& $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) )
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK50 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1327,f1196]) ).
thf(f1318,plain,
( ~ spl0_2
| ~ spl0_55 ),
inference(avatar_contradiction_clause,[],[f1317]) ).
thf(f1317,plain,
( $false
| ~ spl0_2
| ~ spl0_55 ),
inference(trivial_inequality_removal,[],[f1316]) ).
thf(f1316,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_55 ),
inference(forward_demodulation,[],[f1311,f1315]) ).
thf(f1315,plain,
( ( ( sK31 @ sK48 @ sK45 )
= $false )
| ~ spl0_55 ),
inference(boolean_simplification,[],[f1314]) ).
thf(f1314,plain,
( ( $false
= ( $true
=> ( sK31 @ sK48 @ sK45 ) ) )
| ~ spl0_55 ),
inference(backward_demodulation,[],[f1300,f1304]) ).
thf(f1304,plain,
( ( $true
= ( ( sK31 @ sK47 @ sK45 )
& ( sK31 @ sK48 @ sK47 ) ) )
| ~ spl0_55 ),
inference(binary_proxy_clausification,[],[f1300]) ).
thf(f1300,plain,
( ( ( ( ( sK31 @ sK47 @ sK45 )
& ( sK31 @ sK48 @ sK47 ) )
=> ( sK31 @ sK48 @ sK45 ) )
= $false )
| ~ spl0_55 ),
inference(beta_eta_normalization,[],[f1299]) ).
thf(f1299,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK31 @ sK47 @ sK45 )
& ( sK31 @ Y0 @ sK47 ) )
=> ( sK31 @ Y0 @ sK45 ) )
@ sK48 ) )
| ~ spl0_55 ),
inference(sigma_clausification,[],[f1296]) ).
thf(f1296,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK31 @ sK47 @ sK45 )
& ( sK31 @ Y0 @ sK47 ) )
=> ( sK31 @ Y0 @ sK45 ) ) ) )
| ~ spl0_55 ),
inference(beta_eta_normalization,[],[f1295]) ).
thf(f1295,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK31 @ Y0 @ sK45 )
& ( sK31 @ Y1 @ Y0 ) )
=> ( sK31 @ Y1 @ sK45 ) ) )
@ sK47 ) )
| ~ spl0_55 ),
inference(sigma_clausification,[],[f1252]) ).
thf(f1252,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK31 @ Y0 @ sK45 )
& ( sK31 @ Y1 @ Y0 ) )
=> ( sK31 @ Y1 @ sK45 ) ) ) ) )
| ~ spl0_55 ),
inference(beta_eta_normalization,[],[f1251]) ).
thf(f1251,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) )
@ sK45 )
= $false )
| ~ spl0_55 ),
inference(sigma_clausification,[],[f1186]) ).
thf(f1186,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1185]) ).
thf(f1185,plain,
( spl0_55
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
thf(f1311,plain,
( ( ( sK31 @ sK48 @ sK45 )
= $true )
| ~ spl0_2
| ~ spl0_55 ),
inference(trivial_inequality_removal,[],[f1310]) ).
thf(f1310,plain,
( ( $false = $true )
| ( ( sK31 @ sK48 @ sK45 )
= $true )
| ~ spl0_2
| ~ spl0_55 ),
inference(boolean_simplification,[],[f1305]) ).
thf(f1305,plain,
( ( $false
= ( $false
=> ( sK31 @ sK48 @ sK45 ) ) )
| ( ( sK31 @ sK48 @ sK45 )
= $true )
| ~ spl0_2
| ~ spl0_55 ),
inference(superposition,[],[f1300,f1247]) ).
thf(f1247,plain,
( ! [X2: a,X3: a,X1: a] :
( ( $false
= ( ( sK31 @ X3 @ X2 )
& ( sK31 @ X1 @ X3 ) ) )
| ( $true
= ( sK31 @ X1 @ X2 ) ) )
| ~ spl0_2
| ~ spl0_55 ),
inference(binary_proxy_clausification,[],[f1246]) ).
thf(f1246,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK31 @ X3 @ X2 )
& ( sK31 @ X1 @ X3 ) )
=> ( sK31 @ X1 @ X2 ) )
= $true )
| ~ spl0_2
| ~ spl0_55 ),
inference(beta_eta_normalization,[],[f1245]) ).
thf(f1245,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK31 @ Y0 @ X2 )
& ( sK31 @ X1 @ Y0 ) )
=> ( sK31 @ X1 @ X2 ) )
@ X3 ) )
| ~ spl0_2
| ~ spl0_55 ),
inference(pi_clausification,[],[f1244]) ).
thf(f1244,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK31 @ Y0 @ X2 )
& ( sK31 @ X1 @ Y0 ) )
=> ( sK31 @ X1 @ X2 ) ) ) )
| ~ spl0_2
| ~ spl0_55 ),
inference(beta_eta_normalization,[],[f1243]) ).
thf(f1243,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ X1 @ Y1 ) )
=> ( sK31 @ X1 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_2
| ~ spl0_55 ),
inference(pi_clausification,[],[f1239]) ).
thf(f1239,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ X1 @ Y1 ) )
=> ( sK31 @ X1 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_55 ),
inference(beta_eta_normalization,[],[f1238]) ).
thf(f1238,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_55 ),
inference(pi_clausification,[],[f1214]) ).
thf(f1214,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
!= $false )
| ~ spl0_2
| ~ spl0_55 ),
inference(boolean_simplification,[],[f1213]) ).
thf(f1213,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
!= $false )
| ~ spl0_2
| ~ spl0_55 ),
inference(backward_demodulation,[],[f1203,f1212]) ).
thf(f1212,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK43 ) )
= $true )
| ~ spl0_2
| ~ spl0_55 ),
inference(binary_proxy_clausification,[],[f1203]) ).
thf(f1203,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK43 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_55 ),
inference(beta_eta_normalization,[],[f1202]) ).
thf(f1202,plain,
( ( ( ^ [Y0: a > a > $o] : $false
@ sK43 )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y1 @ Y2 )
=> ( sK31 @ Y2 @ Y1 ) ) ) )
& ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y3 @ Y2 )
& ( sK31 @ Y1 @ Y3 ) )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) )
@ sK43 ) )
| ~ spl0_2
| ~ spl0_55 ),
inference(negative_extensionality,[],[f1200]) ).
thf(f1200,plain,
( ( ( ^ [Y0: a > a > $o] : $false )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y1 @ Y2 )
=> ( sK31 @ Y2 @ Y1 ) ) ) )
& ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y3 @ Y2 )
& ( sK31 @ Y1 @ Y3 ) )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_55 ),
inference(boolean_simplification,[],[f1199]) ).
thf(f1199,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y2 @ Y1 )
=> ( sK31 @ Y1 @ Y2 ) ) ) )
& $false ) )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK31 @ Y1 @ Y2 )
=> ( sK31 @ Y2 @ Y1 ) ) ) )
& ( sK31 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK31 @ Y3 @ Y2 )
& ( sK31 @ Y1 @ Y3 ) )
=> ( sK31 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_55 ),
inference(backward_demodulation,[],[f906,f1186]) ).
thf(f1197,plain,
( spl0_56
| spl0_57
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f1190,f1182,f1195,f1192]) ).
thf(f1182,plain,
( spl0_54
<=> ( $false
= ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
thf(f1190,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( sK31 = sK32 ) )
| ~ spl0_54 ),
inference(binary_proxy_clausification,[],[f1183]) ).
thf(f1183,plain,
( ( $false
= ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1182]) ).
thf(f1187,plain,
( spl0_54
| spl0_55
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1180,f933,f1185,f1182]) ).
thf(f933,plain,
( spl0_38
<=> ( $false
= ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
thf(f1180,plain,
( ( $false
= ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) )
| ~ spl0_38 ),
inference(binary_proxy_clausification,[],[f934]) ).
thf(f934,plain,
( ( $false
= ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f933]) ).
thf(f1156,plain,
( spl0_48
| spl0_49
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f1149,f930,f1154,f1151]) ).
thf(f930,plain,
( spl0_37
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
thf(f1149,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 ) ) )
| ~ spl0_37 ),
inference(binary_proxy_clausification,[],[f931]) ).
thf(f931,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f930]) ).
thf(f946,plain,
( ~ spl0_38
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f945]) ).
thf(f945,plain,
( $false
| ~ spl0_38
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f944]) ).
thf(f944,plain,
( ( $false = $true )
| ~ spl0_38
| ~ spl0_40 ),
inference(backward_demodulation,[],[f941,f934]) ).
thf(f942,plain,
( spl0_39
| spl0_40
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f927,f15,f940,f937]) ).
thf(f927,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f908]) ).
thf(f935,plain,
( spl0_37
| spl0_38
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f928,f15,f933,f930]) ).
thf(f928,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y0 @ Y1 )
=> ( sK31 @ Y1 @ Y0 ) ) ) )
& ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( sK31 = sK32 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK31 @ Y1 @ Y0 )
=> ( sK31 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y1 @ Y0 )
& ( sK31 @ Y2 @ Y1 ) )
=> ( sK31 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f908]) ).
thf(f849,plain,
( ~ spl0_15
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f848]) ).
thf(f848,plain,
( $false
| ~ spl0_15
| ~ spl0_17
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f847]) ).
thf(f847,plain,
( ( $false = $true )
| ~ spl0_15
| ~ spl0_17
| ~ spl0_24 ),
inference(backward_demodulation,[],[f839,f845]) ).
thf(f845,plain,
( ( ( sK9 = sK7 )
= $false )
| ~ spl0_15
| ~ spl0_17
| ~ spl0_24 ),
inference(backward_demodulation,[],[f331,f842]) ).
thf(f842,plain,
( ( sK7 = sK8 )
| ~ spl0_15
| ~ spl0_17 ),
inference(equality_proxy_clausification,[],[f820]) ).
thf(f820,plain,
( ( $true
= ( sK8 = sK7 ) )
| ~ spl0_15
| ~ spl0_17 ),
inference(binary_proxy_clausification,[],[f807]) ).
thf(f807,plain,
( ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 ) )
= $true )
| ~ spl0_15
| ~ spl0_17 ),
inference(boolean_simplification,[],[f806]) ).
thf(f806,plain,
( ( $true
= ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& $true ) )
| ~ spl0_15
| ~ spl0_17 ),
inference(backward_demodulation,[],[f775,f804]) ).
thf(f804,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_17 ),
inference(binary_proxy_clausification,[],[f775]) ).
thf(f775,plain,
( ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_17 ),
inference(binary_proxy_clausification,[],[f756]) ).
thf(f756,plain,
( ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_17 ),
inference(boolean_simplification,[],[f755]) ).
thf(f755,plain,
( ( $true
= ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& $true ) )
| ~ spl0_15
| ~ spl0_17 ),
inference(backward_demodulation,[],[f749,f753]) ).
thf(f753,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_17 ),
inference(binary_proxy_clausification,[],[f749]) ).
thf(f749,plain,
( ( $true
= ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_17 ),
inference(not_proxy_clausification,[],[f744]) ).
thf(f744,plain,
( ( $false
= ( ~ ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_17 ),
inference(boolean_simplification,[],[f743]) ).
thf(f743,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_15
| ~ spl0_17 ),
inference(boolean_simplification,[],[f742]) ).
thf(f742,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
=> ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_17 ),
inference(backward_demodulation,[],[f663,f186]) ).
thf(f186,plain,
( ( $false
= ( ( sK9 = sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f185,plain,
( spl0_17
<=> ( $false
= ( ( sK9 = sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f663,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
=> ( ( sK9 = sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f662]) ).
thf(f662,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK7 @ Y1 @ Y2 )
=> ( sK7 @ Y2 @ Y1 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK7 @ Y3 @ Y1 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( ( Y0 = sK8 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
@ sK9 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f657]) ).
thf(f657,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK7 @ Y1 @ Y2 )
=> ( sK7 @ Y2 @ Y1 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK7 @ Y3 @ Y1 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( ( Y0 = sK8 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f656]) ).
thf(f656,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( Y1 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK7 @ Y2 @ Y3 )
=> ( sK7 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK7 @ Y4 @ Y2 )
& ( sK7 @ Y2 @ Y3 ) )
=> ( sK7 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f655]) ).
thf(f655,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( Y1 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK7 @ Y2 @ Y3 )
=> ( sK7 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK7 @ Y4 @ Y2 )
& ( sK7 @ Y2 @ Y3 ) )
=> ( sK7 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f654]) ).
thf(f654,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f153]) ).
thf(f153,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f152]) ).
thf(f152,plain,
( spl0_15
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f331,plain,
( ( $false
= ( sK9 = sK8 ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f330]) ).
thf(f330,plain,
( spl0_24
<=> ( $false
= ( sK9 = sK8 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f839,plain,
( ( ( sK9 = sK7 )
= $true )
| ~ spl0_15
| ~ spl0_17 ),
inference(binary_proxy_clausification,[],[f823]) ).
thf(f823,plain,
( ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_17 ),
inference(boolean_simplification,[],[f822]) ).
thf(f822,plain,
( ( $true
= ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_15
| ~ spl0_17 ),
inference(backward_demodulation,[],[f807,f820]) ).
thf(f741,plain,
( ~ spl0_15
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f740]) ).
thf(f740,plain,
( $false
| ~ spl0_15
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f739]) ).
thf(f739,plain,
( ( $false = $true )
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f732,f642]) ).
thf(f642,plain,
( ( $false
= ( sK9 @ sK24 @ sK23 ) )
| ~ spl0_18 ),
inference(boolean_simplification,[],[f641]) ).
thf(f641,plain,
( ( $false
= ( $true
=> ( sK9 @ sK24 @ sK23 ) ) )
| ~ spl0_18 ),
inference(backward_demodulation,[],[f634,f640]) ).
thf(f640,plain,
( ( ( ( sK9 @ sK24 @ sK25 )
& ( sK9 @ sK25 @ sK23 ) )
= $true )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f634]) ).
thf(f634,plain,
( ( $false
= ( ( ( sK9 @ sK24 @ sK25 )
& ( sK9 @ sK25 @ sK23 ) )
=> ( sK9 @ sK24 @ sK23 ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f633]) ).
thf(f633,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK9 @ sK24 @ Y0 )
& ( sK9 @ Y0 @ sK23 ) )
=> ( sK9 @ sK24 @ sK23 ) )
@ sK25 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[],[f629]) ).
thf(f629,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ sK24 @ Y0 )
& ( sK9 @ Y0 @ sK23 ) )
=> ( sK9 @ sK24 @ sK23 ) ) )
= $false )
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f628]) ).
thf(f628,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ sK23 ) )
=> ( sK9 @ Y0 @ sK23 ) ) )
@ sK24 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[],[f621]) ).
thf(f621,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ sK23 ) )
=> ( sK9 @ Y0 @ sK23 ) ) ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f620]) ).
thf(f620,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) )
@ sK23 )
= $false )
| ~ spl0_18 ),
inference(sigma_clausification,[],[f189]) ).
thf(f189,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f188,plain,
( spl0_18
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f732,plain,
( ( $true
= ( sK9 @ sK24 @ sK23 ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(boolean_simplification,[],[f730]) ).
thf(f730,plain,
( ( $true
= ( $true
=> ( sK9 @ sK24 @ sK23 ) ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f719,f651]) ).
thf(f651,plain,
( ( ( sK9 @ sK24 @ sK26 )
= $true )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f647]) ).
thf(f647,plain,
( ( $true
= ( ( sK9 @ sK24 @ sK26 )
& ( sK9 @ sK26 @ sK23 ) ) )
| ~ spl0_18 ),
inference(not_proxy_clausification,[],[f646]) ).
thf(f646,plain,
( ( $false
= ( ~ ( ( sK9 @ sK24 @ sK26 )
& ( sK9 @ sK26 @ sK23 ) ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f645]) ).
thf(f645,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK9 @ sK24 @ Y0 )
& ( sK9 @ Y0 @ sK23 ) )
@ sK26 )
= $false )
| ~ spl0_18 ),
inference(sigma_clausification,[],[f644]) ).
thf(f644,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK9 @ sK24 @ Y0 )
& ( sK9 @ Y0 @ sK23 ) ) ) )
| ~ spl0_18 ),
inference(boolean_simplification,[],[f643]) ).
thf(f643,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ sK24 @ Y0 )
& ( sK9 @ Y0 @ sK23 ) )
=> $false ) )
= $false )
| ~ spl0_18 ),
inference(backward_demodulation,[],[f629,f642]) ).
thf(f719,plain,
( ! [X0: a] :
( $true
= ( ( sK9 @ X0 @ sK26 )
=> ( sK9 @ X0 @ sK23 ) ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(boolean_simplification,[],[f705]) ).
thf(f705,plain,
( ! [X0: a] :
( ( ( $true
& ( sK9 @ X0 @ sK26 ) )
=> ( sK9 @ X0 @ sK23 ) )
= $true )
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f692,f653]) ).
thf(f653,plain,
( ( ( sK9 @ sK26 @ sK23 )
= $true )
| ~ spl0_18 ),
inference(boolean_simplification,[],[f652]) ).
thf(f652,plain,
( ( ( $true
& ( sK9 @ sK26 @ sK23 ) )
= $true )
| ~ spl0_18 ),
inference(backward_demodulation,[],[f647,f651]) ).
thf(f692,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK9 @ X3 @ X2 )
& ( sK9 @ X1 @ X3 ) )
=> ( sK9 @ X1 @ X2 ) )
= $true )
| ~ spl0_15
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f691]) ).
thf(f691,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK9 @ Y0 @ X2 )
& ( sK9 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ X2 ) )
@ X3 ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(pi_clausification,[],[f690]) ).
thf(f690,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ Y0 @ X2 )
& ( sK9 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ X2 ) ) )
= $true )
| ~ spl0_15
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f689]) ).
thf(f689,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ X1 @ Y1 ) )
=> ( sK9 @ X1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(pi_clausification,[],[f684]) ).
thf(f684,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ X1 @ Y1 ) )
=> ( sK9 @ X1 @ Y0 ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f683]) ).
thf(f683,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_15
| ~ spl0_18 ),
inference(pi_clausification,[],[f679]) ).
thf(f679,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(boolean_simplification,[],[f678]) ).
thf(f678,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(backward_demodulation,[],[f673,f677]) ).
thf(f677,plain,
( ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f673]) ).
thf(f673,plain,
( ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_18 ),
inference(boolean_simplification,[],[f672]) ).
thf(f672,plain,
( ( $true
= ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& $true ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(backward_demodulation,[],[f667,f670]) ).
thf(f670,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f667]) ).
thf(f667,plain,
( ( $true
= ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(not_proxy_clausification,[],[f666]) ).
thf(f666,plain,
( ( $false
= ( ~ ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(boolean_simplification,[],[f665]) ).
thf(f665,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(boolean_simplification,[],[f664]) ).
thf(f664,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
=> ( ( sK9 = sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& $false ) ) )
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f663,f189]) ).
thf(f615,plain,
( ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f614]) ).
thf(f614,plain,
( $false
| ~ spl0_16
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f613]) ).
thf(f613,plain,
( ( $false = $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f606,f483]) ).
thf(f483,plain,
( ( $false
= ( sK10 @ sK18 @ sK19 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(not_proxy_clausification,[],[f469]) ).
thf(f469,plain,
( ( ( ~ ( sK10 @ sK18 @ sK19 ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f452]) ).
thf(f452,plain,
( ( $true
= ( ( sK10 @ sK18 @ sK19 )
=> $false ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f449,f424]) ).
thf(f424,plain,
( ( $false
= ( sK10 @ sK19 @ sK18 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f423]) ).
thf(f423,plain,
( ( $false
= ( $true
=> ( sK10 @ sK19 @ sK18 ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(backward_demodulation,[],[f414,f422]) ).
thf(f422,plain,
( ( $true
= ( ( sK10 @ sK19 @ sK20 )
& ( sK10 @ sK20 @ sK18 ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f414]) ).
thf(f414,plain,
( ( ( ( ( sK10 @ sK19 @ sK20 )
& ( sK10 @ sK20 @ sK18 ) )
=> ( sK10 @ sK19 @ sK18 ) )
= $false )
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f413,f409]) ).
thf(f409,plain,
( ! [X2: a,X1: a] :
( ( sK10 @ X1 @ X2 )
= ( sK11 @ X1 @ X2 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(argument_congruence,[],[f408]) ).
thf(f408,plain,
( ! [X1: a] :
( ( sK10 @ X1 )
= ( sK11 @ X1 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(argument_congruence,[],[f405]) ).
thf(f405,plain,
( ( sK11 = sK10 )
| ~ spl0_16
| ~ spl0_22 ),
inference(equality_proxy_clausification,[],[f404]) ).
thf(f404,plain,
( ( ( sK11 = sK10 )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f403]) ).
thf(f403,plain,
( ( $true
= ( $true
& ( sK11 = sK10 ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(backward_demodulation,[],[f396,f402]) ).
thf(f402,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f396]) ).
thf(f396,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(not_proxy_clausification,[],[f393]) ).
thf(f393,plain,
( ( $false
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f392]) ).
thf(f392,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 ) )
=> $false ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f391]) ).
thf(f391,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 ) )
=> ( $false
& ( sK11 = sK10 ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f390]) ).
thf(f390,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& $false
& ( sK11 = sK10 ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f389,f228]) ).
thf(f228,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f227,plain,
( spl0_22
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f389,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
& ( sK11 = sK10 ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f388]) ).
thf(f388,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y3 @ Y1 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y2 @ Y1 )
=> ( sK10 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( Y0 = sK10 ) ) )
@ sK11 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f387]) ).
thf(f387,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y3 @ Y1 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y2 @ Y1 )
=> ( sK10 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( Y0 = sK10 ) ) ) )
= $false )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f386]) ).
thf(f386,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) )
@ sK10 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f156]) ).
thf(f156,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f155,plain,
( spl0_16
<=> ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f413,plain,
( ( $false
= ( ( ( sK10 @ sK19 @ sK20 )
& ( sK11 @ sK20 @ sK18 ) )
=> ( sK10 @ sK19 @ sK18 ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f412,f409]) ).
thf(f412,plain,
( ( $false
= ( ( ( sK11 @ sK19 @ sK20 )
& ( sK11 @ sK20 @ sK18 ) )
=> ( sK10 @ sK19 @ sK18 ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f411]) ).
thf(f411,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK11 @ sK19 @ Y0 )
& ( sK11 @ Y0 @ sK18 ) )
=> ( sK10 @ sK19 @ sK18 ) )
@ sK20 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(sigma_clausification,[],[f410]) ).
thf(f410,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ sK19 @ Y0 )
& ( sK11 @ Y0 @ sK18 ) )
=> ( sK10 @ sK19 @ sK18 ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(backward_demodulation,[],[f400,f409]) ).
thf(f400,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ sK19 @ Y0 )
& ( sK11 @ Y0 @ sK18 ) )
=> ( sK11 @ sK19 @ sK18 ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f399]) ).
thf(f399,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y1 @ sK18 ) )
=> ( sK11 @ Y0 @ sK18 ) ) )
@ sK19 )
= $false )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f395]) ).
thf(f395,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y1 @ sK18 ) )
=> ( sK11 @ Y0 @ sK18 ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f394]) ).
thf(f394,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
@ sK18 ) )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f228]) ).
thf(f449,plain,
( ! [X2: a,X1: a] :
( ( ( sK10 @ X2 @ X1 )
=> ( sK10 @ X1 @ X2 ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f448]) ).
thf(f448,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK10 @ Y0 @ X1 )
=> ( sK10 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(pi_clausification,[],[f447]) ).
thf(f447,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK10 @ Y0 @ X1 )
=> ( sK10 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f446]) ).
thf(f446,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(pi_clausification,[],[f445]) ).
thf(f445,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f444]) ).
thf(f444,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(backward_demodulation,[],[f402,f443]) ).
thf(f443,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f402]) ).
thf(f606,plain,
( ( $true
= ( sK10 @ sK18 @ sK19 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f603]) ).
thf(f603,plain,
( ( $true
= ( $true
=> ( sK10 @ sK18 @ sK19 ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f549,f473]) ).
thf(f473,plain,
( ( ( sK10 @ sK18 @ sK21 )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f460]) ).
thf(f460,plain,
( ( ( $true
=> ( sK10 @ sK18 @ sK21 ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f449,f438]) ).
thf(f438,plain,
( ( ( sK10 @ sK21 @ sK18 )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f435]) ).
thf(f435,plain,
( ( $true
= ( ( sK10 @ sK19 @ sK21 )
& ( sK10 @ sK21 @ sK18 ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(not_proxy_clausification,[],[f430]) ).
thf(f430,plain,
( ( $false
= ( ~ ( ( sK10 @ sK19 @ sK21 )
& ( sK10 @ sK21 @ sK18 ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f429,f409]) ).
thf(f429,plain,
( ( $false
= ( ~ ( ( sK10 @ sK19 @ sK21 )
& ( sK11 @ sK21 @ sK18 ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f428,f409]) ).
thf(f428,plain,
( ( $false
= ( ~ ( ( sK11 @ sK19 @ sK21 )
& ( sK11 @ sK21 @ sK18 ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f427]) ).
thf(f427,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK11 @ sK19 @ Y0 )
& ( sK11 @ Y0 @ sK18 ) )
@ sK21 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(sigma_clausification,[],[f426]) ).
thf(f426,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK11 @ sK19 @ Y0 )
& ( sK11 @ Y0 @ sK18 ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f425]) ).
thf(f425,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ sK19 @ Y0 )
& ( sK11 @ Y0 @ sK18 ) )
=> $false ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(backward_demodulation,[],[f410,f424]) ).
thf(f549,plain,
( ! [X0: a] :
( $true
= ( ( sK10 @ X0 @ sK21 )
=> ( sK10 @ X0 @ sK19 ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f528]) ).
thf(f528,plain,
( ! [X0: a] :
( ( ( ( sK10 @ X0 @ sK21 )
& $true )
=> ( sK10 @ X0 @ sK19 ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f505,f464]) ).
thf(f464,plain,
( ( $true
= ( sK10 @ sK21 @ sK19 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f462]) ).
thf(f462,plain,
( ( ( $true
=> ( sK10 @ sK21 @ sK19 ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f449,f441]) ).
thf(f441,plain,
( ( ( sK10 @ sK19 @ sK21 )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f440]) ).
thf(f440,plain,
( ( ( ( sK10 @ sK19 @ sK21 )
& $true )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(backward_demodulation,[],[f435,f438]) ).
thf(f505,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK10 @ X3 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X3 @ X2 ) )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f504]) ).
thf(f504,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK10 @ Y0 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ Y0 @ X2 ) )
@ X3 ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(pi_clausification,[],[f499]) ).
thf(f499,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ Y0 @ X2 ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f498]) ).
thf(f498,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ X1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(pi_clausification,[],[f493]) ).
thf(f493,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ X1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_16
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f492]) ).
thf(f492,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_16
| ~ spl0_22 ),
inference(pi_clausification,[],[f443]) ).
thf(f381,plain,
( ~ spl0_15
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f380]) ).
thf(f380,plain,
( $false
| ~ spl0_15
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f379]) ).
thf(f379,plain,
( ( $false = $true )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[],[f378]) ).
thf(f378,plain,
( ( $false = ~ $false )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[],[f377]) ).
thf(f377,plain,
( ( $false
= ( ~ ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& $false ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[],[f376]) ).
thf(f376,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& $false )
=> $false ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[],[f375]) ).
thf(f375,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& $false )
=> ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[],[f374]) ).
thf(f374,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& $false )
=> ( ( sK9 = sK8 )
& $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f373,f328]) ).
thf(f328,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f327]) ).
thf(f327,plain,
( spl0_23
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f373,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
=> ( ( sK9 = sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f372]) ).
thf(f372,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK7 @ Y1 @ Y2 )
=> ( sK7 @ Y2 @ Y1 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK7 @ Y3 @ Y1 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( ( Y0 = sK8 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
@ sK9 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f351]) ).
thf(f351,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK7 @ Y1 @ Y2 )
=> ( sK7 @ Y2 @ Y1 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK7 @ Y3 @ Y1 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( ( Y0 = sK8 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f350]) ).
thf(f350,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( Y1 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK7 @ Y2 @ Y3 )
=> ( sK7 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK7 @ Y4 @ Y2 )
& ( sK7 @ Y2 @ Y3 ) )
=> ( sK7 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f349]) ).
thf(f349,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( Y1 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK7 @ Y2 @ Y3 )
=> ( sK7 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK7 @ Y4 @ Y2 )
& ( sK7 @ Y2 @ Y3 ) )
=> ( sK7 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f348]) ).
thf(f348,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f153]) ).
thf(f332,plain,
( spl0_23
| spl0_24
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f325,f185,f330,f327]) ).
thf(f325,plain,
( ( $false
= ( sK9 = sK8 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_17 ),
inference(binary_proxy_clausification,[],[f186]) ).
thf(f322,plain,
( ~ spl0_16
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f321]) ).
thf(f321,plain,
( $false
| ~ spl0_16
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f320,plain,
( ( $false = $true )
| ~ spl0_16
| ~ spl0_20 ),
inference(boolean_simplification,[],[f319]) ).
thf(f319,plain,
( ( ( sK10 = sK10 )
= $false )
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_demodulation,[],[f216,f247]) ).
thf(f247,plain,
( ( sK11 = sK10 )
| ~ spl0_16 ),
inference(equality_proxy_clausification,[],[f246]) ).
thf(f246,plain,
( ( ( sK11 = sK10 )
= $true )
| ~ spl0_16 ),
inference(boolean_simplification,[],[f245]) ).
thf(f245,plain,
( ( $true
= ( $true
& ( sK11 = sK10 ) ) )
| ~ spl0_16 ),
inference(backward_demodulation,[],[f203,f244]) ).
thf(f244,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f203]) ).
thf(f203,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 ) )
= $true )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f200]) ).
thf(f200,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
& ( sK11 = sK10 ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f199]) ).
thf(f199,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y3 @ Y1 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y2 @ Y1 )
=> ( sK10 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( Y0 = sK10 ) ) )
@ sK11 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f197]) ).
thf(f197,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y3 @ Y1 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y2 @ Y1 )
=> ( sK10 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( Y0 = sK10 ) ) ) )
= $false )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f196]) ).
thf(f196,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) )
@ sK10 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f156]) ).
thf(f216,plain,
( ( ( sK11 = sK10 )
= $false )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f215,plain,
( spl0_20
<=> ( ( sK11 = sK10 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f313,plain,
( ~ spl0_16
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f312]) ).
thf(f312,plain,
( $false
| ~ spl0_16
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f311]) ).
thf(f311,plain,
( ( $false = $true )
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f303,f259]) ).
thf(f259,plain,
( ( $false
= ( sK10 @ sK12 @ sK13 ) )
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f251,f242]) ).
thf(f242,plain,
( ( $false
= ( sK11 @ sK12 @ sK13 ) )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f241]) ).
thf(f241,plain,
( ( ( $true
=> ( sK11 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_21 ),
inference(backward_demodulation,[],[f238,f240]) ).
thf(f240,plain,
( ( ( sK11 @ sK13 @ sK12 )
= $true )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f238]) ).
thf(f238,plain,
( ( $false
= ( ( sK11 @ sK13 @ sK12 )
=> ( sK11 @ sK12 @ sK13 ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f237]) ).
thf(f237,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK11 @ Y0 @ sK12 )
=> ( sK11 @ sK12 @ Y0 ) )
@ sK13 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f235]) ).
thf(f235,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK11 @ Y0 @ sK12 )
=> ( sK11 @ sK12 @ Y0 ) ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f234]) ).
thf(f234,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK12 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f225]) ).
thf(f225,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f224,plain,
( spl0_21
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f251,plain,
( ! [X2: a,X1: a] :
( ( sK10 @ X1 @ X2 )
= ( sK11 @ X1 @ X2 ) )
| ~ spl0_16 ),
inference(argument_congruence,[],[f250]) ).
thf(f250,plain,
( ! [X1: a] :
( ( sK10 @ X1 )
= ( sK11 @ X1 ) )
| ~ spl0_16 ),
inference(argument_congruence,[],[f247]) ).
thf(f303,plain,
( ( ( sK10 @ sK12 @ sK13 )
= $true )
| ~ spl0_16
| ~ spl0_21 ),
inference(boolean_simplification,[],[f301]) ).
thf(f301,plain,
( ( ( $true
=> ( sK10 @ sK12 @ sK13 ) )
= $true )
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f297,f261]) ).
thf(f261,plain,
( ( $true
= ( sK10 @ sK13 @ sK12 ) )
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f240,f251]) ).
thf(f297,plain,
( ! [X2: a,X1: a] :
( ( ( sK10 @ X2 @ X1 )
=> ( sK10 @ X1 @ X2 ) )
= $true )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f296]) ).
thf(f296,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK10 @ Y0 @ X1 )
=> ( sK10 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_16 ),
inference(pi_clausification,[],[f290]) ).
thf(f290,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK10 @ Y0 @ X1 )
=> ( sK10 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f289]) ).
thf(f289,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_16 ),
inference(pi_clausification,[],[f252]) ).
thf(f252,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y1 @ Y0 )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f244]) ).
thf(f229,plain,
( spl0_21
| spl0_22
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f222,f212,f227,f224]) ).
thf(f212,plain,
( spl0_19
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f222,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f213]) ).
thf(f213,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f217,plain,
( spl0_19
| spl0_20
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f210,f155,f215,f212]) ).
thf(f210,plain,
( ( ( sK11 = sK10 )
= $false )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f202]) ).
thf(f202,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK11 @ Y1 @ Y0 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
& ( sK11 = sK10 ) ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f200]) ).
thf(f190,plain,
( spl0_17
| spl0_18
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f183,f152,f188,f185]) ).
thf(f183,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( sK9 = sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f176]) ).
thf(f176,plain,
( ( $false
= ( ( sK9 = sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f175]) ).
thf(f175,plain,
( ( $false
= ( $true
=> ( ( sK9 = sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_15 ),
inference(backward_demodulation,[],[f171,f174]) ).
thf(f174,plain,
( ( $true
= ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f171]) ).
thf(f171,plain,
( ( $false
= ( ( ( sK9 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
=> ( ( sK9 = sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f170]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK7 @ Y1 @ Y2 )
=> ( sK7 @ Y2 @ Y1 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK7 @ Y3 @ Y1 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( ( Y0 = sK8 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
@ sK9 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f167]) ).
thf(f167,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK7 @ Y1 @ Y2 )
=> ( sK7 @ Y2 @ Y1 ) ) ) )
& ( sK8 = sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK7 @ Y3 @ Y1 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( ( Y0 = sK8 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f166]) ).
thf(f166,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( Y1 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK7 @ Y2 @ Y3 )
=> ( sK7 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK7 @ Y4 @ Y2 )
& ( sK7 @ Y2 @ Y3 ) )
=> ( sK7 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f163]) ).
thf(f163,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( Y1 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK7 @ Y2 @ Y3 )
=> ( sK7 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK7 @ Y4 @ Y2 )
& ( sK7 @ Y2 @ Y3 ) )
=> ( sK7 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f162]) ).
thf(f162,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f153]) ).
thf(f157,plain,
( spl0_15
| spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f150,f12,f155,f152]) ).
thf(f12,plain,
( spl0_1
<=> ( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f150,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) ) ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f13]) ).
thf(f13,plain,
( ( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f12]) ).
thf(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f10,f15,f12]) ).
thf(f10,plain,
( ( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) ) ) ) )
| ( $false
= ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y2 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) ) )
& ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y2 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) ) )
& ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y2 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y0 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y3 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( Y1 = Y0 ) ) ) ) )
& ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y2 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ( ( ( ^ [X0: a > a > $o,X1: a > a > $o] :
( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X0 @ X6 @ X5 ) )
& ( X0 = X1 ) ) )
= ( ^ [X7: a > a > $o,X8: a > a > $o] :
( ! [X9: a,X10: a,X11: a] :
( ( ( X7 @ X11 @ X9 )
& ( X7 @ X9 @ X10 ) )
=> ( X7 @ X11 @ X10 ) )
& ( X7 = X8 )
& ! [X12: a,X13: a] :
( ( X7 @ X13 @ X12 )
=> ( X7 @ X12 @ X13 ) ) ) ) )
& ! [X14: a > a > $o,X15: a > a > $o] :
( ( ( X14 = X15 )
& ! [X16: a,X17: a] :
( ( X15 @ X16 @ X17 )
=> ( X15 @ X17 @ X16 ) )
& ! [X18: a,X19: a,X20: a] :
( ( ( X15 @ X20 @ X19 )
& ( X15 @ X18 @ X20 ) )
=> ( X15 @ X18 @ X19 ) ) )
=> ( ( X14 = X15 )
& ! [X21: a,X22: a,X23: a] :
( ( ( X14 @ X21 @ X23 )
& ( X14 @ X22 @ X21 ) )
=> ( X14 @ X22 @ X23 ) )
& ! [X24: a,X25: a] :
( ( X14 @ X24 @ X25 )
=> ( X14 @ X25 @ X24 ) ) ) )
& ! [X26: a > a > $o,X27: a > a > $o,X28: a > a > $o] :
( ( ! [X29: a,X30: a] :
( ( X26 @ X29 @ X30 )
=> ( X26 @ X30 @ X29 ) )
& ! [X31: a,X32: a,X33: a] :
( ( ( X26 @ X33 @ X31 )
& ( X26 @ X31 @ X32 ) )
=> ( X26 @ X33 @ X32 ) )
& ! [X34: a,X35: a,X36: a] :
( ( ( X28 @ X36 @ X35 )
& ( X28 @ X34 @ X36 ) )
=> ( X28 @ X34 @ X35 ) )
& ( X27 = X28 )
& ! [X37: a,X38: a] :
( ( X28 @ X38 @ X37 )
=> ( X28 @ X37 @ X38 ) )
& ( X26 = X28 ) )
=> ( ! [X39: a,X40: a,X41: a] :
( ( ( X26 @ X39 @ X41 )
& ( X26 @ X40 @ X39 ) )
=> ( X26 @ X40 @ X41 ) )
& ! [X42: a,X43: a] :
( ( X26 @ X42 @ X43 )
=> ( X26 @ X43 @ X42 ) )
& ( X26 = X27 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ! [X0: a,X1: a,X4: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ! [X0: a,X1: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) )
& ( X6 = X7 ) ) )
= ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ! [X1: a,X4: a,X0: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ( X6 = X7 )
& ! [X1: a,X0: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) ) ) ) )
& ! [X1: a > a > $o,X0: a > a > $o] :
( ( ( X0 = X1 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X2: a,X4: a,X3: a] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X4 ) ) )
=> ( ( X0 = X1 )
& ! [X3: a,X2: a,X4: a] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X4 ) )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) )
& ! [X0: a > a > $o,X4: a > a > $o,X1: a > a > $o] :
( ( ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X3: a,X5: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X5 ) )
=> ( X0 @ X2 @ X5 ) )
& ! [X2: a,X5: a,X3: a] :
( ( ( X1 @ X3 @ X5 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X5 ) )
& ( X1 = X4 )
& ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ( X0 = X1 ) )
=> ( ! [X3: a,X2: a,X5: a] :
( ( ( X0 @ X3 @ X5 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X5 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ( X0 = X4 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ! [X0: a,X1: a,X4: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ! [X0: a,X1: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) )
& ( X6 = X7 ) ) )
= ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ! [X1: a,X4: a,X0: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ( X6 = X7 )
& ! [X1: a,X0: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) ) ) ) )
& ! [X1: a > a > $o,X0: a > a > $o] :
( ( ( X0 = X1 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X2: a,X4: a,X3: a] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X4 ) ) )
=> ( ( X0 = X1 )
& ! [X3: a,X2: a,X4: a] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X4 ) )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) )
& ! [X0: a > a > $o,X4: a > a > $o,X1: a > a > $o] :
( ( ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X3: a,X5: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X5 ) )
=> ( X0 @ X2 @ X5 ) )
& ! [X2: a,X5: a,X3: a] :
( ( ( X1 @ X3 @ X5 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X5 ) )
& ( X1 = X4 )
& ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ( X0 = X1 ) )
=> ( ! [X3: a,X2: a,X5: a] :
( ( ( X0 @ X3 @ X5 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X5 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ( X0 = X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM515_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV040^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.11 % Command : run_vampire %s %d THM
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 21 18:22:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.34 This is a TH0_THM_EQU_NAR problem
% 0.11/0.34 Running higher-order theorem proving
% 0.11/0.34 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.11/0.35 % (367)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 theBenchmark for (2999ds/27Mi)
% 0.18/0.36 % (366)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 theBenchmark for (2999ds/4Mi)
% 0.18/0.36 % (368)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.36 % (365)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.18/0.36 % (369)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.36 % (370)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.18/0.36 % (371)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.36 % (366)Instruction limit reached!
% 0.18/0.36 % (366)------------------------------
% 0.18/0.36 % (366)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.36 % (366)Termination reason: Unknown
% 0.18/0.36 % (366)Termination phase: Property scanning
% 0.18/0.36
% 0.18/0.36 % (366)Memory used [KB]: 1023
% 0.18/0.36 % (366)Time elapsed: 0.004 s
% 0.18/0.36 % (366)Instructions burned: 4 (million)
% 0.18/0.36 % (366)------------------------------
% 0.18/0.36 % (366)------------------------------
% 0.18/0.36 % (368)Instruction limit reached!
% 0.18/0.36 % (368)------------------------------
% 0.18/0.36 % (368)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.36 % (368)Termination reason: Unknown
% 0.18/0.36 % (368)Termination phase: Preprocessing 1
% 0.18/0.36
% 0.18/0.36 % (368)Memory used [KB]: 1023
% 0.18/0.36 % (368)Time elapsed: 0.004 s
% 0.18/0.36 % (368)Instructions burned: 3 (million)
% 0.18/0.36 % (368)------------------------------
% 0.18/0.36 % (368)------------------------------
% 0.18/0.36 % (369)Instruction limit reached!
% 0.18/0.36 % (369)------------------------------
% 0.18/0.36 % (369)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.36 % (369)Termination reason: Unknown
% 0.18/0.36 % (369)Termination phase: shuffling
% 0.18/0.36
% 0.18/0.36 % (369)Memory used [KB]: 1023
% 0.18/0.36 % (369)Time elapsed: 0.004 s
% 0.18/0.36 % (369)Instructions burned: 3 (million)
% 0.18/0.36 % (369)------------------------------
% 0.18/0.36 % (369)------------------------------
% 0.18/0.36 % (367)Instruction limit reached!
% 0.18/0.36 % (367)------------------------------
% 0.18/0.36 % (367)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.36 % (367)Termination reason: Unknown
% 0.18/0.36 % (367)Termination phase: Saturation
% 0.18/0.36
% 0.18/0.36 % (367)Memory used [KB]: 5884
% 0.18/0.36 % (367)Time elapsed: 0.011 s
% 0.18/0.36 % (367)Instructions burned: 28 (million)
% 0.18/0.36 % (367)------------------------------
% 0.18/0.36 % (367)------------------------------
% 0.18/0.37 % (375)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.37 % (371)Instruction limit reached!
% 0.18/0.37 % (371)------------------------------
% 0.18/0.37 % (371)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.37 % (371)Termination reason: Unknown
% 0.18/0.37 % (371)Termination phase: Saturation
% 0.18/0.37
% 0.18/0.37 % (371)Memory used [KB]: 5628
% 0.18/0.37 % (371)Time elapsed: 0.014 s
% 0.18/0.37 % (371)Instructions burned: 19 (million)
% 0.18/0.37 % (371)------------------------------
% 0.18/0.37 % (371)------------------------------
% 0.18/0.37 % (375)Instruction limit reached!
% 0.18/0.37 % (375)------------------------------
% 0.18/0.37 % (375)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.37 % (375)Termination reason: Unknown
% 0.18/0.37 % (375)Termination phase: Preprocessing 1
% 0.18/0.37
% 0.18/0.37 % (375)Memory used [KB]: 1023
% 0.18/0.37 % (375)Time elapsed: 0.002 s
% 0.18/0.37 % (375)Instructions burned: 3 (million)
% 0.18/0.37 % (375)------------------------------
% 0.18/0.37 % (375)------------------------------
% 0.18/0.38 % (372)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.38 % (373)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 theBenchmark for (2999ds/37Mi)
% 0.18/0.38 % (374)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 theBenchmark for (2999ds/15Mi)
% 0.18/0.38 % (372)Instruction limit reached!
% 0.18/0.38 % (372)------------------------------
% 0.18/0.38 % (372)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.38 % (372)Termination reason: Unknown
% 0.18/0.38 % (372)Termination phase: Preprocessing 3
% 0.18/0.38
% 0.18/0.38 % (372)Memory used [KB]: 1023
% 0.18/0.38 % (372)Time elapsed: 0.004 s
% 0.18/0.38 % (372)Instructions burned: 3 (million)
% 0.18/0.38 % (372)------------------------------
% 0.18/0.38 % (372)------------------------------
% 0.18/0.38 % (376)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 theBenchmark for (2999ds/1041Mi)
% 0.18/0.39 % (374)Instruction limit reached!
% 0.18/0.39 % (374)------------------------------
% 0.18/0.39 % (374)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.39 % (374)Termination reason: Unknown
% 0.18/0.39 % (374)Termination phase: Saturation
% 0.18/0.39
% 0.18/0.39 % (374)Memory used [KB]: 5756
% 0.18/0.39 % (374)Time elapsed: 0.012 s
% 0.18/0.39 % (374)Instructions burned: 15 (million)
% 0.18/0.39 % (374)------------------------------
% 0.18/0.39 % (374)------------------------------
% 0.18/0.39 % (377)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.39 % (377)Instruction limit reached!
% 0.18/0.39 % (377)------------------------------
% 0.18/0.39 % (377)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.39 % (377)Termination reason: Unknown
% 0.18/0.39 % (377)Termination phase: Property scanning
% 0.18/0.39
% 0.18/0.39 % (377)Memory used [KB]: 1023
% 0.18/0.39 % (377)Time elapsed: 0.006 s
% 0.18/0.39 % (377)Instructions burned: 7 (million)
% 0.18/0.39 % (377)------------------------------
% 0.18/0.39 % (377)------------------------------
% 0.18/0.39 % (378)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.40 % (373)Instruction limit reached!
% 0.18/0.40 % (373)------------------------------
% 0.18/0.40 % (373)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.40 % (373)Termination reason: Unknown
% 0.18/0.40 % (373)Termination phase: Saturation
% 0.18/0.40
% 0.18/0.40 % (373)Memory used [KB]: 5628
% 0.18/0.40 % (373)Time elapsed: 0.023 s
% 0.18/0.40 % (373)Instructions burned: 37 (million)
% 0.18/0.40 % (373)------------------------------
% 0.18/0.40 % (373)------------------------------
% 0.18/0.40 % (378)Instruction limit reached!
% 0.18/0.40 % (378)------------------------------
% 0.18/0.40 % (378)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.40 % (378)Termination reason: Unknown
% 0.18/0.40 % (378)Termination phase: Saturation
% 0.18/0.40
% 0.18/0.40 % (378)Memory used [KB]: 5756
% 0.18/0.40 % (378)Time elapsed: 0.012 s
% 0.18/0.40 % (378)Instructions burned: 16 (million)
% 0.18/0.40 % (378)------------------------------
% 0.18/0.40 % (378)------------------------------
% 0.18/0.40 % (379)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 theBenchmark for (2999ds/3Mi)
% 0.18/0.41 % (379)Instruction limit reached!
% 0.18/0.41 % (379)------------------------------
% 0.18/0.41 % (379)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.41 % (379)Termination reason: Unknown
% 0.18/0.41 % (379)Termination phase: Naming
% 0.18/0.41
% 0.18/0.41 % (379)Memory used [KB]: 1023
% 0.18/0.41 % (379)Time elapsed: 0.004 s
% 0.18/0.41 % (379)Instructions burned: 3 (million)
% 0.18/0.41 % (379)------------------------------
% 0.18/0.41 % (379)------------------------------
% 0.18/0.41 % (380)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 theBenchmark for (2999ds/3Mi)
% 0.18/0.41 % (380)Instruction limit reached!
% 0.18/0.41 % (380)------------------------------
% 0.18/0.41 % (380)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.41 % (380)Termination reason: Unknown
% 0.18/0.41 % (380)Termination phase: Naming
% 0.18/0.41
% 0.18/0.41 % (380)Memory used [KB]: 1023
% 0.18/0.41 % (380)Time elapsed: 0.004 s
% 0.18/0.41 % (380)Instructions burned: 3 (million)
% 0.18/0.41 % (380)------------------------------
% 0.18/0.41 % (380)------------------------------
% 0.18/0.42 % (381)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.42 % (382)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.42 % (381)Instruction limit reached!
% 0.18/0.42 % (381)------------------------------
% 0.18/0.42 % (381)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.42 % (381)Termination reason: Unknown
% 0.18/0.42 % (381)Termination phase: Property scanning
% 0.18/0.42
% 0.18/0.42 % (381)Memory used [KB]: 1023
% 0.18/0.42 % (381)Time elapsed: 0.006 s
% 0.18/0.42 % (381)Instructions burned: 7 (million)
% 0.18/0.42 % (381)------------------------------
% 0.18/0.42 % (381)------------------------------
% 0.18/0.42 % (382)Instruction limit reached!
% 0.18/0.42 % (382)------------------------------
% 0.18/0.42 % (382)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.42 % (382)Termination reason: Unknown
% 0.18/0.42 % (382)Termination phase: Property scanning
% 0.18/0.42
% 0.18/0.42 % (382)Memory used [KB]: 1023
% 0.18/0.42 % (382)Time elapsed: 0.004 s
% 0.18/0.42 % (382)Instructions burned: 3 (million)
% 0.18/0.42 % (382)------------------------------
% 0.18/0.42 % (382)------------------------------
% 0.18/0.42 % (383)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.18/0.42 % (383)Instruction limit reached!
% 0.18/0.42 % (383)------------------------------
% 0.18/0.42 % (383)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.42 % (383)Termination reason: Unknown
% 0.18/0.42 % (383)Termination phase: Property scanning
% 0.18/0.42
% 0.18/0.42 % (383)Memory used [KB]: 1023
% 0.18/0.42 % (383)Time elapsed: 0.005 s
% 0.18/0.42 % (383)Instructions burned: 5 (million)
% 0.18/0.42 % (383)------------------------------
% 0.18/0.42 % (383)------------------------------
% 0.18/0.43 % (384)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.43 % (385)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.18/0.44 % (386)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.44 % (384)Instruction limit reached!
% 0.18/0.44 % (384)------------------------------
% 0.18/0.44 % (384)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.44 % (384)Termination reason: Unknown
% 0.18/0.44 % (384)Termination phase: Saturation
% 0.18/0.44
% 0.18/0.44 % (384)Memory used [KB]: 5628
% 0.18/0.44 % (384)Time elapsed: 0.013 s
% 0.18/0.44 % (384)Instructions burned: 18 (million)
% 0.18/0.44 % (384)------------------------------
% 0.18/0.44 % (384)------------------------------
% 0.18/0.44 % (386)Instruction limit reached!
% 0.18/0.44 % (386)------------------------------
% 0.18/0.44 % (386)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.44 % (386)Termination reason: Unknown
% 0.18/0.44 % (386)Termination phase: Equality resolution with deletion
% 0.18/0.44
% 0.18/0.44 % (386)Memory used [KB]: 1023
% 0.18/0.44 % (386)Time elapsed: 0.005 s
% 0.18/0.44 % (386)Instructions burned: 6 (million)
% 0.18/0.44 % (386)------------------------------
% 0.18/0.44 % (386)------------------------------
% 0.18/0.44 % (387)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 theBenchmark for (2999ds/902Mi)
% 0.18/0.45 % (389)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.18/0.45 % (389)Instruction limit reached!
% 0.18/0.45 % (389)------------------------------
% 0.18/0.45 % (389)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.45 % (389)Termination reason: Unknown
% 0.18/0.45 % (389)Termination phase: Saturation
% 0.18/0.45
% 0.18/0.45 % (389)Memory used [KB]: 5500
% 0.18/0.45 % (389)Time elapsed: 0.004 s
% 0.18/0.45 % (389)Instructions burned: 6 (million)
% 0.18/0.45 % (389)------------------------------
% 0.18/0.45 % (389)------------------------------
% 0.18/0.45 % (388)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 theBenchmark for (2999ds/21Mi)
% 0.18/0.46 % (365)Instruction limit reached!
% 0.18/0.46 % (365)------------------------------
% 0.18/0.46 % (365)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.46 % (365)Termination reason: Unknown
% 0.18/0.46 % (365)Termination phase: Saturation
% 0.18/0.46
% 0.18/0.46 % (365)Memory used [KB]: 6396
% 0.18/0.46 % (365)Time elapsed: 0.102 s
% 0.18/0.46 % (365)Instructions burned: 183 (million)
% 0.18/0.46 % (365)------------------------------
% 0.18/0.46 % (365)------------------------------
% 0.18/0.46 % (390)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 theBenchmark for (2998ds/6Mi)
% 0.18/0.46 % (390)Instruction limit reached!
% 0.18/0.46 % (390)------------------------------
% 0.18/0.46 % (390)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.46 % (390)Termination reason: Unknown
% 0.18/0.46 % (390)Termination phase: Saturation
% 0.18/0.46
% 0.18/0.46 % (390)Memory used [KB]: 5500
% 0.18/0.46 % (390)Time elapsed: 0.004 s
% 0.18/0.46 % (390)Instructions burned: 7 (million)
% 0.18/0.46 % (390)------------------------------
% 0.18/0.46 % (390)------------------------------
% 0.18/0.46 % (388)Instruction limit reached!
% 0.18/0.46 % (388)------------------------------
% 0.18/0.46 % (388)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.46 % (388)Termination reason: Unknown
% 0.18/0.46 % (388)Termination phase: Saturation
% 0.18/0.46
% 0.18/0.46 % (388)Memory used [KB]: 5756
% 0.18/0.46 % (388)Time elapsed: 0.014 s
% 0.18/0.46 % (388)Instructions burned: 21 (million)
% 0.18/0.46 % (388)------------------------------
% 0.18/0.46 % (388)------------------------------
% 0.18/0.47 % (392)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 theBenchmark for (2998ds/779Mi)
% 0.18/0.47 % (391)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.18/0.47 % (393)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 theBenchmark for (2998ds/19Mi)
% 0.18/0.48 % (393)Instruction limit reached!
% 0.18/0.48 % (393)------------------------------
% 0.18/0.48 % (393)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.48 % (393)Termination reason: Unknown
% 0.18/0.48 % (393)Termination phase: Saturation
% 0.18/0.48
% 0.18/0.48 % (393)Memory used [KB]: 5500
% 0.18/0.48 % (393)Time elapsed: 0.007 s
% 0.18/0.48 % (393)Instructions burned: 20 (million)
% 0.18/0.48 % (393)------------------------------
% 0.18/0.48 % (393)------------------------------
% 0.18/0.49 % (394)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.18/0.50 % (370)Instruction limit reached!
% 0.18/0.50 % (370)------------------------------
% 0.18/0.50 % (370)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.50 % (370)Termination reason: Unknown
% 0.18/0.50 % (370)Termination phase: Saturation
% 0.18/0.50
% 0.18/0.50 % (370)Memory used [KB]: 6396
% 0.18/0.50 % (370)Time elapsed: 0.137 s
% 0.18/0.50 % (370)Instructions burned: 275 (million)
% 0.18/0.50 % (370)------------------------------
% 0.18/0.50 % (370)------------------------------
% 0.18/0.51 % (395)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.18/0.51 % (395)Instruction limit reached!
% 0.18/0.51 % (395)------------------------------
% 0.18/0.51 % (395)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.51 % (395)Termination reason: Unknown
% 0.18/0.51 % (395)Termination phase: Saturation
% 0.18/0.51
% 0.18/0.51 % (395)Memory used [KB]: 5756
% 0.18/0.51 % (395)Time elapsed: 0.008 s
% 0.18/0.51 % (395)Instructions burned: 18 (million)
% 0.18/0.51 % (395)------------------------------
% 0.18/0.51 % (395)------------------------------
% 0.18/0.52 % (396)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.18/0.52 % (396)Instruction limit reached!
% 0.18/0.52 % (396)------------------------------
% 0.18/0.52 % (396)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.52 % (396)Termination reason: Unknown
% 0.18/0.52 % (396)Termination phase: Preprocessing 3
% 0.18/0.52
% 0.18/0.52 % (396)Memory used [KB]: 1023
% 0.18/0.52 % (396)Time elapsed: 0.003 s
% 0.18/0.52 % (396)Instructions burned: 4 (million)
% 0.18/0.52 % (396)------------------------------
% 0.18/0.52 % (396)------------------------------
% 0.18/0.53 % (397)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.18/0.53 % (376)First to succeed.
% 0.18/0.54 % (397)Instruction limit reached!
% 0.18/0.54 % (397)------------------------------
% 0.18/0.54 % (397)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.54 % (397)Termination reason: Unknown
% 0.18/0.54 % (397)Termination phase: Saturation
% 0.18/0.54
% 0.18/0.54 % (397)Memory used [KB]: 5756
% 0.18/0.54 % (397)Time elapsed: 0.012 s
% 0.18/0.54 % (397)Instructions burned: 30 (million)
% 0.18/0.54 % (397)------------------------------
% 0.18/0.54 % (397)------------------------------
% 0.18/0.54 % (376)Refutation found. Thanks to Tanya!
% 0.18/0.54 % SZS status Theorem for theBenchmark
% 0.18/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 1.45/0.55 % (376)------------------------------
% 1.45/0.55 % (376)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.45/0.55 % (376)Termination reason: Refutation
% 1.45/0.55
% 1.45/0.55 % (376)Memory used [KB]: 6908
% 1.45/0.55 % (376)Time elapsed: 0.161 s
% 1.45/0.55 % (376)Instructions burned: 401 (million)
% 1.45/0.55 % (376)------------------------------
% 1.45/0.55 % (376)------------------------------
% 1.45/0.55 % (364)Success in time 0.185 s
%------------------------------------------------------------------------------