%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV150^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 : Wed Feb 25 09:40:24 AM UTC 2026
% Result : Theorem 8.68s 2.53s
% Output : Refutation 8.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 24
% Syntax : Number of formulae : 395 ( 16 unt; 0 typ; 23 def)
% Number of atoms : 3783 ( 372 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 10038 ( 634 ~; 821 |; 715 &;5565 @)
% ( 23 <=>;1069 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 571 ( 571 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 81 usr; 65 con; 0-2 aty)
% (1211 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1431 (1310 ^; 121 !; 0 ?;1431 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_22,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK2: a > a > $o ).
thf(func_def_24,type,
sK3: a > a > $o ).
thf(func_def_25,type,
sK4: a ).
thf(func_def_26,type,
sK5: a ).
thf(func_def_27,type,
sK6: a > $o ).
thf(func_def_28,type,
sK7: a ).
thf(func_def_29,type,
sK8: a ).
thf(func_def_30,type,
sK9: a ).
thf(func_def_31,type,
sK10: a > $o ).
thf(func_def_32,type,
sK11: a ).
thf(func_def_33,type,
sK12: a ).
thf(func_def_34,type,
sK13: a > $o ).
thf(func_def_35,type,
sK14: a > $o ).
thf(func_def_36,type,
sK15: a > $o ).
thf(func_def_37,type,
sK16: a > $o ).
thf(func_def_38,type,
sK17: a ).
thf(func_def_39,type,
sK18: a ).
thf(func_def_40,type,
sK19: a ).
thf(func_def_41,type,
sK20: a ).
thf(func_def_42,type,
sK21: a > $o ).
thf(func_def_43,type,
sK22: a > $o ).
thf(func_def_44,type,
sK23: a > $o ).
thf(func_def_45,type,
sK24: a > $o ).
thf(func_def_46,type,
sK25: a > $o ).
thf(func_def_47,type,
sK26: ( a > $o ) > a ).
thf(func_def_48,type,
sK27: a > $o ).
thf(func_def_49,type,
sK28: a ).
thf(func_def_50,type,
sK29: a ).
thf(func_def_51,type,
sK30: a ).
thf(func_def_52,type,
sK31: a ).
thf(func_def_53,type,
sK32: a ).
thf(func_def_54,type,
sK33: a > $o ).
thf(func_def_55,type,
sK34: a > $o ).
thf(func_def_56,type,
sK35: a ).
thf(func_def_57,type,
sK36: a ).
thf(func_def_58,type,
sK37: a ).
thf(func_def_59,type,
sK38: a ).
thf(func_def_60,type,
sK39: a ).
thf(func_def_61,type,
sK40: a ).
thf(func_def_62,type,
sK41: a ).
thf(func_def_63,type,
sK42: a ).
thf(func_def_64,type,
sK43: a ).
thf(func_def_65,type,
sK44: a ).
thf(func_def_66,type,
sK45: a ).
thf(func_def_67,type,
sK46: a ).
thf(func_def_68,type,
sK47: a ).
thf(func_def_69,type,
sK48: ( a > $o ) > a ).
thf(func_def_70,type,
sK49: a ).
thf(func_def_71,type,
sK50: a ).
thf(func_def_72,type,
sK51: a ).
thf(func_def_73,type,
sK52: a ).
thf(func_def_74,type,
sK53: a ).
thf(func_def_75,type,
sK54: a ).
thf(func_def_76,type,
sK55: a ).
thf(func_def_77,type,
sK56: a ).
thf(func_def_78,type,
sK57: a ).
thf(func_def_79,type,
sK58: a ).
thf(f5379,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f34,f128,f132,f205,f269,f285,f493,f521,f540,f710,f1097,f2679,f2685,f3476,f3627,f3694,f3736,f3893,f4110,f4457,f4728,f4863,f4924,f5018,f5378]) ).
thf(f5378,plain,
( ~ spl0_3
| ~ spl0_80 ),
inference(avatar_contradiction_clause,[status(thm)],[f5377]) ).
thf(f5377,plain,
( $false
| ~ spl0_3
| ~ spl0_80 ),
inference(trivial_inequality_removal,[status(thm)],[f5376]) ).
thf(f5376,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_80 ),
inference(forward_demodulation,[status(thm)],[f5375,f5299]) ).
thf(f5299,plain,
( ( ( sK6 @ sK58 )
= $false )
| ~ spl0_80 ),
inference(binary_proxy_clausification,[status(thm)],[f5285]) ).
thf(f5285,plain,
( ( $false
= ( ( ( sK6 @ sK57 )
& ( sK3 @ sK57 @ sK58 ) )
=> ( sK6 @ sK58 ) ) )
| ~ spl0_80 ),
inference(beta_eta_normalization,[status(thm)],[f5284]) ).
thf(f5284,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK57 )
& ( sK3 @ sK57 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ sK58 ) )
| ~ spl0_80 ),
inference(sigma_clausification,[status(thm)],[f5270]) ).
thf(f5270,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK57 )
& ( sK3 @ sK57 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_80 ),
inference(beta_eta_normalization,[status(thm)],[f5268]) ).
thf(f5268,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) )
@ sK57 ) )
| ~ spl0_80 ),
inference(sigma_clausification,[status(thm)],[f4456]) ).
thf(f4456,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_80 ),
inference(avatar_component_clause,[status(thm)],[f4455]) ).
thf(f4455,definition,
( spl0_80
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_80])],[avatar_definition]) ).
thf(f5375,plain,
( ( ( sK6 @ sK58 )
= $true )
| ~ spl0_3
| ~ spl0_80 ),
inference(boolean_simplification,[status(thm)],[f5374]) ).
thf(f5374,plain,
( ( $true
= ( $true
=> ( sK6 @ sK58 ) ) )
| ~ spl0_3
| ~ spl0_80 ),
inference(forward_demodulation,[status(thm)],[f5373,f5341]) ).
thf(f5341,plain,
( ( $true
= ( sK6 @ sK57 ) )
| ~ spl0_80 ),
inference(binary_proxy_clausification,[status(thm)],[f5300]) ).
thf(f5300,plain,
( ( $true
= ( ( sK6 @ sK57 )
& ( sK3 @ sK57 @ sK58 ) ) )
| ~ spl0_80 ),
inference(binary_proxy_clausification,[status(thm)],[f5285]) ).
thf(f5373,plain,
( ( $true
= ( ( sK6 @ sK57 )
=> ( sK6 @ sK58 ) ) )
| ~ spl0_3
| ~ spl0_80 ),
inference(boolean_simplification,[status(thm)],[f5372]) ).
thf(f5372,plain,
( ( $true
= ( ( $true
& ( sK6 @ sK57 ) )
=> ( sK6 @ sK58 ) ) )
| ~ spl0_3
| ~ spl0_80 ),
inference(boolean_simplification,[status(thm)],[f5371]) ).
thf(f5371,plain,
( ( ( ( ( ( sK2 @ sK57 @ sK58 )
| $true )
& ( sK6 @ sK57 ) )
=> ( sK6 @ sK58 ) )
= $true )
| ~ spl0_3
| ~ spl0_80 ),
inference(superposition,[status(thm)],[f2721,f5343]) ).
thf(f5343,plain,
( ( $true
= ( sK3 @ sK57 @ sK58 ) )
| ~ spl0_80 ),
inference(boolean_simplification,[status(thm)],[f5342]) ).
thf(f5342,plain,
( ( ( $true
& ( sK3 @ sK57 @ sK58 ) )
= $true )
| ~ spl0_80 ),
inference(backward_demodulation,[status(thm)],[f5300,f5341]) ).
thf(f2721,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( ( sK2 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) )
& ( sK6 @ X1 ) )
=> ( sK6 @ X2 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f2720]) ).
thf(f2720,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
& ( sK6 @ X1 ) )
=> ( sK6 @ Y0 ) )
@ X2 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f2719]) ).
thf(f2719,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
& ( sK6 @ X1 ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f2718]) ).
thf(f2718,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f2707]) ).
thf(f2707,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f2706]) ).
thf(f2706,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f2691,f2704]) ).
thf(f2704,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f2691]) ).
thf(f2691,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f2689]) ).
thf(f2689,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK5 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f2688]) ).
thf(f2688,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl0_3
<=> ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f5018,plain,
( ~ spl0_3
| ~ spl0_85 ),
inference(avatar_contradiction_clause,[status(thm)],[f5017]) ).
thf(f5017,plain,
( $false
| ~ spl0_3
| ~ spl0_85 ),
inference(trivial_inequality_removal,[status(thm)],[f5016]) ).
thf(f5016,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_85 ),
inference(forward_demodulation,[status(thm)],[f5015,f4946]) ).
thf(f4946,plain,
( ( ( sK6 @ sK54 )
= $false )
| ~ spl0_85 ),
inference(binary_proxy_clausification,[status(thm)],[f4937]) ).
thf(f4937,plain,
( ( ( ( ( sK6 @ sK55 )
& ( sK2 @ sK55 @ sK54 ) )
=> ( sK6 @ sK54 ) )
= $false )
| ~ spl0_85 ),
inference(beta_eta_normalization,[status(thm)],[f4936]) ).
thf(f4936,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ sK54 ) )
=> ( sK6 @ sK54 ) )
@ sK55 )
= $false )
| ~ spl0_85 ),
inference(sigma_clausification,[status(thm)],[f4931]) ).
thf(f4931,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ sK54 ) )
=> ( sK6 @ sK54 ) ) ) )
| ~ spl0_85 ),
inference(beta_eta_normalization,[status(thm)],[f4927]) ).
thf(f4927,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
@ sK54 )
= $false )
| ~ spl0_85 ),
inference(sigma_clausification,[status(thm)],[f4862]) ).
thf(f4862,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_85 ),
inference(avatar_component_clause,[status(thm)],[f4861]) ).
thf(f4861,definition,
( spl0_85
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_85])],[avatar_definition]) ).
thf(f5015,plain,
( ( ( sK6 @ sK54 )
= $true )
| ~ spl0_3
| ~ spl0_85 ),
inference(boolean_simplification,[status(thm)],[f5014]) ).
thf(f5014,plain,
( ( ( $true
=> ( sK6 @ sK54 ) )
= $true )
| ~ spl0_3
| ~ spl0_85 ),
inference(forward_demodulation,[status(thm)],[f5013,f4994]) ).
thf(f4994,plain,
( ( ( sK6 @ sK56 )
= $true )
| ~ spl0_85 ),
inference(binary_proxy_clausification,[status(thm)],[f4985]) ).
thf(f4985,plain,
( ( $true
= ( ( sK6 @ sK56 )
& ( sK2 @ sK56 @ sK54 ) ) )
| ~ spl0_85 ),
inference(not_proxy_clausification,[status(thm)],[f4970]) ).
thf(f4970,plain,
( ( $false
= ( ~ ( ( sK6 @ sK56 )
& ( sK2 @ sK56 @ sK54 ) ) ) )
| ~ spl0_85 ),
inference(beta_eta_normalization,[status(thm)],[f4969]) ).
thf(f4969,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ sK54 ) )
@ sK56 ) )
| ~ spl0_85 ),
inference(sigma_clausification,[status(thm)],[f4951]) ).
thf(f4951,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ sK54 ) ) ) )
| ~ spl0_85 ),
inference(boolean_simplification,[status(thm)],[f4949]) ).
thf(f4949,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ sK54 ) )
=> $false ) ) )
| ~ spl0_85 ),
inference(backward_demodulation,[status(thm)],[f4931,f4946]) ).
thf(f5013,plain,
( ( $true
= ( ( sK6 @ sK56 )
=> ( sK6 @ sK54 ) ) )
| ~ spl0_3
| ~ spl0_85 ),
inference(boolean_simplification,[status(thm)],[f5012]) ).
thf(f5012,plain,
( ( ( ( $true
& ( sK6 @ sK56 ) )
=> ( sK6 @ sK54 ) )
= $true )
| ~ spl0_3
| ~ spl0_85 ),
inference(boolean_simplification,[status(thm)],[f5011]) ).
thf(f5011,plain,
( ( ( ( ( $true
| ( sK3 @ sK56 @ sK54 ) )
& ( sK6 @ sK56 ) )
=> ( sK6 @ sK54 ) )
= $true )
| ~ spl0_3
| ~ spl0_85 ),
inference(superposition,[status(thm)],[f2721,f4996]) ).
thf(f4996,plain,
( ( $true
= ( sK2 @ sK56 @ sK54 ) )
| ~ spl0_85 ),
inference(boolean_simplification,[status(thm)],[f4995]) ).
thf(f4995,plain,
( ( ( $true
& ( sK2 @ sK56 @ sK54 ) )
= $true )
| ~ spl0_85 ),
inference(backward_demodulation,[status(thm)],[f4985,f4994]) ).
thf(f4924,plain,
( ~ spl0_3
| ~ spl0_84 ),
inference(avatar_contradiction_clause,[status(thm)],[f4923]) ).
thf(f4923,plain,
( $false
| ~ spl0_3
| ~ spl0_84 ),
inference(trivial_inequality_removal,[status(thm)],[f4922]) ).
thf(f4922,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_84 ),
inference(boolean_simplification,[status(thm)],[f4921]) ).
thf(f4921,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_3
| ~ spl0_84 ),
inference(boolean_simplification,[status(thm)],[f4920]) ).
thf(f4920,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK4 @ sK53 ) ) ) )
| ~ spl0_3
| ~ spl0_84 ),
inference(forward_demodulation,[status(thm)],[f4914,f4900]) ).
thf(f4900,plain,
( ( ( sK2 @ sK4 @ sK53 )
= $true )
| ~ spl0_84 ),
inference(binary_proxy_clausification,[status(thm)],[f4882]) ).
thf(f4882,plain,
( ( $false
= ( ( sK2 @ sK4 @ sK53 )
=> ( sK6 @ sK53 ) ) )
| ~ spl0_84 ),
inference(beta_eta_normalization,[status(thm)],[f4880]) ).
thf(f4880,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK53 )
= $false )
| ~ spl0_84 ),
inference(sigma_clausification,[status(thm)],[f4859]) ).
thf(f4859,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_84 ),
inference(avatar_component_clause,[status(thm)],[f4858]) ).
thf(f4858,definition,
( spl0_84
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_84])],[avatar_definition]) ).
thf(f4914,plain,
( ( ( ~ ( ( sK2 @ sK4 @ sK53 )
| ( sK3 @ sK4 @ sK53 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_84 ),
inference(boolean_simplification,[status(thm)],[f4908]) ).
thf(f4908,plain,
( ( ( ( ( sK2 @ sK4 @ sK53 )
| ( sK3 @ sK4 @ sK53 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_84 ),
inference(superposition,[status(thm)],[f2794,f4899]) ).
thf(f4899,plain,
( ( ( sK6 @ sK53 )
= $false )
| ~ spl0_84 ),
inference(binary_proxy_clausification,[status(thm)],[f4882]) ).
thf(f2794,plain,
( ! [X1: a] :
( $true
= ( ( ( sK2 @ sK4 @ X1 )
| ( sK3 @ sK4 @ X1 ) )
=> ( sK6 @ X1 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f2793]) ).
thf(f2793,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f2704]) ).
thf(f4863,plain,
( spl0_84
| spl0_85
| ~ spl0_6
| ~ spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f4854,f488,f126,f4861,f4858]) ).
thf(f126,definition,
( spl0_6
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f488,definition,
( spl0_13
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f4854,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f4839]) ).
thf(f4839,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(not_proxy_clausification,[status(thm)],[f4668]) ).
thf(f4668,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ) ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f4666]) ).
thf(f4666,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f4651,f4470]) ).
thf(f4470,plain,
( ( $false
= ( sK6 @ sK9 ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f4469]) ).
thf(f4469,plain,
( ( ( $true
=> ( sK6 @ sK9 ) )
= $false )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f4468]) ).
thf(f4468,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
| $true )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f4120,f489]) ).
thf(f489,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f488]) ).
thf(f4120,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
=> ( sK6 @ sK9 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f4114]) ).
thf(f4114,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) )
@ sK9 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f126]) ).
thf(f4651,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK9 ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f4650]) ).
thf(f4650,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) )
@ X1 ) )
| ~ spl0_13 ),
inference(pi_clausification,[status(thm)],[f489]) ).
thf(f4728,plain,
( ~ spl0_3
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[status(thm)],[f4727]) ).
thf(f4727,plain,
( $false
| ~ spl0_3
| ~ spl0_79 ),
inference(trivial_inequality_removal,[status(thm)],[f4726]) ).
thf(f4726,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_79 ),
inference(boolean_simplification,[status(thm)],[f4725]) ).
thf(f4725,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_3
| ~ spl0_79 ),
inference(boolean_simplification,[status(thm)],[f4724]) ).
thf(f4724,plain,
( ( ( ~ ( ( sK2 @ sK4 @ sK49 )
| $true ) )
= $true )
| ~ spl0_3
| ~ spl0_79 ),
inference(forward_demodulation,[status(thm)],[f4716,f4704]) ).
thf(f4704,plain,
( ( ( sK3 @ sK4 @ sK49 )
= $true )
| ~ spl0_79 ),
inference(binary_proxy_clausification,[status(thm)],[f4687]) ).
thf(f4687,plain,
( ( ( ( sK3 @ sK4 @ sK49 )
=> ( sK6 @ sK49 ) )
= $false )
| ~ spl0_79 ),
inference(beta_eta_normalization,[status(thm)],[f4686]) ).
thf(f4686,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK49 )
= $false )
| ~ spl0_79 ),
inference(sigma_clausification,[status(thm)],[f4453]) ).
thf(f4453,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_79 ),
inference(avatar_component_clause,[status(thm)],[f4452]) ).
thf(f4452,definition,
( spl0_79
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_79])],[avatar_definition]) ).
thf(f4716,plain,
( ( ( ~ ( ( sK2 @ sK4 @ sK49 )
| ( sK3 @ sK4 @ sK49 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_79 ),
inference(boolean_simplification,[status(thm)],[f4712]) ).
thf(f4712,plain,
( ( ( ( ( sK2 @ sK4 @ sK49 )
| ( sK3 @ sK4 @ sK49 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_79 ),
inference(superposition,[status(thm)],[f2794,f4703]) ).
thf(f4703,plain,
( ( ( sK6 @ sK49 )
= $false )
| ~ spl0_79 ),
inference(binary_proxy_clausification,[status(thm)],[f4687]) ).
thf(f4457,plain,
( spl0_79
| spl0_80
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f4448,f491,f126,f4455,f4452]) ).
thf(f491,definition,
( spl0_14
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f4448,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(binary_proxy_clausification,[status(thm)],[f4436]) ).
thf(f4436,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(not_proxy_clausification,[status(thm)],[f4294]) ).
thf(f4294,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f4293]) ).
thf(f4293,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f4276,f4123]) ).
thf(f4123,plain,
( ( $false
= ( sK6 @ sK9 ) )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f4122]) ).
thf(f4122,plain,
( ( ( $true
=> ( sK6 @ sK9 ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f4121]) ).
thf(f4121,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f4120,f492]) ).
thf(f492,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f491]) ).
thf(f4276,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK9 ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f4275]) ).
thf(f4275,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ X1 )
= $true )
| ~ spl0_14 ),
inference(pi_clausification,[status(thm)],[f492]) ).
thf(f4110,plain,
( ~ spl0_3
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f4109]) ).
thf(f4109,plain,
( $false
| ~ spl0_3
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f4108]) ).
thf(f4108,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f4107,f4040]) ).
thf(f4040,plain,
( ( ( sK6 @ sK42 )
= $false )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f4023]) ).
thf(f4023,plain,
( ( ( ( ( sK3 @ sK41 @ sK42 )
& ( sK6 @ sK41 ) )
=> ( sK6 @ sK42 ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f4022]) ).
thf(f4022,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ sK41 @ Y0 )
& ( sK6 @ sK41 ) )
=> ( sK6 @ Y0 ) )
@ sK42 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f4013]) ).
thf(f4013,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK41 @ Y0 )
& ( sK6 @ sK41 ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f4011]) ).
thf(f4011,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK41 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f281]) ).
thf(f281,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f280]) ).
thf(f280,definition,
( spl0_11
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f4107,plain,
( ( ( sK6 @ sK42 )
= $true )
| ~ spl0_3
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f4106]) ).
thf(f4106,plain,
( ( ( $true
=> ( sK6 @ sK42 ) )
= $true )
| ~ spl0_3
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f4105,f4066]) ).
thf(f4066,plain,
( ( $true
= ( sK6 @ sK41 ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f4041]) ).
thf(f4041,plain,
( ( $true
= ( ( sK3 @ sK41 @ sK42 )
& ( sK6 @ sK41 ) ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f4023]) ).
thf(f4105,plain,
( ( ( ( sK6 @ sK41 )
=> ( sK6 @ sK42 ) )
= $true )
| ~ spl0_3
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f4104]) ).
thf(f4104,plain,
( ( ( ( $true
& ( sK6 @ sK41 ) )
=> ( sK6 @ sK42 ) )
= $true )
| ~ spl0_3
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f4103]) ).
thf(f4103,plain,
( ( ( ( ( ( sK2 @ sK41 @ sK42 )
| $true )
& ( sK6 @ sK41 ) )
=> ( sK6 @ sK42 ) )
= $true )
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f2721,f4069]) ).
thf(f4069,plain,
( ( $true
= ( sK3 @ sK41 @ sK42 ) )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f4068]) ).
thf(f4068,plain,
( ( $true
= ( ( sK3 @ sK41 @ sK42 )
& $true ) )
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f4041,f4066]) ).
thf(f3893,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f3892]) ).
thf(f3892,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f3891]) ).
thf(f3891,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f3890]) ).
thf(f3890,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f3889]) ).
thf(f3889,plain,
( ( ( ~ ( ( sK2 @ sK7 @ sK40 )
| $true ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f3880,f3840]) ).
thf(f3840,plain,
( ( $true
= ( sK3 @ sK7 @ sK40 ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f3827]) ).
thf(f3827,plain,
( ( $false
= ( ( sK3 @ sK7 @ sK40 )
=> ( sK6 @ sK40 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f3823]) ).
thf(f3823,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK40 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f284]) ).
thf(f284,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f283]) ).
thf(f283,definition,
( spl0_12
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f3880,plain,
( ( $true
= ( ~ ( ( sK2 @ sK7 @ sK40 )
| ( sK3 @ sK7 @ sK40 ) ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f3867]) ).
thf(f3867,plain,
( ( $true
= ( ( ( sK2 @ sK7 @ sK40 )
| ( sK3 @ sK7 @ sK40 ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f3724,f3842]) ).
thf(f3842,plain,
( ( ( sK6 @ sK40 )
= $false )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f3841]) ).
thf(f3841,plain,
( ( $false
= ( $true
=> ( sK6 @ sK40 ) ) )
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f3827,f3840]) ).
thf(f3724,plain,
( ! [X0: a] :
( $true
= ( ( ( sK2 @ sK7 @ X0 )
| ( sK3 @ sK7 @ X0 ) )
=> ( sK6 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f3718]) ).
thf(f3718,plain,
( ! [X0: a] :
( $true
= ( ( ( ( sK2 @ sK7 @ X0 )
| ( sK3 @ sK7 @ X0 ) )
& $true )
=> ( sK6 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f2721,f3699]) ).
thf(f3699,plain,
( ( $true
= ( sK6 @ sK7 ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f3697]) ).
thf(f3697,plain,
( ( $false
= ( ( sK6 @ sK7 )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f3696]) ).
thf(f3696,plain,
( ( ( ( ( sK6 @ sK7 )
& $true )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f3695]) ).
thf(f3695,plain,
( ( $false
= ( ( ( sK6 @ sK7 )
& ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f2848,f201]) ).
thf(f201,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f200]) ).
thf(f200,definition,
( spl0_7
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f2848,plain,
( ( ( ( ( sK6 @ sK7 )
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f2847]) ).
thf(f2847,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK7 )
& ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ Y0 ) )
@ sK8 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f2836]) ).
thf(f2836,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK7 )
& ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f2834]) ).
thf(f2834,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK6 @ Y1 ) ) )
@ sK7 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f123]) ).
thf(f123,definition,
( spl0_5
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f3736,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[status(thm)],[f3735]) ).
thf(f3735,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_68 ),
inference(trivial_inequality_removal,[status(thm)],[f3734]) ).
thf(f3734,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_68 ),
inference(forward_demodulation,[status(thm)],[f3733,f3667]) ).
thf(f3667,plain,
( ( $false
= ( sK6 @ sK39 ) )
| ~ spl0_68 ),
inference(binary_proxy_clausification,[status(thm)],[f3632]) ).
thf(f3632,plain,
( ( $false
= ( ( sK2 @ sK7 @ sK39 )
=> ( sK6 @ sK39 ) ) )
| ~ spl0_68 ),
inference(beta_eta_normalization,[status(thm)],[f3630]) ).
thf(f3630,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK39 )
= $false )
| ~ spl0_68 ),
inference(sigma_clausification,[status(thm)],[f3475]) ).
thf(f3475,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_68 ),
inference(avatar_component_clause,[status(thm)],[f3474]) ).
thf(f3474,definition,
( spl0_68
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_68])],[avatar_definition]) ).
thf(f3733,plain,
( ( $true
= ( sK6 @ sK39 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_68 ),
inference(boolean_simplification,[status(thm)],[f3732]) ).
thf(f3732,plain,
( ( $true
= ( $true
=> ( sK6 @ sK39 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_68 ),
inference(forward_demodulation,[status(thm)],[f3731,f3699]) ).
thf(f3731,plain,
( ( ( ( sK6 @ sK7 )
=> ( sK6 @ sK39 ) )
= $true )
| ~ spl0_3
| ~ spl0_68 ),
inference(boolean_simplification,[status(thm)],[f3730]) ).
thf(f3730,plain,
( ( ( ( $true
& ( sK6 @ sK7 ) )
=> ( sK6 @ sK39 ) )
= $true )
| ~ spl0_3
| ~ spl0_68 ),
inference(boolean_simplification,[status(thm)],[f3729]) ).
thf(f3729,plain,
( ( $true
= ( ( ( $true
| ( sK3 @ sK7 @ sK39 ) )
& ( sK6 @ sK7 ) )
=> ( sK6 @ sK39 ) ) )
| ~ spl0_3
| ~ spl0_68 ),
inference(superposition,[status(thm)],[f2721,f3668]) ).
thf(f3668,plain,
( ( ( sK2 @ sK7 @ sK39 )
= $true )
| ~ spl0_68 ),
inference(binary_proxy_clausification,[status(thm)],[f3632]) ).
thf(f3694,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[status(thm)],[f3693]) ).
thf(f3693,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_68 ),
inference(trivial_inequality_removal,[status(thm)],[f3692]) ).
thf(f3692,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_68 ),
inference(boolean_simplification,[status(thm)],[f3691]) ).
thf(f3691,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_68 ),
inference(boolean_simplification,[status(thm)],[f3690]) ).
thf(f3690,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK7 @ sK39 ) ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_68 ),
inference(forward_demodulation,[status(thm)],[f3689,f3668]) ).
thf(f3689,plain,
( ( ( ~ ( ( sK2 @ sK7 @ sK39 )
| ( sK3 @ sK7 @ sK39 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_68 ),
inference(boolean_simplification,[status(thm)],[f3678]) ).
thf(f3678,plain,
( ( $true
= ( ( ( sK2 @ sK7 @ sK39 )
| ( sK3 @ sK7 @ sK39 ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_68 ),
inference(superposition,[status(thm)],[f2880,f3667]) ).
thf(f2880,plain,
( ! [X0: a] :
( $true
= ( ( ( sK2 @ sK7 @ X0 )
| ( sK3 @ sK7 @ X0 ) )
=> ( sK6 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2875]) ).
thf(f2875,plain,
( ! [X0: a] :
( $true
= ( ( ( ( sK2 @ sK7 @ X0 )
| ( sK3 @ sK7 @ X0 ) )
& $true )
=> ( sK6 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f2721,f2861]) ).
thf(f2861,plain,
( ( $true
= ( sK6 @ sK7 ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f2851]) ).
thf(f2851,plain,
( ( $false
= ( ( sK6 @ sK7 )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2850]) ).
thf(f2850,plain,
( ( ( ( ( sK6 @ sK7 )
& $true )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2849]) ).
thf(f2849,plain,
( ( ( ( ( sK6 @ sK7 )
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| $true ) )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f2848,f204]) ).
thf(f204,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f203]) ).
thf(f203,definition,
( spl0_8
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f3627,plain,
( ~ spl0_3
| ~ spl0_67 ),
inference(avatar_contradiction_clause,[status(thm)],[f3626]) ).
thf(f3626,plain,
( $false
| ~ spl0_3
| ~ spl0_67 ),
inference(trivial_inequality_removal,[status(thm)],[f3625]) ).
thf(f3625,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_67 ),
inference(forward_demodulation,[status(thm)],[f3624,f3523]) ).
thf(f3523,plain,
( ( $false
= ( sK6 @ sK36 ) )
| ~ spl0_67 ),
inference(binary_proxy_clausification,[status(thm)],[f3511]) ).
thf(f3511,plain,
( ( $false
= ( ( ( sK2 @ sK35 @ sK36 )
& ( sK6 @ sK35 ) )
=> ( sK6 @ sK36 ) ) )
| ~ spl0_67 ),
inference(beta_eta_normalization,[status(thm)],[f3510]) ).
thf(f3510,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ sK35 @ Y0 )
& ( sK6 @ sK35 ) )
=> ( sK6 @ Y0 ) )
@ sK36 ) )
| ~ spl0_67 ),
inference(sigma_clausification,[status(thm)],[f3496]) ).
thf(f3496,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK35 @ Y0 )
& ( sK6 @ sK35 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_67 ),
inference(beta_eta_normalization,[status(thm)],[f3492]) ).
thf(f3492,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK35 )
= $false )
| ~ spl0_67 ),
inference(sigma_clausification,[status(thm)],[f3472]) ).
thf(f3472,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
| ~ spl0_67 ),
inference(avatar_component_clause,[status(thm)],[f3471]) ).
thf(f3471,definition,
( spl0_67
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_67])],[avatar_definition]) ).
thf(f3624,plain,
( ( $true
= ( sK6 @ sK36 ) )
| ~ spl0_3
| ~ spl0_67 ),
inference(boolean_simplification,[status(thm)],[f3623]) ).
thf(f3623,plain,
( ( ( $true
=> ( sK6 @ sK36 ) )
= $true )
| ~ spl0_3
| ~ spl0_67 ),
inference(forward_demodulation,[status(thm)],[f3622,f3592]) ).
thf(f3592,plain,
( ( $true
= ( sK6 @ sK35 ) )
| ~ spl0_67 ),
inference(binary_proxy_clausification,[status(thm)],[f3524]) ).
thf(f3524,plain,
( ( $true
= ( ( sK2 @ sK35 @ sK36 )
& ( sK6 @ sK35 ) ) )
| ~ spl0_67 ),
inference(binary_proxy_clausification,[status(thm)],[f3511]) ).
thf(f3622,plain,
( ( $true
= ( ( sK6 @ sK35 )
=> ( sK6 @ sK36 ) ) )
| ~ spl0_3
| ~ spl0_67 ),
inference(boolean_simplification,[status(thm)],[f3621]) ).
thf(f3621,plain,
( ( ( ( $true
& ( sK6 @ sK35 ) )
=> ( sK6 @ sK36 ) )
= $true )
| ~ spl0_3
| ~ spl0_67 ),
inference(boolean_simplification,[status(thm)],[f3620]) ).
thf(f3620,plain,
( ( ( ( ( $true
| ( sK3 @ sK35 @ sK36 ) )
& ( sK6 @ sK35 ) )
=> ( sK6 @ sK36 ) )
= $true )
| ~ spl0_3
| ~ spl0_67 ),
inference(superposition,[status(thm)],[f2721,f3595]) ).
thf(f3595,plain,
( ( $true
= ( sK2 @ sK35 @ sK36 ) )
| ~ spl0_67 ),
inference(boolean_simplification,[status(thm)],[f3594]) ).
thf(f3594,plain,
( ( $true
= ( ( sK2 @ sK35 @ sK36 )
& $true ) )
| ~ spl0_67 ),
inference(backward_demodulation,[status(thm)],[f3524,f3592]) ).
thf(f3476,plain,
( spl0_67
| spl0_68
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f3467,f203,f123,f3474,f3471]) ).
thf(f3467,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f3453]) ).
thf(f3453,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(not_proxy_clausification,[status(thm)],[f3074]) ).
thf(f3074,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f3071]) ).
thf(f3071,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f3058,f2863]) ).
thf(f2863,plain,
( ( $false
= ( sK6 @ sK8 ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2862]) ).
thf(f2862,plain,
( ( ( $true
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f2851,f2861]) ).
thf(f3058,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK8 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f3057]) ).
thf(f3057,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f204]) ).
thf(f2685,plain,
( spl0_28
| ~ spl0_4
| ~ spl0_16 ),
inference(avatar_split_clause,[status(thm)],[f2684,f519,f32,f1154]) ).
thf(f1154,definition,
( spl0_28
<=> ( $true
= ( sK3 @ sK19 @ sK20 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition]) ).
thf(f32,definition,
( spl0_4
<=> ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f519,definition,
( spl0_16
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f2684,plain,
( ( $true
= ( sK3 @ sK19 @ sK20 ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f2683]) ).
thf(f2683,plain,
( ( ( $false
| ( sK3 @ sK19 @ sK20 ) )
= $true )
| ~ spl0_4
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f1140,f1748]) ).
thf(f1748,plain,
( ( $false
= ( sK2 @ sK19 @ sK20 ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(not_proxy_clausification,[status(thm)],[f1723]) ).
thf(f1723,plain,
( ( $true
= ( ~ ( sK2 @ sK19 @ sK20 ) ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f1722]) ).
thf(f1722,plain,
( ( $true
= ( ( sK2 @ sK19 @ sK20 )
=> $false ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f1720,f1530]) ).
thf(f1530,plain,
( ( ( sK24 @ sK20 )
= $false )
| ~ spl0_4
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f1511]) ).
thf(f1511,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK24 @ Y0 ) )
=> ( sK24 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK19 @ Y0 )
=> ( sK24 @ Y0 ) ) ) )
=> ( sK24 @ sK20 ) )
= $false )
| ~ spl0_4
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f1507]) ).
thf(f1507,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK19 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK20 ) )
@ sK24 ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f1491]) ).
thf(f1491,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK19 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK20 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f1490]) ).
thf(f1490,plain,
( ( ( $false
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK19 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK20 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f1341,f1484]) ).
thf(f1484,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK19 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f1341]) ).
thf(f1341,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK19 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK19 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK20 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f1335]) ).
thf(f1335,plain,
( ( ( $true
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK19 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK19 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK20 ) ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f1315,f1137]) ).
thf(f1137,plain,
( ( $true
= ( sK10 @ sK19 ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f1125]) ).
thf(f1125,plain,
( ( $true
= ( ( ( sK2 @ sK19 @ sK20 )
| ( sK3 @ sK19 @ sK20 ) )
& ( sK10 @ sK19 ) ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f1118]) ).
thf(f1118,plain,
( ( ( ( ( ( sK2 @ sK19 @ sK20 )
| ( sK3 @ sK19 @ sK20 ) )
& ( sK10 @ sK19 ) )
=> ( sK10 @ sK20 ) )
= $false )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f1117]) ).
thf(f1117,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK2 @ sK19 @ Y0 )
| ( sK3 @ sK19 @ Y0 ) )
& ( sK10 @ sK19 ) )
=> ( sK10 @ Y0 ) )
@ sK20 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f1112]) ).
thf(f1112,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK2 @ sK19 @ Y0 )
| ( sK3 @ sK19 @ Y0 ) )
& ( sK10 @ sK19 ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f1107]) ).
thf(f1107,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) )
@ sK19 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f520]) ).
thf(f520,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
= $false )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f519]) ).
thf(f1315,plain,
( ! [X0: a] :
( ( ( sK10 @ X0 )
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK20 ) ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_16 ),
inference(not_proxy_clausification,[status(thm)],[f1134]) ).
thf(f1134,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK10 @ X0 )
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK20 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f1130]) ).
thf(f1130,plain,
( ! [X0: a] :
( $true
= ( ( ( sK10 @ X0 )
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK20 ) ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f610,f1127]) ).
thf(f1127,plain,
( ( $false
= ( sK10 @ sK20 ) )
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f1126]) ).
thf(f1126,plain,
( ( ( $true
=> ( sK10 @ sK20 ) )
= $false )
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f1118,f1125]) ).
thf(f610,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK10 @ X1 )
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X1 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ X2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X1 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ X2 ) ) ) ) )
=> ( sK10 @ X2 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f609]) ).
thf(f609,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ X1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ X1 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( sK10 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f605]) ).
thf(f605,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ X1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ X1 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f604]) ).
thf(f604,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK10 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f543]) ).
thf(f543,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f504]) ).
thf(f504,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f500]) ).
thf(f500,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
=> ( sK10 @ sK5 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f499]) ).
thf(f499,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f1720,plain,
( ! [X1: a] :
( ( ( sK2 @ sK19 @ X1 )
=> ( sK24 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f1719]) ).
thf(f1719,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ sK19 @ Y0 )
=> ( sK24 @ Y0 ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(pi_clausification,[status(thm)],[f1714]) ).
thf(f1714,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK19 @ Y0 )
=> ( sK24 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f1713]) ).
thf(f1713,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK19 @ Y0 )
=> ( sK24 @ Y0 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f1531,f1712]) ).
thf(f1712,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK24 @ Y0 ) )
=> ( sK24 @ Y1 ) ) ) ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f1531]) ).
thf(f1531,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK24 @ Y0 ) )
=> ( sK24 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK19 @ Y0 )
=> ( sK24 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f1511]) ).
thf(f1140,plain,
( ( $true
= ( ( sK2 @ sK19 @ sK20 )
| ( sK3 @ sK19 @ sK20 ) ) )
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f1139]) ).
thf(f1139,plain,
( ( ( ( ( sK2 @ sK19 @ sK20 )
| ( sK3 @ sK19 @ sK20 ) )
& $true )
= $true )
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f1125,f1137]) ).
thf(f2679,plain,
( ~ spl0_4
| ~ spl0_16
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f2678]) ).
thf(f2678,plain,
( $false
| ~ spl0_4
| ~ spl0_16
| ~ spl0_28 ),
inference(trivial_inequality_removal,[status(thm)],[f2677]) ).
thf(f2677,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_28 ),
inference(forward_demodulation,[status(thm)],[f2669,f1781]) ).
thf(f1781,plain,
( ( $false
= ( sK27 @ sK20 ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f1763]) ).
thf(f1763,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK19 @ Y0 )
=> ( sK27 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK27 @ Y0 ) )
=> ( sK27 @ Y1 ) ) ) ) )
=> ( sK27 @ sK20 ) ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f1757]) ).
thf(f1757,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK19 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 ) )
@ sK27 )
= $false )
| ~ spl0_4
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f1484]) ).
thf(f2669,plain,
( ( $true
= ( sK27 @ sK20 ) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f2664]) ).
thf(f2664,plain,
( ( $true
= ( $true
=> ( sK27 @ sK20 ) ) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_28 ),
inference(superposition,[status(thm)],[f2651,f1155]) ).
thf(f1155,plain,
( ( $true
= ( sK3 @ sK19 @ sK20 ) )
| ~ spl0_28 ),
inference(avatar_component_clause,[status(thm)],[f1154]) ).
thf(f2651,plain,
( ! [X1: a] :
( $true
= ( ( sK3 @ sK19 @ X1 )
=> ( sK27 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f2650]) ).
thf(f2650,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ sK19 @ Y0 )
=> ( sK27 @ Y0 ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(pi_clausification,[status(thm)],[f2633]) ).
thf(f2633,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK19 @ Y0 )
=> ( sK27 @ Y0 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f2632]) ).
thf(f2632,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK19 @ Y0 )
=> ( sK27 @ Y0 ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f1782,f2630]) ).
thf(f2630,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK27 @ Y0 ) )
=> ( sK27 @ Y1 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f1782]) ).
thf(f1782,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK19 @ Y0 )
=> ( sK27 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK27 @ Y0 ) )
=> ( sK27 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f1763]) ).
thf(f1097,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f1096]) ).
thf(f1096,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f1095]) ).
thf(f1095,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f1088,f720]) ).
thf(f720,plain,
( ( $false
= ( sK16 @ sK12 ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f719]) ).
thf(f719,plain,
( ( ( $true
=> ( sK16 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_15 ),
inference(backward_demodulation,[status(thm)],[f694,f718]) ).
thf(f718,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK16 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK16 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK16 @ Y0 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f694]) ).
thf(f694,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK16 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK16 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK16 @ Y0 ) ) ) )
=> ( sK16 @ sK12 ) ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f691]) ).
thf(f691,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK16 ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f581]) ).
thf(f581,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f575]) ).
thf(f575,plain,
( ( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(not_proxy_clausification,[status(thm)],[f553]) ).
thf(f553,plain,
( ( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f551]) ).
thf(f551,plain,
( ( $true
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f548,f532]) ).
thf(f532,plain,
( ( ( sK10 @ sK12 )
= $false )
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f531]) ).
thf(f531,plain,
( ( ( $true
=> ( sK10 @ sK12 ) )
= $false )
| ~ spl0_15 ),
inference(backward_demodulation,[status(thm)],[f528,f530]) ).
thf(f530,plain,
( ( ( ( sK2 @ sK4 @ sK12 )
| ( sK3 @ sK4 @ sK12 ) )
= $true )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f528]) ).
thf(f528,plain,
( ( ( ( ( sK2 @ sK4 @ sK12 )
| ( sK3 @ sK4 @ sK12 ) )
=> ( sK10 @ sK12 ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f524]) ).
thf(f524,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK10 @ Y0 ) )
@ sK12 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f517]) ).
thf(f517,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f516]) ).
thf(f516,definition,
( spl0_15
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f548,plain,
( ! [X1: a] :
( $true
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ X1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ X1 ) ) ) )
=> ( sK10 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f547]) ).
thf(f547,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK10 @ Y0 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f546]) ).
thf(f546,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f545]) ).
thf(f545,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK10 @ Y0 ) ) )
& $true ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f504,f543]) ).
thf(f1088,plain,
( ( $true
= ( sK16 @ sK12 ) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f1086]) ).
thf(f1086,plain,
( ( ( $true
=> ( sK16 @ sK12 ) )
= $true )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f1073,f536]) ).
thf(f536,plain,
( ( ( sK3 @ sK4 @ sK12 )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f535]) ).
thf(f535,definition,
( spl0_17
<=> ( ( sK3 @ sK4 @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f1073,plain,
( ! [X1: a] :
( ( ( sK3 @ sK4 @ X1 )
=> ( sK16 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f1072]) ).
thf(f1072,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK16 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_15 ),
inference(pi_clausification,[status(thm)],[f874]) ).
thf(f874,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK16 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f718]) ).
thf(f710,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f709]) ).
thf(f709,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f708]) ).
thf(f708,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[status(thm)],[f701,f598]) ).
thf(f598,plain,
( ( ( sK14 @ sK12 )
= $false )
| ~ spl0_4
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f592]) ).
thf(f592,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) ) )
=> ( sK14 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f590]) ).
thf(f590,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK14 ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f585]) ).
thf(f585,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f584]) ).
thf(f584,plain,
( ( ( $false
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_15 ),
inference(backward_demodulation,[status(thm)],[f575,f581]) ).
thf(f701,plain,
( ( ( sK14 @ sK12 )
= $true )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f700]) ).
thf(f700,plain,
( ( ( $true
=> ( sK14 @ sK12 ) )
= $true )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f658,f539]) ).
thf(f539,plain,
( ( ( sK2 @ sK4 @ sK12 )
= $true )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f538]) ).
thf(f538,definition,
( spl0_18
<=> ( ( sK2 @ sK4 @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f658,plain,
( ! [X1: a] :
( $true
= ( ( sK2 @ sK4 @ X1 )
=> ( sK14 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f657]) ).
thf(f657,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK14 @ Y0 ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(pi_clausification,[status(thm)],[f633]) ).
thf(f633,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f599]) ).
thf(f599,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f592]) ).
thf(f540,plain,
( spl0_17
| spl0_18
| ~ spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f533,f516,f538,f535]) ).
thf(f533,plain,
( ( ( sK2 @ sK4 @ sK12 )
= $true )
| ( ( sK3 @ sK4 @ sK12 )
= $true )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f530]) ).
thf(f521,plain,
( spl0_15
| spl0_16
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f512,f32,f22,f519,f516]) ).
thf(f22,definition,
( spl0_1
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f512,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f509]) ).
thf(f509,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f508]) ).
thf(f508,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f507]) ).
thf(f507,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f497,f506]) ).
thf(f506,plain,
( ( $false
= ( sK10 @ sK5 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f505]) ).
thf(f505,plain,
( ( $false
= ( $true
=> ( sK10 @ sK5 ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f500,f504]) ).
thf(f497,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK5 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f496]) ).
thf(f496,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f493,plain,
( spl0_13
| spl0_14
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f486,f126,f491,f488]) ).
thf(f486,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f373]) ).
thf(f373,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f355]) ).
thf(f355,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
=> ( sK6 @ sK9 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f351]) ).
thf(f351,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) )
@ sK9 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f127]) ).
thf(f285,plain,
( spl0_11
| spl0_12
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f276,f200,f123,f283,f280]) ).
thf(f276,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_5
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f271]) ).
thf(f271,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(not_proxy_clausification,[status(thm)],[f232]) ).
thf(f232,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f229]) ).
thf(f229,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f218,f168]) ).
thf(f168,plain,
( ( $false
= ( sK6 @ sK8 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
( ( ( ( ( sK6 @ sK7 )
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f163]) ).
thf(f163,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK7 )
& ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ Y0 ) )
@ sK8 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f149]) ).
thf(f149,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK7 )
& ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f148]) ).
thf(f148,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK6 @ Y1 ) ) )
@ sK7 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f124]) ).
thf(f218,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK8 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f217]) ).
thf(f217,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f201]) ).
thf(f269,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f268]) ).
thf(f268,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f267]) ).
thf(f267,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f26,f33]) ).
thf(f26,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl0_2
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f205,plain,
( spl0_7
| spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f198,f123,f203,f200]) ).
thf(f198,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
= $true )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f188]) ).
thf(f188,plain,
( ( ( $true
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
= $true )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f169,f187]) ).
thf(f187,plain,
( ( $true
= ( sK6 @ sK7 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
( ( $true
= ( ( sK6 @ sK7 )
& ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f164]) ).
thf(f132,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f131]) ).
thf(f131,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f23,f30]) ).
thf(f128,plain,
( spl0_5
| spl0_6
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f119,f29,f25,f126,f123]) ).
thf(f119,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f46,f39]) ).
thf(f39,plain,
( ( ( sK6 @ sK5 )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK5 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f46,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f34,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f20,f32,f29]) ).
thf(f20,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
!= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ sK4 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ sK4 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK4 @ Y2 )
| ( sK3 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ sK4 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ sK4 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK4 @ Y2 )
| ( sK3 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK4 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( Y0 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( Y0 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X7 )
& ( ( X0 @ X7 @ X6 )
| ( X1 @ X7 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
= ( ^ [X8: a,X9: a] :
! [X10: a > $o] :
( ( ! [X11: a,X12: a] :
( ( ( ! [X13: a > $o] :
( ( ! [X14: a] :
( ( X1 @ X12 @ X14 )
=> ( X13 @ X14 ) )
& ! [X15: a,X16: a] :
( ( ( X13 @ X16 )
& ( X1 @ X16 @ X15 ) )
=> ( X13 @ X15 ) ) )
=> ( X13 @ X11 ) )
| ! [X17: a > $o] :
( ( ! [X18: a,X19: a] :
( ( ( X17 @ X19 )
& ( X0 @ X19 @ X18 ) )
=> ( X17 @ X18 ) )
& ! [X20: a] :
( ( X0 @ X12 @ X20 )
=> ( X17 @ X20 ) ) )
=> ( X17 @ X11 ) ) )
& ( X10 @ X12 ) )
=> ( X10 @ X11 ) )
& ! [X21: a] :
( ( ! [X22: a > $o] :
( ( ! [X23: a,X24: a] :
( ( ( X1 @ X23 @ X24 )
& ( X22 @ X23 ) )
=> ( X22 @ X24 ) )
& ! [X25: a] :
( ( X1 @ X8 @ X25 )
=> ( X22 @ X25 ) ) )
=> ( X22 @ X21 ) )
| ! [X26: a > $o] :
( ( ! [X27: a] :
( ( X0 @ X8 @ X27 )
=> ( X26 @ X27 ) )
& ! [X28: a,X29: a] :
( ( ( X0 @ X29 @ X28 )
& ( X26 @ X29 ) )
=> ( X26 @ X28 ) ) )
=> ( X26 @ X21 ) ) )
=> ( X10 @ X21 ) ) )
=> ( X10 @ X9 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ! [X8: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X6 @ X5 )
=> ( X8 @ X5 ) )
& ! [X11: a,X10: a] :
( ( ( X8 @ X10 )
& ( X1 @ X10 @ X11 ) )
=> ( X8 @ X11 ) ) )
=> ( X8 @ X7 ) )
| ! [X8: a > $o] :
( ( ! [X11: a,X10: a] :
( ( ( X8 @ X10 )
& ( X0 @ X10 @ X11 ) )
=> ( X8 @ X11 ) )
& ! [X5: a] :
( ( X0 @ X6 @ X5 )
=> ( X8 @ X5 ) ) )
=> ( X8 @ X7 ) ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ! [X8: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X1 @ X6 @ X7 )
& ( X8 @ X6 ) )
=> ( X8 @ X7 ) )
& ! [X9: a] :
( ( X1 @ X2 @ X9 )
=> ( X8 @ X9 ) ) )
=> ( X8 @ X5 ) )
| ! [X8: a > $o] :
( ( ! [X9: a] :
( ( X0 @ X2 @ X9 )
=> ( X8 @ X9 ) )
& ! [X7: a,X6: a] :
( ( ( X0 @ X6 @ X7 )
& ( X8 @ X6 ) )
=> ( X8 @ X7 ) ) )
=> ( X8 @ X5 ) ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ! [X8: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X6 @ X5 )
=> ( X8 @ X5 ) )
& ! [X11: a,X10: a] :
( ( ( X8 @ X10 )
& ( X1 @ X10 @ X11 ) )
=> ( X8 @ X11 ) ) )
=> ( X8 @ X7 ) )
| ! [X8: a > $o] :
( ( ! [X11: a,X10: a] :
( ( ( X8 @ X10 )
& ( X0 @ X10 @ X11 ) )
=> ( X8 @ X11 ) )
& ! [X5: a] :
( ( X0 @ X6 @ X5 )
=> ( X8 @ X5 ) ) )
=> ( X8 @ X7 ) ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ! [X8: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X1 @ X6 @ X7 )
& ( X8 @ X6 ) )
=> ( X8 @ X7 ) )
& ! [X9: a] :
( ( X1 @ X2 @ X9 )
=> ( X8 @ X9 ) ) )
=> ( X8 @ X5 ) )
| ! [X8: a > $o] :
( ( ! [X9: a] :
( ( X0 @ X2 @ X9 )
=> ( X8 @ X9 ) )
& ! [X7: a,X6: a] :
( ( ( X0 @ X6 @ X7 )
& ( X8 @ X6 ) )
=> ( X8 @ X7 ) ) )
=> ( X8 @ X5 ) ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.syb1jpMQsL/DTF2THF_16357.p',cTHM251A_pme) ).
thf(f27,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f25,f22]) ).
thf(f19,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV150^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n015.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:41:16 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV150^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory (Relations)
% 0.29/0.46 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_1188 [Bro09]
% 0.29/0.46 % : tps_1189 [Bro09]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.78 v9.1.0, 0.75 v9.0.0, 0.90 v8.2.0, 0.92 v8.1.0, 0.91 v7.5.0, 0.86 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 1.00 v6.3.0, 0.80 v6.2.0, 0.86 v6.1.0, 1.00 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.46 % Number of connectives : 82 ( 0 ~; 4 |; 12 &; 48 @)
% 0.29/0.46 % ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 3 ( 3 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.46 % Number of variables : 30 ( 4 ^; 26 !; 0 ?; 30 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cTHM251A_pme,conjecture,
% 0.29/0.46 ! [R: a > a > $o,S: a > a > $o] :
% 0.29/0.46 ( ( ^ [Xp: a,Xq: a] :
% 0.29/0.46 ! [Xq0: a > $o] :
% 0.29/0.46 ( ( ! [Xw: a] :
% 0.29/0.46 ( ( ( R @ Xp @ Xw )
% 0.29/0.46 | ( S @ Xp @ Xw ) )
% 0.29/0.46 => ( Xq0 @ Xw ) )
% 0.29/0.46 & ! [Xu: a,Xv: a] :
% 0.29/0.46 ( ( ( Xq0 @ Xu )
% 0.29/0.46 & ( ( R @ Xu @ Xv )
% 0.29/0.46 | ( S @ Xu @ Xv ) ) )
% 0.29/0.46 => ( Xq0 @ Xv ) ) )
% 0.29/0.46 => ( Xq0 @ Xq ) ) )
% 0.29/0.46 = ( ^ [Xp: a,Xq: a] :
% 0.29/0.46 ! [Xq0: a > $o] :
% 0.29/0.46 ( ( ! [Xw: a] :
% 0.29/0.46 ( ( ! [Xq1: a > $o] :
% 0.29/0.46 ( ( ! [Xw0: a] :
% 0.29/0.46 ( ( R @ Xp @ Xw0 )
% 0.29/0.46 => ( Xq1 @ Xw0 ) )
% 0.29/0.46 & ! [Xu: a,Xv: a] :
% 0.29/0.46 ( ( ( Xq1 @ Xu )
% 0.29/0.46 & ( R @ Xu @ Xv ) )
% 0.29/0.46 => ( Xq1 @ Xv ) ) )
% 0.29/0.46 => ( Xq1 @ Xw ) )
% 0.29/0.46 | ! [Xq1: a > $o] :
% 0.29/0.46 ( ( ! [Xw0: a] :
% 0.29/0.46 ( ( S @ Xp @ Xw0 )
% 0.29/0.46 => ( Xq1 @ Xw0 ) )
% 0.29/0.46 & ! [Xu: a,Xv: a] :
% 0.29/0.46 ( ( ( Xq1 @ Xu )
% 0.29/0.46 & ( S @ Xu @ Xv ) )
% 0.29/0.46 => ( Xq1 @ Xv ) ) )
% 0.29/0.46 => ( Xq1 @ Xw ) ) )
% 0.29/0.46 => ( Xq0 @ Xw ) )
% 0.29/0.46 & ! [Xu: a,Xv: a] :
% 0.29/0.46 ( ( ( Xq0 @ Xu )
% 0.29/0.46 & ( ! [Xq1: a > $o] :
% 0.29/0.46 ( ( ! [Xw: a] :
% 0.29/0.46 ( ( R @ Xu @ Xw )
% 0.29/0.46 => ( Xq1 @ Xw ) )
% 0.29/0.46 & ! [Xu0: a,Xv0: a] :
% 0.29/0.46 ( ( ( Xq1 @ Xu0 )
% 0.29/0.46 & ( R @ Xu0 @ Xv0 ) )
% 0.29/0.46 => ( Xq1 @ Xv0 ) ) )
% 0.29/0.46 => ( Xq1 @ Xv ) )
% 0.29/0.46 | ! [Xq1: a > $o] :
% 0.29/0.46 ( ( ! [Xw: a] :
% 0.29/0.46 ( ( S @ Xu @ Xw )
% 0.29/0.46 => ( Xq1 @ Xw ) )
% 0.29/0.46 & ! [Xu0: a,Xv0: a] :
% 0.29/0.46 ( ( ( Xq1 @ Xu0 )
% 0.29/0.46 & ( S @ Xu0 @ Xv0 ) )
% 0.29/0.46 => ( Xq1 @ Xv0 ) ) )
% 0.29/0.46 => ( Xq1 @ Xv ) ) ) )
% 0.29/0.46 => ( Xq0 @ Xv ) ) )
% 0.29/0.46 => ( Xq0 @ Xq ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.48/1.28 ---- Embedded in THF ---
% 1.48/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.28 %%% Generated on Tue Feb 24 12:41:17 EST 2026
% 1.48/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.28 %%% Logic specification used:
% 1.48/1.28 %%% thf(spec, logic, $$dhol).
% 1.48/1.28
% 1.48/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.syb1jpMQsL/DTF2DTF16357.p
% See solution above
% 1.48/1.28 ------------------------
% 1.48/1.29 ---- Cleaned THF ---
% 1.48/1.29 thf(a_type,type,
% 1.48/1.29 a: $tType ).
% 1.48/1.29
% 1.48/1.29 thf(cTHM251A_pme,conjecture,
% 1.48/1.29 ! [R: a > a > $o,S: a > a > $o] :
% 1.48/1.29 ( ( ^ [Xp: a,Xq: a] :
% 1.48/1.29 ! [Xq0: a > $o] :
% 1.48/1.29 ( ( ! [Xw: a] :
% 1.48/1.29 ( ( ( R @ Xp @ Xw )
% 1.48/1.29 | ( S @ Xp @ Xw ) )
% 1.48/1.29 => ( Xq0 @ Xw ) )
% 1.48/1.29 & ! [Xu: a,Xv: a] :
% 1.48/1.29 ( ( ( Xq0 @ Xu )
% 1.48/1.29 & ( ( R @ Xu @ Xv )
% 1.48/1.29 | ( S @ Xu @ Xv ) ) )
% 1.48/1.29 => ( Xq0 @ Xv ) ) )
% 1.48/1.29 => ( Xq0 @ Xq ) ) )
% 1.48/1.29 = ( ^ [Xp: a,Xq: a] :
% 1.48/1.29 ! [Xq0: a > $o] :
% 1.48/1.29 ( ( ! [Xw: a] :
% 1.48/1.29 ( ( ! [Xq1: a > $o] :
% 1.48/1.29 ( ( ! [Xw0: a] :
% 1.48/1.29 ( ( R @ Xp @ Xw0 )
% 1.48/1.29 => ( Xq1 @ Xw0 ) )
% 1.48/1.29 & ! [Xu: a,Xv: a] :
% 1.48/1.29 ( ( ( Xq1 @ Xu )
% 1.48/1.29 & ( R @ Xu @ Xv ) )
% 1.48/1.29 => ( Xq1 @ Xv ) ) )
% 1.48/1.29 => ( Xq1 @ Xw ) )
% 1.48/1.29 | ! [Xq1: a > $o] :
% 1.48/1.29 ( ( ! [Xw0: a] :
% 1.48/1.29 ( ( S @ Xp @ Xw0 )
% 1.48/1.29 => ( Xq1 @ Xw0 ) )
% 1.48/1.29 & ! [Xu: a,Xv: a] :
% 1.48/1.29 ( ( ( Xq1 @ Xu )
% 1.48/1.29 & ( S @ Xu @ Xv ) )
% 1.48/1.29 => ( Xq1 @ Xv ) ) )
% 1.48/1.29 => ( Xq1 @ Xw ) ) )
% 1.48/1.29 => ( Xq0 @ Xw ) )
% 1.48/1.29 & ! [Xu: a,Xv: a] :
% 1.48/1.29 ( ( ( Xq0 @ Xu )
% 1.48/1.29 & ( ! [Xq1: a > $o] :
% 1.48/1.29 ( ( ! [Xw: a] :
% 1.48/1.29 ( ( R @ Xu @ Xw )
% 1.48/1.29 => ( Xq1 @ Xw ) )
% 1.48/1.29 & ! [Xu0: a,Xv0: a] :
% 1.48/1.29 ( ( ( Xq1 @ Xu0 )
% 1.48/1.29 & ( R @ Xu0 @ Xv0 ) )
% 1.48/1.29 => ( Xq1 @ Xv0 ) ) )
% 1.48/1.29 => ( Xq1 @ Xv ) )
% 1.48/1.29 | ! [Xq1: a > $o] :
% 1.48/1.29 ( ( ! [Xw: a] :
% 1.48/1.29 ( ( S @ Xu @ Xw )
% 1.48/1.29 => ( Xq1 @ Xw ) )
% 1.48/1.29 & ! [Xu0: a,Xv0: a] :
% 1.48/1.29 ( ( ( Xq1 @ Xu0 )
% 1.48/1.29 & ( S @ Xu0 @ Xv0 ) )
% 1.48/1.29 => ( Xq1 @ Xv0 ) ) )
% 1.48/1.29 => ( Xq1 @ Xv ) ) ) )
% 1.48/1.29 => ( Xq0 @ Xv ) ) )
% 1.48/1.29 => ( Xq0 @ Xq ) ) ) ) ).
% 1.48/1.29 ------------------------
% 1.67/1.31 % (16629)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/183Mi)
% 1.67/1.31 % (16630)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 DTF2THF_16357 for (2999ds/4Mi)
% 1.67/1.31 % (16630)Instruction limit reached!
% 1.67/1.31 % (16630)------------------------------
% 1.67/1.31 % (16630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (16630)Termination reason: Unknown
% 1.67/1.31 % (16630)Termination phase: Preprocessing 3
% 1.67/1.31
% 1.67/1.31 % (16630)Memory used [KB]: 1023
% 1.67/1.31 % (16630)Time elapsed: 0.002 s
% 1.67/1.31 % (16630)Instructions burned: 4 (million)
% 1.67/1.31 % (16630)------------------------------
% 1.67/1.31 % (16630)------------------------------
% 1.67/1.32 % (16631)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 DTF2THF_16357 for (2999ds/27Mi)
% 1.67/1.32 % (16632)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/2Mi)
% 1.67/1.32 % (16633)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/2Mi)
% 1.67/1.32 % (16634)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/275Mi)
% 1.67/1.32 % (16635)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/18Mi)
% 1.67/1.32 % (16632)Instruction limit reached!
% 1.67/1.32 % (16632)------------------------------
% 1.67/1.32 % (16632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (16632)Termination reason: Unknown
% 1.67/1.32 % (16632)Termination phase: shuffling
% 1.67/1.32
% 1.67/1.32 % (16632)Memory used [KB]: 1023
% 1.67/1.32 % (16632)Time elapsed: 0.003 s
% 1.67/1.32 % (16632)Instructions burned: 2 (million)
% 1.67/1.32 % (16632)------------------------------
% 1.67/1.32 % (16632)------------------------------
% 1.67/1.32 % (16633)Instruction limit reached!
% 1.67/1.32 % (16633)------------------------------
% 1.67/1.32 % (16633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (16633)Termination reason: Unknown
% 1.67/1.32 % (16633)Termination phase: shuffling
% 1.67/1.32
% 1.67/1.32 % (16633)Memory used [KB]: 1023
% 1.67/1.32 % (16633)Time elapsed: 0.003 s
% 1.67/1.32 % (16633)Instructions burned: 2 (million)
% 1.67/1.32 % (16633)------------------------------
% 1.67/1.32 % (16633)------------------------------
% 1.67/1.32 % (16636)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/3Mi)
% 1.67/1.32 % (16636)Instruction limit reached!
% 1.67/1.32 % (16636)------------------------------
% 1.67/1.32 % (16636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (16636)Termination reason: Unknown
% 1.67/1.32 % (16636)Termination phase: Property scanning
% 1.67/1.32
% 1.67/1.32 % (16636)Memory used [KB]: 1023
% 1.67/1.32 % (16636)Time elapsed: 0.003 s
% 1.67/1.32 % (16636)Instructions burned: 5 (million)
% 1.67/1.32 % (16636)------------------------------
% 1.67/1.32 % (16636)------------------------------
% 1.67/1.33 % (16635)Instruction limit reached!
% 1.67/1.33 % (16635)------------------------------
% 1.67/1.33 % (16635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (16635)Termination reason: Unknown
% 1.67/1.33 % (16635)Termination phase: Saturation
% 1.67/1.33
% 1.67/1.33 % (16635)Memory used [KB]: 5628
% 1.67/1.33 % (16635)Time elapsed: 0.012 s
% 1.67/1.33 % (16635)Instructions burned: 19 (million)
% 1.67/1.33 % (16635)------------------------------
% 1.67/1.33 % (16635)------------------------------
% 1.67/1.33 % (16631)Instruction limit reached!
% 1.67/1.33 % (16631)------------------------------
% 1.67/1.33 % (16631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (16631)Termination reason: Unknown
% 1.67/1.33 % (16631)Termination phase: Saturation
% 1.67/1.33
% 1.67/1.33 % (16631)Memory used [KB]: 5628
% 1.67/1.33 % (16631)Time elapsed: 0.016 s
% 1.67/1.33 % (16631)Instructions burned: 27 (million)
% 1.67/1.33 % (16631)------------------------------
% 1.67/1.33 % (16631)------------------------------
% 1.67/1.33 % (16639)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/3Mi)
% 1.67/1.33 % (16639)Instruction limit reached!
% 1.67/1.33 % (16639)------------------------------
% 1.67/1.33 % (16639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (16639)Termination reason: Unknown
% 1.67/1.33 % (16639)Termination phase: Property scanning
% 1.67/1.33
% 1.67/1.33 % (16639)Memory used [KB]: 1023
% 1.67/1.33 % (16639)Time elapsed: 0.003 s
% 1.67/1.33 % (16639)Instructions burned: 5 (million)
% 1.67/1.33 % (16639)------------------------------
% 1.67/1.33 % (16639)------------------------------
% 1.67/1.33 % (16637)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 DTF2THF_16357 for (2999ds/37Mi)
% 1.67/1.33 % (16638)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 DTF2THF_16357 for (2999ds/15Mi)
% 1.67/1.34 % (16642)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/16Mi)
% 1.67/1.34 % (16638)Instruction limit reached!
% 1.67/1.34 % (16638)------------------------------
% 1.67/1.34 % (16638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (16638)Termination reason: Unknown
% 1.67/1.34 % (16638)Termination phase: Saturation
% 1.67/1.34
% 1.67/1.34 % (16638)Memory used [KB]: 5756
% 1.67/1.34 % (16638)Time elapsed: 0.010 s
% 1.67/1.34 % (16638)Instructions burned: 15 (million)
% 1.67/1.34 % (16638)------------------------------
% 1.67/1.34 % (16638)------------------------------
% 1.67/1.34 % (16640)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 DTF2THF_16357 for (2999ds/1041Mi)
% 1.67/1.35 % (16641)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/7Mi)
% 1.67/1.35 % (16642)Instruction limit reached!
% 1.67/1.35 % (16642)------------------------------
% 1.67/1.35 % (16642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (16642)Termination reason: Unknown
% 1.67/1.35 % (16642)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (16642)Memory used [KB]: 5756
% 1.67/1.35 % (16642)Time elapsed: 0.007 s
% 1.67/1.35 % (16642)Instructions burned: 16 (million)
% 1.67/1.35 % (16642)------------------------------
% 1.67/1.35 % (16642)------------------------------
% 1.67/1.35 % (16641)Instruction limit reached!
% 1.67/1.35 % (16641)------------------------------
% 1.67/1.35 % (16641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (16641)Termination reason: Unknown
% 1.67/1.35 % (16641)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (16641)Memory used [KB]: 1023
% 1.67/1.35 % (16641)Time elapsed: 0.006 s
% 1.67/1.35 % (16641)Instructions burned: 8 (million)
% 1.67/1.35 % (16641)------------------------------
% 1.67/1.35 % (16641)------------------------------
% 1.67/1.35 % (16637)Instruction limit reached!
% 1.67/1.35 % (16637)------------------------------
% 1.67/1.35 % (16637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (16637)Termination reason: Unknown
% 1.67/1.35 % (16637)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (16637)Memory used [KB]: 5628
% 1.67/1.35 % (16637)Time elapsed: 0.022 s
% 1.67/1.35 % (16637)Instructions burned: 38 (million)
% 1.67/1.35 % (16637)------------------------------
% 1.67/1.35 % (16637)------------------------------
% 1.67/1.36 % (16644)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 DTF2THF_16357 for (2999ds/3Mi)
% 1.67/1.36 % (16644)Instruction limit reached!
% 1.67/1.36 % (16644)------------------------------
% 1.67/1.36 % (16644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (16644)Termination reason: Unknown
% 1.67/1.36 % (16644)Termination phase: Property scanning
% 1.67/1.36
% 1.67/1.36 % (16644)Memory used [KB]: 1023
% 1.67/1.36 % (16644)Time elapsed: 0.003 s
% 1.67/1.36 % (16644)Instructions burned: 5 (million)
% 1.67/1.36 % (16644)------------------------------
% 1.67/1.36 % (16644)------------------------------
% 1.67/1.36 % (16643)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 DTF2THF_16357 for (2999ds/3Mi)
% 1.67/1.36 % (16629)Instruction limit reached!
% 1.67/1.36 % (16629)------------------------------
% 1.67/1.36 % (16629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (16629)Termination reason: Unknown
% 1.67/1.36 % (16629)Termination phase: Saturation
% 1.67/1.36
% 1.67/1.36 % (16629)Memory used [KB]: 6268
% 1.67/1.36 % (16629)Time elapsed: 0.054 s
% 1.67/1.36 % (16629)Instructions burned: 184 (million)
% 1.67/1.36 % (16629)------------------------------
% 1.67/1.36 % (16629)------------------------------
% 1.67/1.36 % (16643)Instruction limit reached!
% 1.67/1.36 % (16643)------------------------------
% 1.67/1.36 % (16643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (16643)Termination reason: Unknown
% 1.67/1.36 % (16643)Termination phase: Preprocessing 3
% 1.67/1.36
% 1.67/1.36 % (16643)Memory used [KB]: 1023
% 1.67/1.36 % (16643)Time elapsed: 0.004 s
% 1.67/1.36 % (16643)Instructions burned: 4 (million)
% 1.67/1.36 % (16643)------------------------------
% 1.67/1.36 % (16643)------------------------------
% 1.67/1.37 % (16645)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/7Mi)
% 1.67/1.37 % (16647)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/4Mi)
% 1.67/1.37 % (16648)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/18Mi)
% 1.67/1.37 % (16647)Instruction limit reached!
% 1.67/1.37 % (16647)------------------------------
% 1.67/1.37 % (16647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (16647)Termination reason: Unknown
% 1.67/1.37 % (16647)Termination phase: Property scanning
% 1.67/1.37
% 1.67/1.37 % (16647)Memory used [KB]: 1023
% 1.67/1.37 % (16647)Time elapsed: 0.003 s
% 1.67/1.37 % (16647)Instructions burned: 5 (million)
% 1.67/1.37 % (16647)------------------------------
% 1.67/1.37 % (16647)------------------------------
% 1.67/1.37 % (16646)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/3Mi)
% 1.67/1.37 % (16645)Instruction limit reached!
% 1.67/1.37 % (16645)------------------------------
% 1.67/1.37 % (16645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (16645)Termination reason: Unknown
% 1.67/1.37 % (16645)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (16645)Memory used [KB]: 5500
% 1.67/1.37 % (16645)Time elapsed: 0.006 s
% 1.67/1.37 % (16645)Instructions burned: 8 (million)
% 1.67/1.37 % (16645)------------------------------
% 1.67/1.37 % (16645)------------------------------
% 1.67/1.37 % (16646)Instruction limit reached!
% 1.67/1.37 % (16646)------------------------------
% 1.67/1.37 % (16646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (16646)Termination reason: Unknown
% 1.67/1.37 % (16646)Termination phase: Property scanning
% 1.67/1.37
% 1.67/1.37 % (16646)Memory used [KB]: 1023
% 1.67/1.37 % (16646)Time elapsed: 0.003 s
% 1.67/1.37 % (16646)Instructions burned: 3 (million)
% 1.67/1.37 % (16646)------------------------------
% 1.67/1.37 % (16646)------------------------------
% 1.67/1.37 % (16648)Instruction limit reached!
% 1.67/1.37 % (16648)------------------------------
% 1.67/1.37 % (16648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (16648)Termination reason: Unknown
% 1.67/1.37 % (16648)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (16648)Memory used [KB]: 5500
% 1.67/1.37 % (16648)Time elapsed: 0.006 s
% 1.67/1.37 % (16648)Instructions burned: 19 (million)
% 1.67/1.37 % (16648)------------------------------
% 1.67/1.37 % (16648)------------------------------
% 1.67/1.38 % (16649)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/710Mi)
% 1.67/1.38 % (16650)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/6Mi)
% 1.67/1.38 % (16650)Instruction limit reached!
% 1.67/1.38 % (16650)------------------------------
% 1.67/1.38 % (16650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (16650)Termination reason: Unknown
% 1.67/1.38 % (16650)Termination phase: Saturation
% 1.67/1.38
% 1.67/1.38 % (16650)Memory used [KB]: 5500
% 1.67/1.38 % (16650)Time elapsed: 0.004 s
% 1.67/1.38 % (16650)Instructions burned: 8 (million)
% 1.67/1.38 % (16650)------------------------------
% 1.67/1.38 % (16650)------------------------------
% 1.67/1.38 % (16653)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/5Mi)
% 1.67/1.39 % (16653)Instruction limit reached!
% 1.67/1.39 % (16653)------------------------------
% 1.67/1.39 % (16653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (16653)Termination reason: Unknown
% 1.67/1.39 % (16653)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (16653)Memory used [KB]: 5500
% 1.67/1.39 % (16653)Time elapsed: 0.003 s
% 1.67/1.39 % (16653)Instructions burned: 7 (million)
% 1.67/1.39 % (16653)------------------------------
% 1.67/1.39 % (16653)------------------------------
% 1.67/1.39 % (16651)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 DTF2THF_16357 for (2999ds/902Mi)
% 1.67/1.39 % (16652)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 DTF2THF_16357 for (2999ds/21Mi)
% 1.67/1.39 % (16654)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 DTF2THF_16357 for (2999ds/6Mi)
% 1.67/1.39 % (16654)Instruction limit reached!
% 1.67/1.39 % (16654)------------------------------
% 1.67/1.39 % (16654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (16654)Termination reason: Unknown
% 1.67/1.39 % (16654)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (16654)Memory used [KB]: 5500
% 1.67/1.39 % (16654)Time elapsed: 0.004 s
% 1.67/1.39 % (16654)Instructions burned: 8 (million)
% 1.67/1.39 % (16654)------------------------------
% 1.67/1.39 % (16654)------------------------------
% 1.67/1.40 % (16655)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16357 for (2999ds/377Mi)
% 1.67/1.40 % (16652)Instruction limit reached!
% 1.67/1.40 % (16652)------------------------------
% 1.67/1.40 % (16652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.40 % (16652)Termination reason: Unknown
% 1.67/1.40 % (16652)Termination phase: Saturation
% 1.67/1.40
% 1.67/1.40 % (16652)Memory used [KB]: 5628
% 1.67/1.40 % (16652)Time elapsed: 0.015 s
% 1.67/1.40 % (16652)Instructions burned: 21 (million)
% 1.67/1.40 % (16652)------------------------------
% 1.67/1.40 % (16652)------------------------------
% 1.67/1.40 % (16656)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 DTF2THF_16357 for (2999ds/779Mi)
% 1.67/1.42 % (16657)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 DTF2THF_16357 for (2999ds/19Mi)
% 1.67/1.43 % (16657)Instruction limit reached!
% 1.67/1.43 % (16657)------------------------------
% 1.67/1.43 % (16657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (16657)Termination reason: Unknown
% 1.67/1.43 % (16657)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.43 % (16657)Memory used [KB]: 5500
% 1.67/1.43 % (16657)Time elapsed: 0.011 s
% 1.67/1.43 % (16657)Instructions burned: 19 (million)
% 1.67/1.43 % (16657)------------------------------
% 1.67/1.43 % (16657)------------------------------
% 1.67/1.44 % (16634)Instruction limit reached!
% 1.67/1.44 % (16634)------------------------------
% 1.67/1.44 % (16634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (16634)Termination reason: Unknown
% 1.67/1.44 % (16634)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (16634)Memory used [KB]: 6652
% 1.67/1.44 % (16634)Time elapsed: 0.123 s
% 1.67/1.44 % (16634)Instructions burned: 277 (million)
% 1.67/1.44 % (16634)------------------------------
% 1.67/1.44 % (16634)------------------------------
% 1.67/1.44 % (16658)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16357 for (2998ds/879Mi)
% 1.67/1.45 % (16659)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16357 for (2998ds/17Mi)
% 1.67/1.45 % (16659)Instruction limit reached!
% 1.67/1.45 % (16659)------------------------------
% 1.67/1.45 % (16659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (16659)Termination reason: Unknown
% 1.67/1.45 % (16659)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (16659)Memory used [KB]: 5884
% 1.67/1.45 % (16659)Time elapsed: 0.007 s
% 1.67/1.45 % (16659)Instructions burned: 18 (million)
% 1.67/1.45 % (16659)------------------------------
% 1.67/1.45 % (16659)------------------------------
% 1.67/1.46 % (16660)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16357 for (2998ds/3Mi)
% 1.67/1.46 % (16660)Instruction limit reached!
% 1.67/1.46 % (16660)------------------------------
% 1.67/1.46 % (16660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (16660)Termination reason: Unknown
% 1.67/1.46 % (16660)Termination phase: Preprocessing 3
% 1.67/1.46
% 1.67/1.46 % (16660)Memory used [KB]: 1023
% 1.67/1.46 % (16660)Time elapsed: 0.003 s
% 1.67/1.46 % (16660)Instructions burned: 5 (million)
% 1.67/1.46 % (16660)------------------------------
% 1.67/1.46 % (16660)------------------------------
% 1.67/1.47 % (16661)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16357 for (2998ds/30Mi)
% 1.67/1.48 % (16661)Refutation not found, incomplete strategy
% 1.67/1.48 % (16661)------------------------------
% 1.67/1.48 % (16661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.48 % (16661)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.48
% 1.67/1.48
% 1.67/1.48 % (16661)Memory used [KB]: 5628
% 1.67/1.48 % (16661)Time elapsed: 0.007 s
% 1.67/1.48 % (16661)Instructions burned: 18 (million)
% 1.67/1.48 % (16661)------------------------------
% 1.67/1.48 % (16661)------------------------------
% 1.67/1.49 % (16662)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16357 for (2998ds/127Mi)
% 1.67/1.50 % (16655)Instruction limit reached!
% 1.67/1.50 % (16655)------------------------------
% 1.67/1.50 % (16655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.50 % (16655)Termination reason: Unknown
% 1.67/1.50 % (16655)Termination phase: Saturation
% 1.67/1.50
% 1.67/1.50 % (16655)Memory used [KB]: 6908
% 1.67/1.50 % (16655)Time elapsed: 0.108 s
% 1.67/1.50 % (16655)Instructions burned: 377 (million)
% 1.67/1.50 % (16655)------------------------------
% 1.67/1.50 % (16655)------------------------------
% 1.67/1.51 % (16663)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16357 for (2998ds/100Mi)
% 1.67/1.53 % (16662)Instruction limit reached!
% 1.67/1.53 % (16662)------------------------------
% 1.67/1.53 % (16662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.53 % (16662)Termination reason: Unknown
% 1.67/1.53 % (16662)Termination phase: Saturation
% 1.67/1.53
% 1.67/1.53 % (16662)Memory used [KB]: 6140
% 1.67/1.53 % (16662)Time elapsed: 0.040 s
% 1.67/1.53 % (16662)Instructions burned: 130 (million)
% 1.67/1.53 % (16662)------------------------------
% 1.67/1.53 % (16662)------------------------------
% 1.67/1.54 % (16664)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_16357 for (2997ds/3Mi)
% 1.67/1.54 % (16664)Instruction limit reached!
% 1.67/1.54 % (16664)------------------------------
% 1.67/1.54 % (16664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.54 % (16664)Termination reason: Unknown
% 1.67/1.54 % (16664)Termination phase: Saturation
% 1.67/1.54
% 1.67/1.54 % (16664)Memory used [KB]: 1023
% 1.67/1.54 % (16664)Time elapsed: 0.003 s
% 1.67/1.54 % (16664)Instructions burned: 5 (million)
% 1.67/1.54 % (16664)------------------------------
% 1.67/1.54 % (16664)------------------------------
% 1.67/1.54 % (16663)Instruction limit reached!
% 1.67/1.54 % (16663)------------------------------
% 1.67/1.54 % (16663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.54 % (16663)Termination reason: Unknown
% 1.67/1.54 % (16663)Termination phase: Saturation
% 1.67/1.54
% 1.67/1.54 % (16663)Memory used [KB]: 5756
% 1.67/1.54 % (16663)Time elapsed: 0.029 s
% 1.67/1.54 % (16663)Instructions burned: 101 (million)
% 1.67/1.54 % (16663)------------------------------
% 1.67/1.54 % (16663)------------------------------
% 1.67/1.55 % (16666)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_16357 for (2997ds/86Mi)
% 1.67/1.55 % (16665)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_16357 for (2997ds/20Mi)
% 1.67/1.55 % (16665)Refutation not found, incomplete strategy
% 1.67/1.55 % (16665)------------------------------
% 1.67/1.55 % (16665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.55 % (16665)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.55
% 1.67/1.55
% 1.67/1.55 % (16665)Memory used [KB]: 5500
% 1.67/1.55 % (16665)Time elapsed: 0.025 s
% 1.67/1.55 % (16665)Instructions burned: 8 (million)
% 1.67/1.55 % (16665)------------------------------
% 1.67/1.55 % (16665)------------------------------
% 1.67/1.56 % (16667)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_16357 for (2997ds/107Mi)
% 1.67/1.57 % (16666)Instruction limit reached!
% 1.67/1.57 % (16666)------------------------------
% 1.67/1.57 % (16666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.57 % (16666)Termination reason: Unknown
% 1.67/1.57 % (16666)Termination phase: Saturation
% 1.67/1.57
% 1.67/1.57 % (16666)Memory used [KB]: 5884
% 1.67/1.57 % (16666)Time elapsed: 0.025 s
% 1.67/1.57 % (16666)Instructions burned: 88 (million)
% 1.67/1.57 % (16666)------------------------------
% 1.67/1.57 % (16666)------------------------------
% 1.67/1.58 % (16668)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_16357 for (2997ds/39Mi)
% 1.67/1.59 % (16668)Instruction limit reached!
% 1.67/1.59 % (16668)------------------------------
% 1.67/1.59 % (16668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.59 % (16668)Termination reason: Unknown
% 1.67/1.59 % (16668)Termination phase: Saturation
% 1.67/1.59
% 1.67/1.59 % (16668)Memory used [KB]: 5884
% 1.67/1.59 % (16668)Time elapsed: 0.012 s
% 1.67/1.59 % (16668)Instructions burned: 39 (million)
% 1.67/1.59 % (16668)------------------------------
% 1.67/1.59 % (16668)------------------------------
% 1.67/1.59 % (16667)Instruction limit reached!
% 1.67/1.59 % (16667)------------------------------
% 1.67/1.59 % (16667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.59 % (16667)Termination reason: Unknown
% 1.67/1.59 % (16667)Termination phase: Saturation
% 1.67/1.59
% 1.67/1.59 % (16667)Memory used [KB]: 6012
% 1.67/1.59 % (16667)Time elapsed: 0.034 s
% 1.67/1.59 % (16667)Instructions burned: 108 (million)
% 1.67/1.59 % (16667)------------------------------
% 1.67/1.59 % (16667)------------------------------
% 1.67/1.60 % (16669)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_16357 for (2997ds/448Mi)
% 1.67/1.60 % (16670)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_16357 for (2996ds/46Mi)
% 1.67/1.62 % (16670)Instruction limit reached!
% 1.67/1.62 % (16670)------------------------------
% 1.67/1.62 % (16670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.62 % (16670)Termination reason: Unknown
% 1.67/1.62 % (16670)Termination phase: Saturation
% 1.67/1.62
% 1.67/1.62 % (16670)Memory used [KB]: 5756
% 1.67/1.62 % (16670)Time elapsed: 0.018 s
% 1.67/1.62 % (16670)Instructions burned: 49 (million)
% 1.67/1.62 % (16670)------------------------------
% 1.67/1.62 % (16670)------------------------------
% 1.67/1.63 % (16649)Instruction limit reached!
% 1.67/1.63 % (16649)------------------------------
% 1.67/1.63 % (16649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.63 % (16649)Termination reason: Unknown
% 1.67/1.63 % (16649)Termination phase: Saturation
% 1.67/1.63
% 1.67/1.63 % (16649)Memory used [KB]: 8571
% 1.67/1.63 % (16649)Time elapsed: 0.248 s
% 1.67/1.63 % (16649)Instructions burned: 712 (million)
% 1.67/1.63 % (16649)------------------------------
% 1.67/1.63 % (16649)------------------------------
% 1.67/1.63 % (16671)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_16357 for (2996ds/98Mi)
% 1.67/1.64 % (16672)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_16357 for (2996ds/507Mi)
% 1.67/1.66 % (16656)Instruction limit reached!
% 1.67/1.66 % (16656)------------------------------
% 1.67/1.66 % (16656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.66 % (16656)Termination reason: Unknown
% 1.67/1.66 % (16656)Termination phase: Saturation
% 1.67/1.66
% 1.67/1.66 % (16656)Memory used [KB]: 6524
% 1.67/1.66 % (16656)Time elapsed: 0.253 s
% 1.67/1.66 % (16656)Instructions burned: 780 (million)
% 1.67/1.66 % (16656)------------------------------
% 1.67/1.66 % (16656)------------------------------
% 1.67/1.66 % (16671)Instruction limit reached!
% 1.67/1.66 % (16671)------------------------------
% 1.67/1.66 % (16671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.66 % (16671)Termination reason: Unknown
% 1.67/1.66 % (16671)Termination phase: Saturation
% 1.67/1.66
% 1.67/1.66 % (16671)Memory used [KB]: 1279
% 1.67/1.66 % (16671)Time elapsed: 0.033 s
% 1.67/1.66 % (16671)Instructions burned: 100 (million)
% 1.67/1.66 % (16671)------------------------------
% 1.67/1.66 % (16671)------------------------------
% 1.67/1.67 % (16673)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_16357 for (2996ds/149Mi)
% 1.67/1.67 % (16674)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_16357 for (2996ds/39Mi)
% 1.67/1.68 % (16674)Instruction limit reached!
% 1.67/1.68 % (16674)------------------------------
% 1.67/1.68 % (16674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.68 % (16674)Termination reason: Unknown
% 1.67/1.68 % (16674)Termination phase: Saturation
% 1.67/1.68
% 1.67/1.68 % (16674)Memory used [KB]: 5628
% 1.67/1.68 % (16674)Time elapsed: 0.013 s
% 1.67/1.68 % (16674)Instructions burned: 39 (million)
% 1.67/1.68 % (16674)------------------------------
% 1.67/1.68 % (16674)------------------------------
% 1.67/1.69 % (16651)Instruction limit reached!
% 1.67/1.69 % (16651)------------------------------
% 1.67/1.69 % (16651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.69 % (16651)Termination reason: Unknown
% 1.67/1.69 % (16651)Termination phase: Saturation
% 1.67/1.69
% 1.67/1.69 % (16651)Memory used [KB]: 9210
% 1.67/1.69 % (16651)Time elapsed: 0.299 s
% 1.67/1.69 % (16651)Instructions burned: 904 (million)
% 1.67/1.69 % (16651)------------------------------
% 1.67/1.69 % (16651)------------------------------
% 1.67/1.69 % (16675)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_16357 for (2996ds/6Mi)
% 1.67/1.70 % (16675)Instruction limit reached!
% 1.67/1.70 % (16675)------------------------------
% 1.67/1.70 % (16675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.70 % (16675)Termination reason: Unknown
% 1.67/1.70 % (16675)Termination phase: Saturation
% 1.67/1.70
% 1.67/1.70 % (16675)Memory used [KB]: 9978
% 1.67/1.70 % (16675)Time elapsed: 0.004 s
% 1.67/1.70 % (16675)Instructions burned: 6 (million)
% 1.67/1.70 % (16675)------------------------------
% 1.67/1.70 % (16675)------------------------------
% 1.67/1.70 % (16676)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_16357 for (2996ds/1087Mi)
% 1.67/1.71 % (16677)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_16357 for (2996ds/47Mi)
% 1.67/1.71 % (16673)Instruction limit reached!
% 1.67/1.71 % (16673)------------------------------
% 1.67/1.71 % (16673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.71 % (16673)Termination reason: Unknown
% 1.67/1.71 % (16673)Termination phase: Saturation
% 1.67/1.71
% 1.67/1.71 % (16673)Memory used [KB]: 5756
% 1.67/1.71 % (16673)Time elapsed: 0.043 s
% 1.67/1.71 % (16673)Instructions burned: 152 (million)
% 1.67/1.71 % (16673)------------------------------
% 1.67/1.71 % (16673)------------------------------
% 1.67/1.71 % (16658)Instruction limit reached!
% 1.67/1.71 % (16658)------------------------------
% 1.67/1.71 % (16658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.71 % (16658)Termination reason: Unknown
% 1.67/1.71 % (16658)Termination phase: Saturation
% 1.67/1.71
% 1.67/1.71 % (16658)Memory used [KB]: 9210
% 1.67/1.71 % (16658)Time elapsed: 0.271 s
% 1.67/1.71 % (16658)Instructions burned: 879 (million)
% 1.67/1.71 % (16658)------------------------------
% 1.67/1.71 % (16658)------------------------------
% 1.67/1.72 % (16678)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/44Mi)
% 1.67/1.72 % (16677)Instruction limit reached!
% 1.67/1.72 % (16677)------------------------------
% 1.67/1.72 % (16677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.72 % (16677)Termination reason: Unknown
% 1.67/1.72 % (16677)Termination phase: Saturation
% 1.67/1.72
% 1.67/1.72 % (16677)Memory used [KB]: 5756
% 1.67/1.72 % (16677)Time elapsed: 0.016 s
% 1.67/1.72 % (16677)Instructions burned: 47 (million)
% 1.67/1.72 % (16677)------------------------------
% 1.67/1.72 % (16677)------------------------------
% 1.67/1.72 % (16679)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/432Mi)
% 1.67/1.73 % (16640)Instruction limit reached!
% 1.67/1.73 % (16640)------------------------------
% 1.67/1.73 % (16640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.73 % (16640)Termination reason: Unknown
% 1.67/1.73 % (16640)Termination phase: Saturation
% 1.67/1.73
% 1.67/1.73 % (16640)Memory used [KB]: 8187
% 1.67/1.73 % (16640)Time elapsed: 0.385 s
% 1.67/1.73 % (16640)Instructions burned: 1043 (million)
% 1.67/1.73 % (16640)------------------------------
% 1.67/1.73 % (16640)------------------------------
% 1.67/1.73 % (16678)Instruction limit reached!
% 1.67/1.73 % (16678)------------------------------
% 1.67/1.73 % (16678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.73 % (16678)Termination reason: Unknown
% 1.67/1.73 % (16678)Termination phase: Saturation
% 1.67/1.73
% 1.67/1.73 % (16678)Memory used [KB]: 1151
% 1.67/1.73 % (16678)Time elapsed: 0.013 s
% 1.67/1.73 % (16678)Instructions burned: 46 (million)
% 1.67/1.73 % (16678)------------------------------
% 1.67/1.73 % (16678)------------------------------
% 1.67/1.73 % (16680)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/62Mi)
% 1.67/1.74 % (16681)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/31Mi)
% 1.67/1.74 % (16682)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/96Mi)
% 1.67/1.74 % (16669)Instruction limit reached!
% 1.67/1.74 % (16669)------------------------------
% 1.67/1.74 % (16669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.74 % (16669)Termination reason: Unknown
% 1.67/1.74 % (16669)Termination phase: Saturation
% 1.67/1.74
% 1.67/1.74 % (16669)Memory used [KB]: 6652
% 1.67/1.74 % (16669)Time elapsed: 0.143 s
% 1.67/1.74 % (16669)Instructions burned: 448 (million)
% 1.67/1.74 % (16669)------------------------------
% 1.67/1.74 % (16669)------------------------------
% 1.67/1.75 % (16681)Instruction limit reached!
% 1.67/1.75 % (16681)------------------------------
% 1.67/1.75 % (16681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.75 % (16681)Termination reason: Unknown
% 1.67/1.75 % (16681)Termination phase: Saturation
% 1.67/1.75
% 1.67/1.75 % (16681)Memory used [KB]: 5628
% 1.67/1.75 % (16681)Time elapsed: 0.011 s
% 1.67/1.75 % (16681)Instructions burned: 32 (million)
% 1.67/1.75 % (16681)------------------------------
% 1.67/1.75 % (16681)------------------------------
% 1.67/1.75 % (16680)Instruction limit reached!
% 1.67/1.75 % (16680)------------------------------
% 1.67/1.75 % (16680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.75 % (16680)Termination reason: Unknown
% 1.67/1.75 % (16680)Termination phase: Saturation
% 1.67/1.75
% 1.67/1.75 % (16680)Memory used [KB]: 5756
% 1.67/1.75 % (16680)Time elapsed: 0.020 s
% 1.67/1.75 % (16680)Instructions burned: 65 (million)
% 1.67/1.75 % (16680)------------------------------
% 1.67/1.75 % (16680)------------------------------
% 1.67/1.75 % (16683)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/453Mi)
% 1.67/1.76 % (16684)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/71Mi)
% 1.67/1.76 % (16685)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/83Mi)
% 1.67/1.77 % (16682)Instruction limit reached!
% 1.67/1.77 % (16682)------------------------------
% 1.67/1.77 % (16682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.77 % (16682)Termination reason: Unknown
% 1.67/1.77 % (16682)Termination phase: Saturation
% 1.67/1.77
% 1.67/1.77 % (16682)Memory used [KB]: 6012
% 1.67/1.77 % (16682)Time elapsed: 0.028 s
% 1.67/1.77 % (16682)Instructions burned: 99 (million)
% 1.67/1.77 % (16682)------------------------------
% 1.67/1.77 % (16682)------------------------------
% 1.67/1.77 % (16686)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/11Mi)
% 1.67/1.78 % (16686)Instruction limit reached!
% 1.67/1.78 % (16686)------------------------------
% 1.67/1.78 % (16686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.78 % (16686)Termination reason: Unknown
% 1.67/1.78 % (16686)Termination phase: Saturation
% 1.67/1.78
% 1.67/1.78 % (16686)Memory used [KB]: 5500
% 1.67/1.78 % (16686)Time elapsed: 0.005 s
% 1.67/1.78 % (16686)Instructions burned: 14 (million)
% 1.67/1.78 % (16686)------------------------------
% 1.67/1.78 % (16686)------------------------------
% 1.67/1.78 % (16684)Instruction limit reached!
% 1.67/1.78 % (16684)------------------------------
% 1.67/1.78 % (16684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.78 % (16684)Termination reason: Unknown
% 1.67/1.78 % (16684)Termination phase: Saturation
% 1.67/1.78
% 1.67/1.78 % (16684)Memory used [KB]: 5628
% 1.67/1.78 % (16684)Time elapsed: 0.025 s
% 1.67/1.78 % (16684)Instructions burned: 73 (million)
% 1.67/1.78 % (16684)------------------------------
% 1.67/1.78 % (16684)------------------------------
% 1.67/1.78 % (16685)Instruction limit reached!
% 1.67/1.78 % (16685)------------------------------
% 1.67/1.78 % (16685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.78 % (16685)Termination reason: Unknown
% 1.67/1.78 % (16685)Termination phase: Saturation
% 1.67/1.78
% 1.67/1.78 % (16685)Memory used [KB]: 5884
% 1.67/1.78 % (16685)Time elapsed: 0.024 s
% 1.67/1.78 % (16685)Instructions burned: 84 (million)
% 1.67/1.78 % (16685)------------------------------
% 1.67/1.78 % (16685)------------------------------
% 1.67/1.79 % (16687)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/41Mi)
% 1.67/1.79 % (16688)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/6Mi)
% 1.67/1.79 % (16689)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/150Mi)
% 1.67/1.79 % (16688)Instruction limit reached!
% 1.67/1.79 % (16688)------------------------------
% 1.67/1.79 % (16688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.79 % (16688)Termination reason: Unknown
% 1.67/1.79 % (16688)Termination phase: Saturation
% 1.67/1.79
% 1.67/1.79 % (16688)Memory used [KB]: 5500
% 1.67/1.79 % (16688)Time elapsed: 0.003 s
% 1.67/1.79 % (16688)Instructions burned: 7 (million)
% 1.67/1.79 % (16688)------------------------------
% 1.67/1.79 % (16688)------------------------------
% 1.67/1.79 % (16687)Refutation not found, incomplete strategy
% 1.67/1.79 % (16687)------------------------------
% 1.67/1.79 % (16687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.79 % (16687)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.79
% 1.67/1.79
% 1.67/1.79 % (16687)Memory used [KB]: 5500
% 1.67/1.79 % (16687)Time elapsed: 0.005 s
% 1.67/1.79 % (16687)Instructions burned: 10 (million)
% 1.67/1.79 % (16672)Instruction limit reached!
% 1.67/1.79 % (16672)------------------------------
% 1.67/1.79 % (16672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.79 % (16687)------------------------------
% 1.67/1.79 % (16687)------------------------------
% 1.67/1.79 % (16672)Termination reason: Unknown
% 1.67/1.79 % (16672)Termination phase: Saturation
% 1.67/1.79
% 1.67/1.79 % (16672)Memory used [KB]: 6140
% 1.67/1.79 % (16672)Time elapsed: 0.158 s
% 1.67/1.79 % (16672)Instructions burned: 508 (million)
% 1.67/1.79 % (16672)------------------------------
% 1.67/1.79 % (16672)------------------------------
% 1.67/1.80 % (16689)Refutation not found, incomplete strategy
% 1.67/1.80 % (16689)------------------------------
% 1.67/1.80 % (16689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.80 % (16689)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.80
% 1.67/1.80
% 1.67/1.80 % (16689)Memory used [KB]: 5628
% 1.67/1.80 % (16689)Time elapsed: 0.006 s
% 1.67/1.80 % (16689)Instructions burned: 17 (million)
% 1.67/1.80 % (16689)------------------------------
% 1.67/1.80 % (16689)------------------------------
% 1.67/1.80 % (16690)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/343Mi)
% 1.67/1.80 % (16692)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/253Mi)
% 1.67/1.80 % (16691)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/109Mi)
% 1.67/1.81 % (16693)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_16357 for (2995ds/140Mi)
% 1.67/1.82 % (16693)Refutation not found, incomplete strategy
% 1.67/1.82 % (16693)------------------------------
% 1.67/1.82 % (16693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.82 % (16693)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.82
% 1.67/1.82
% 1.67/1.82 % (16693)Memory used [KB]: 5500
% 1.67/1.82 % (16693)Time elapsed: 0.007 s
% 1.67/1.82 % (16693)Instructions burned: 7 (million)
% 1.67/1.82 % (16693)------------------------------
% 1.67/1.82 % (16693)------------------------------
% 1.67/1.83 % (16691)Instruction limit reached!
% 1.67/1.83 % (16691)------------------------------
% 1.67/1.83 % (16691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.83 % (16691)Termination reason: Unknown
% 1.67/1.83 % (16691)Termination phase: Saturation
% 1.67/1.83
% 1.67/1.83 % (16691)Memory used [KB]: 6012
% 1.67/1.83 % (16691)Time elapsed: 0.032 s
% 1.67/1.83 % (16691)Instructions burned: 112 (million)
% 1.67/1.83 % (16691)------------------------------
% 1.67/1.83 % (16691)------------------------------
% 1.67/1.84 % (16694)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_16357 for (2994ds/614Mi)
% 1.67/1.84 % (16695)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_16357 for (2994ds/202Mi)
% 1.67/1.85 % (16679)Instruction limit reached!
% 1.67/1.85 % (16679)------------------------------
% 1.67/1.85 % (16679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.85 % (16679)Termination reason: Unknown
% 1.67/1.85 % (16679)Termination phase: Saturation
% 1.67/1.85
% 1.67/1.85 % (16679)Memory used [KB]: 3709
% 1.67/1.85 % (16679)Time elapsed: 0.125 s
% 1.67/1.85 % (16679)Instructions burned: 435 (million)
% 1.67/1.85 % (16679)------------------------------
% 1.67/1.85 % (16679)------------------------------
% 1.67/1.86 % (16696)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_16357 for (2994ds/339Mi)
% 1.67/1.86 % (16696)Refutation not found, incomplete strategy
% 1.67/1.86 % (16696)------------------------------
% 1.67/1.86 % (16696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.86 % (16696)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.86
% 1.67/1.86
% 1.67/1.86 % (16696)Memory used [KB]: 5500
% 1.67/1.86 % (16696)Time elapsed: 0.003 s
% 1.67/1.86 % (16696)Instructions burned: 6 (million)
% 1.67/1.86 % (16696)------------------------------
% 1.67/1.86 % (16696)------------------------------
% 1.67/1.87 % (16697)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_16357 for (2994ds/283Mi)
% 1.67/1.87 % (16692)Instruction limit reached!
% 1.67/1.87 % (16692)------------------------------
% 1.67/1.87 % (16692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.87 % (16692)Termination reason: Unknown
% 1.67/1.87 % (16692)Termination phase: Saturation
% 1.67/1.87
% 1.67/1.87 % (16692)Memory used [KB]: 6524
% 1.67/1.87 % (16692)Time elapsed: 0.073 s
% 1.67/1.87 % (16692)Instructions burned: 254 (million)
% 1.67/1.87 % (16692)------------------------------
% 1.67/1.87 % (16692)------------------------------
% 1.67/1.88 % (16698)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_16357 for (2994ds/134Mi)
% 1.67/1.90 % (16683)Instruction limit reached!
% 1.67/1.90 % (16683)------------------------------
% 1.67/1.90 % (16683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.90 % (16683)Termination reason: Unknown
% 1.67/1.90 % (16683)Termination phase: Saturation
% 1.67/1.90
% 1.67/1.90 % (16683)Memory used [KB]: 6524
% 1.67/1.90 % (16683)Time elapsed: 0.142 s
% 1.67/1.90 % (16683)Instructions burned: 455 (million)
% 1.67/1.90 % (16683)------------------------------
% 1.67/1.90 % (16683)------------------------------
% 1.67/1.90 % (16690)Instruction limit reached!
% 1.67/1.90 % (16690)------------------------------
% 1.67/1.90 % (16690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.90 % (16690)Termination reason: Unknown
% 1.67/1.90 % (16690)Termination phase: Saturation
% 1.67/1.90
% 1.67/1.90 % (16690)Memory used [KB]: 6908
% 1.67/1.90 % (16690)Time elapsed: 0.098 s
% 1.67/1.90 % (16690)Instructions burned: 344 (million)
% 1.67/1.90 % (16690)------------------------------
% 1.67/1.90 % (16690)------------------------------
% 1.67/1.90 % (16695)Instruction limit reached!
% 1.67/1.90 % (16695)------------------------------
% 1.67/1.90 % (16695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.90 % (16695)Termination reason: Unknown
% 1.67/1.90 % (16695)Termination phase: Saturation
% 1.67/1.90
% 1.67/1.90 % (16695)Memory used [KB]: 6268
% 1.67/1.90 % (16695)Time elapsed: 0.058 s
% 1.67/1.90 % (16695)Instructions burned: 204 (million)
% 1.67/1.90 % (16695)------------------------------
% 1.67/1.90 % (16695)------------------------------
% 1.67/1.90 % (16699)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_16357 for (2994ds/298Mi)
% 1.67/1.91 % (16700)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_16357 for (2994ds/192Mi)
% 1.67/1.91 % (16701)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_16357 for (2994ds/258Mi)
% 1.67/1.92 % (16698)Instruction limit reached!
% 1.67/1.92 % (16698)------------------------------
% 1.67/1.92 % (16698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.92 % (16698)Termination reason: Unknown
% 1.67/1.92 % (16698)Termination phase: Saturation
% 1.67/1.92
% 1.67/1.92 % (16698)Memory used [KB]: 6140
% 1.67/1.92 % (16698)Time elapsed: 0.042 s
% 1.67/1.92 % (16698)Instructions burned: 136 (million)
% 1.67/1.92 % (16698)------------------------------
% 1.67/1.92 % (16698)------------------------------
% 1.67/1.93 % (16702)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_16357 for (2993ds/90Mi)
% 1.67/1.94 % (16697)Instruction limit reached!
% 1.67/1.94 % (16697)------------------------------
% 1.67/1.94 % (16697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.94 % (16697)Termination reason: Unknown
% 1.67/1.94 % (16697)Termination phase: Saturation
% 1.67/1.94
% 1.67/1.94 % (16697)Memory used [KB]: 7419
% 1.67/1.94 % (16697)Time elapsed: 0.076 s
% 1.67/1.94 % (16697)Instructions burned: 283 (million)
% 1.67/1.94 % (16697)------------------------------
% 1.67/1.94 % (16697)------------------------------
% 1.67/1.95 % (16703)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_16357 for (2993ds/231Mi)
% 1.67/1.96 % (16700)Instruction limit reached!
% 1.67/1.96 % (16700)------------------------------
% 1.67/1.96 % (16700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.96 % (16700)Termination reason: Unknown
% 1.67/1.96 % (16700)Termination phase: Saturation
% 1.67/1.96
% 1.67/1.96 % (16700)Memory used [KB]: 6268
% 1.67/1.96 % (16700)Time elapsed: 0.054 s
% 1.67/1.96 % (16700)Instructions burned: 192 (million)
% 1.67/1.96 % (16700)------------------------------
% 1.67/1.96 % (16700)------------------------------
% 1.67/1.96 % (16702)Instruction limit reached!
% 1.67/1.96 % (16702)------------------------------
% 1.67/1.96 % (16702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.96 % (16702)Termination reason: Unknown
% 1.67/1.96 % (16702)Termination phase: Saturation
% 1.67/1.96
% 1.67/1.96 % (16702)Memory used [KB]: 6012
% 1.67/1.96 % (16702)Time elapsed: 0.028 s
% 1.67/1.96 % (16702)Instructions burned: 91 (million)
% 1.67/1.96 % (16702)------------------------------
% 1.67/1.96 % (16702)------------------------------
% 1.67/1.97 % (16704)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_16357 for (2993ds/458Mi)
% 1.67/1.97 % (16705)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_16357 for (2993ds/31Mi)
% 1.67/1.98 % (16705)Instruction limit reached!
% 1.67/1.98 % (16705)------------------------------
% 1.67/1.98 % (16705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.98 % (16705)Termination reason: Unknown
% 1.67/1.98 % (16705)Termination phase: Saturation
% 1.67/1.98
% 1.67/1.98 % (16705)Memory used [KB]: 5628
% 1.67/1.98 % (16705)Time elapsed: 0.031 s
% 1.67/1.98 % (16705)Instructions burned: 31 (million)
% 1.67/1.98 % (16705)------------------------------
% 1.67/1.98 % (16705)------------------------------
% 1.67/1.98 % (16701)Instruction limit reached!
% 1.67/1.98 % (16701)------------------------------
% 1.67/1.98 % (16701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.98 % (16701)Termination reason: Unknown
% 1.67/1.98 % (16701)Termination phase: Saturation
% 1.67/1.98
% 1.67/1.98 % (16701)Memory used [KB]: 6652
% 1.67/1.98 % (16701)Time elapsed: 0.074 s
% 1.67/1.98 % (16701)Instructions burned: 259 (million)
% 1.67/1.98 % (16701)------------------------------
% 1.67/1.98 % (16701)------------------------------
% 1.67/1.99 % (16706)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_16357 for (2993ds/297Mi)
% 1.67/1.99 % (16707)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_16357 for (2993ds/987Mi)
% 1.67/2.00 % (16699)Instruction limit reached!
% 1.67/2.00 % (16699)------------------------------
% 1.67/2.00 % (16699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/2.00 % (16699)Termination reason: Unknown
% 1.67/2.00 % (16699)Termination phase: Saturation
% 1.67/2.00
% 1.67/2.00 % (16699)Memory used [KB]: 6140
% 1.67/2.00 % (16699)Time elapsed: 0.097 s
% 1.67/2.00 % (16699)Instructions burned: 298 (million)
% 1.67/2.00 % (16699)------------------------------
% 1.67/2.00 % (16699)------------------------------
% 1.67/2.01 % (16708)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_16357 for (2993ds/182Mi)
% 6.60/2.02 % (16703)Instruction limit reached!
% 6.60/2.02 % (16703)------------------------------
% 6.60/2.02 % (16703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.02 % (16703)Termination reason: Unknown
% 6.60/2.02 % (16703)Termination phase: Saturation
% 6.60/2.02
% 6.60/2.02 % (16703)Memory used [KB]: 6268
% 6.60/2.02 % (16703)Time elapsed: 0.085 s
% 6.60/2.02 % (16703)Instructions burned: 232 (million)
% 6.60/2.02 % (16703)------------------------------
% 6.60/2.02 % (16703)------------------------------
% 6.60/2.02 % (16676)Instruction limit reached!
% 6.60/2.02 % (16676)------------------------------
% 6.60/2.02 % (16676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.02 % (16676)Termination reason: Unknown
% 6.60/2.02 % (16676)Termination phase: Saturation
% 6.60/2.02
% 6.60/2.02 % (16676)Memory used [KB]: 10234
% 6.60/2.02 % (16676)Time elapsed: 0.322 s
% 6.60/2.02 % (16676)Instructions burned: 1089 (million)
% 6.60/2.02 % (16676)------------------------------
% 6.60/2.02 % (16676)------------------------------
% 6.60/2.03 % (16709)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_16357 for (2993ds/182Mi)
% 6.60/2.03 % (16710)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_16357 for (2993ds/154Mi)
% 6.60/2.05 % (16694)Instruction limit reached!
% 6.60/2.05 % (16694)------------------------------
% 6.60/2.05 % (16694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.05 % (16694)Termination reason: Unknown
% 6.60/2.05 % (16694)Termination phase: Saturation
% 6.60/2.05
% 6.60/2.05 % (16694)Memory used [KB]: 7547
% 6.60/2.05 % (16694)Time elapsed: 0.219 s
% 6.60/2.05 % (16694)Instructions burned: 616 (million)
% 6.60/2.05 % (16694)------------------------------
% 6.60/2.05 % (16694)------------------------------
% 6.60/2.06 % (16708)Instruction limit reached!
% 6.60/2.06 % (16708)------------------------------
% 6.60/2.06 % (16708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.06 % (16708)Termination reason: Unknown
% 6.60/2.06 % (16708)Termination phase: Saturation
% 6.60/2.06
% 6.60/2.06 % (16708)Memory used [KB]: 6396
% 6.60/2.06 % (16708)Time elapsed: 0.079 s
% 6.60/2.06 % (16708)Instructions burned: 185 (million)
% 6.60/2.06 % (16708)------------------------------
% 6.60/2.06 % (16708)------------------------------
% 6.60/2.06 % (16711)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_16357 for (2992ds/79Mi)
% 6.60/2.07 % (16706)Instruction limit reached!
% 6.60/2.07 % (16706)------------------------------
% 6.60/2.07 % (16706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.07 % (16706)Termination reason: Unknown
% 6.60/2.07 % (16706)Termination phase: Saturation
% 6.60/2.07
% 6.60/2.07 % (16706)Memory used [KB]: 6268
% 6.60/2.07 % (16706)Time elapsed: 0.104 s
% 6.60/2.07 % (16706)Instructions burned: 297 (million)
% 6.60/2.07 % (16706)------------------------------
% 6.60/2.07 % (16706)------------------------------
% 6.60/2.07 % (16710)Instruction limit reached!
% 6.60/2.07 % (16710)------------------------------
% 6.60/2.07 % (16710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.07 % (16710)Termination reason: Unknown
% 6.60/2.07 % (16710)Termination phase: Saturation
% 6.60/2.07
% 6.60/2.07 % (16710)Memory used [KB]: 6268
% 6.60/2.07 % (16710)Time elapsed: 0.072 s
% 6.60/2.07 % (16710)Instructions burned: 154 (million)
% 6.60/2.07 % (16710)------------------------------
% 6.60/2.07 % (16710)------------------------------
% 6.60/2.07 % (16712)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_16357 for (2992ds/216Mi)
% 6.60/2.08 % (16713)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_16357 for (2992ds/114Mi)
% 6.60/2.08 % (16709)Instruction limit reached!
% 6.60/2.08 % (16709)------------------------------
% 6.60/2.08 % (16709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.08 % (16709)Termination reason: Unknown
% 6.60/2.08 % (16709)Termination phase: Saturation
% 6.60/2.08
% 6.60/2.08 % (16709)Memory used [KB]: 6396
% 6.60/2.08 % (16709)Time elapsed: 0.053 s
% 6.60/2.08 % (16709)Instructions burned: 183 (million)
% 6.60/2.08 % (16709)------------------------------
% 6.60/2.08 % (16709)------------------------------
% 6.60/2.08 % (16713)Refutation not found, incomplete strategy
% 6.60/2.08 % (16713)------------------------------
% 6.60/2.08 % (16713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.08 % (16713)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.08
% 6.60/2.08
% 6.60/2.08 % (16713)Memory used [KB]: 5500
% 6.60/2.08 % (16713)Time elapsed: 0.003 s
% 6.60/2.08 % (16713)Instructions burned: 7 (million)
% 6.60/2.08 % (16713)------------------------------
% 6.60/2.08 % (16713)------------------------------
% 6.60/2.08 % (16714)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_16357 for (2992ds/922Mi)
% 6.60/2.09 % (16711)Instruction limit reached!
% 6.60/2.09 % (16711)------------------------------
% 6.60/2.09 % (16711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.09 % (16711)Termination reason: Unknown
% 6.60/2.09 % (16711)Termination phase: Saturation
% 6.60/2.09
% 6.60/2.09 % (16711)Memory used [KB]: 5884
% 6.60/2.09 % (16711)Time elapsed: 0.023 s
% 6.60/2.09 % (16711)Instructions burned: 81 (million)
% 6.60/2.09 % (16711)------------------------------
% 6.60/2.09 % (16711)------------------------------
% 6.60/2.09 % (16715)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_16357 for (2992ds/182Mi)
% 6.60/2.09 % (16716)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_16357 for (2992ds/164Mi)
% 6.60/2.09 % (16715)Refutation not found, incomplete strategy
% 6.60/2.09 % (16715)------------------------------
% 6.60/2.09 % (16715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.09 % (16715)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.09
% 6.60/2.09
% 6.60/2.09 % (16715)Memory used [KB]: 5500
% 6.60/2.09 % (16715)Time elapsed: 0.004 s
% 6.60/2.09 % (16715)Instructions burned: 11 (million)
% 6.60/2.09 % (16715)------------------------------
% 6.60/2.09 % (16715)------------------------------
% 6.60/2.09 % (16717)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_16357 for (2992ds/50Mi)
% 6.60/2.10 % (16704)Instruction limit reached!
% 6.60/2.10 % (16704)------------------------------
% 6.60/2.10 % (16704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.10 % (16704)Termination reason: Unknown
% 6.60/2.10 % (16704)Termination phase: Saturation
% 6.60/2.10
% 6.60/2.10 % (16704)Memory used [KB]: 7547
% 6.60/2.10 % (16704)Time elapsed: 0.133 s
% 6.60/2.10 % (16704)Instructions burned: 460 (million)
% 6.60/2.10 % (16704)------------------------------
% 6.60/2.10 % (16704)------------------------------
% 6.60/2.10 % (16718)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_16357 for (2992ds/368Mi)
% 6.60/2.11 % (16717)Instruction limit reached!
% 6.60/2.11 % (16717)------------------------------
% 6.60/2.11 % (16717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.11 % (16717)Termination reason: Unknown
% 6.60/2.11 % (16717)Termination phase: Saturation
% 6.60/2.11
% 6.60/2.11 % (16717)Memory used [KB]: 10490
% 6.60/2.11 % (16717)Time elapsed: 0.016 s
% 6.60/2.11 % (16717)Instructions burned: 52 (million)
% 6.60/2.11 % (16717)------------------------------
% 6.60/2.11 % (16717)------------------------------
% 6.60/2.11 % (16719)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_16357 for (2991ds/1021Mi)
% 7.21/2.11 % (16712)Refutation not found, incomplete strategy
% 7.21/2.11 % (16712)------------------------------
% 7.21/2.11 % (16712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.11 % (16712)Termination reason: Refutation not found, incomplete strategy
% 7.21/2.11
% 7.21/2.11
% 7.21/2.11 % (16712)Memory used [KB]: 5884
% 7.21/2.11 % (16712)Time elapsed: 0.043 s
% 7.21/2.11 % (16712)Instructions burned: 139 (million)
% 7.21/2.11 % (16712)------------------------------
% 7.21/2.11 % (16712)------------------------------
% 7.21/2.12 % (16720)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_16357 for (2991ds/267Mi)
% 7.21/2.12 % (16721)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_16357 for (2991ds/204Mi)
% 7.21/2.13 % (16716)Instruction limit reached!
% 7.21/2.13 % (16716)------------------------------
% 7.21/2.13 % (16716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.13 % (16716)Termination reason: Unknown
% 7.21/2.13 % (16716)Termination phase: Saturation
% 7.21/2.13
% 7.21/2.13 % (16716)Memory used [KB]: 1279
% 7.21/2.13 % (16716)Time elapsed: 0.045 s
% 7.21/2.13 % (16716)Instructions burned: 167 (million)
% 7.21/2.13 % (16716)------------------------------
% 7.21/2.13 % (16716)------------------------------
% 7.21/2.14 % (16722)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_16357 for (2991ds/26Mi)
% 7.21/2.15 % (16722)Refutation not found, incomplete strategy
% 7.21/2.15 % (16722)------------------------------
% 7.21/2.15 % (16722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.15 % (16722)Termination reason: Refutation not found, incomplete strategy
% 7.21/2.15
% 7.21/2.15
% 7.21/2.15 % (16722)Memory used [KB]: 5500
% 7.21/2.15 % (16722)Time elapsed: 0.005 s
% 7.21/2.15 % (16722)Instructions burned: 14 (million)
% 7.21/2.15 % (16722)------------------------------
% 7.21/2.15 % (16722)------------------------------
% 7.21/2.16 % (16723)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_16357 for (2991ds/53Mi)
% 7.21/2.17 % (16723)Instruction limit reached!
% 7.21/2.17 % (16723)------------------------------
% 7.21/2.17 % (16723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.17 % (16723)Termination reason: Unknown
% 7.21/2.17 % (16723)Termination phase: Saturation
% 7.21/2.17
% 7.21/2.17 % (16723)Memory used [KB]: 5756
% 7.21/2.17 % (16723)Time elapsed: 0.017 s
% 7.21/2.17 % (16723)Instructions burned: 55 (million)
% 7.21/2.17 % (16723)------------------------------
% 7.21/2.17 % (16723)------------------------------
% 7.21/2.18 % (16724)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_16357 for (2991ds/4436Mi)
% 7.21/2.18 % (16721)Instruction limit reached!
% 7.21/2.18 % (16721)------------------------------
% 7.21/2.18 % (16721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.18 % (16721)Termination reason: Unknown
% 7.21/2.18 % (16721)Termination phase: Saturation
% 7.21/2.18
% 7.21/2.18 % (16721)Memory used [KB]: 6396
% 7.21/2.18 % (16721)Time elapsed: 0.060 s
% 7.21/2.18 % (16721)Instructions burned: 205 (million)
% 7.21/2.18 % (16721)------------------------------
% 7.21/2.18 % (16721)------------------------------
% 7.21/2.19 % (16725)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_16357 for (2991ds/1539Mi)
% 7.51/2.20 % (16720)Instruction limit reached!
% 7.51/2.20 % (16720)------------------------------
% 7.51/2.20 % (16720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.20 % (16720)Termination reason: Unknown
% 7.51/2.20 % (16720)Termination phase: Saturation
% 7.51/2.20
% 7.51/2.20 % (16720)Memory used [KB]: 6396
% 7.51/2.20 % (16720)Time elapsed: 0.084 s
% 7.51/2.20 % (16720)Instructions burned: 270 (million)
% 7.51/2.20 % (16720)------------------------------
% 7.51/2.20 % (16720)------------------------------
% 7.51/2.21 % (16718)Instruction limit reached!
% 7.51/2.21 % (16718)------------------------------
% 7.51/2.21 % (16718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.21 % (16718)Termination reason: Unknown
% 7.51/2.21 % (16718)Termination phase: Saturation
% 7.51/2.21
% 7.51/2.21 % (16718)Memory used [KB]: 7419
% 7.51/2.21 % (16718)Time elapsed: 0.108 s
% 7.51/2.21 % (16718)Instructions burned: 370 (million)
% 7.51/2.21 % (16718)------------------------------
% 7.51/2.21 % (16718)------------------------------
% 7.51/2.21 % (16726)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_16357 for (2991ds/408Mi)
% 7.51/2.22 % (16727)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_16357 for (2990ds/5205Mi)
% 7.51/2.29 % (16707)Instruction limit reached!
% 7.51/2.29 % (16707)------------------------------
% 7.51/2.29 % (16707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.29 % (16707)Termination reason: Unknown
% 7.51/2.29 % (16707)Termination phase: Saturation
% 7.51/2.29
% 7.51/2.29 % (16707)Memory used [KB]: 7931
% 7.51/2.29 % (16707)Time elapsed: 0.325 s
% 7.51/2.29 % (16707)Instructions burned: 987 (million)
% 7.51/2.29 % (16707)------------------------------
% 7.51/2.29 % (16707)------------------------------
% 7.82/2.30 % (16728)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_16357 for (2990ds/1913Mi)
% 7.82/2.33 % (16726)Instruction limit reached!
% 7.82/2.33 % (16726)------------------------------
% 7.82/2.33 % (16726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.33 % (16726)Termination reason: Unknown
% 7.82/2.33 % (16726)Termination phase: Saturation
% 7.82/2.33
% 7.82/2.33 % (16726)Memory used [KB]: 7164
% 7.82/2.33 % (16726)Time elapsed: 0.115 s
% 7.82/2.33 % (16726)Instructions burned: 408 (million)
% 7.82/2.33 % (16726)------------------------------
% 7.82/2.33 % (16726)------------------------------
% 7.82/2.34 % (16729)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_16357 for (2989ds/4350Mi)
% 7.82/2.35 % (16714)Instruction limit reached!
% 7.82/2.35 % (16714)------------------------------
% 7.82/2.35 % (16714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.35 % (16714)Termination reason: Unknown
% 7.82/2.35 % (16714)Termination phase: Saturation
% 7.82/2.35
% 7.82/2.35 % (16714)Memory used [KB]: 9722
% 7.82/2.35 % (16714)Time elapsed: 0.266 s
% 7.82/2.35 % (16714)Instructions burned: 924 (million)
% 7.82/2.35 % (16714)------------------------------
% 7.82/2.35 % (16714)------------------------------
% 7.82/2.36 % (16730)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_16357 for (2989ds/68Mi)
% 7.82/2.38 % (16730)Instruction limit reached!
% 7.82/2.38 % (16730)------------------------------
% 7.82/2.38 % (16730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.38 % (16730)Termination reason: Unknown
% 7.82/2.38 % (16730)Termination phase: Saturation
% 7.82/2.38
% 7.82/2.38 % (16730)Memory used [KB]: 5756
% 7.82/2.38 % (16730)Time elapsed: 0.020 s
% 7.82/2.38 % (16730)Instructions burned: 70 (million)
% 7.82/2.38 % (16730)------------------------------
% 7.82/2.38 % (16730)------------------------------
% 7.82/2.38 % (16731)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_16357 for (2989ds/358Mi)
% 8.25/2.40 % (16719)Instruction limit reached!
% 8.25/2.40 % (16719)------------------------------
% 8.25/2.40 % (16719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.25/2.40 % (16719)Termination reason: Unknown
% 8.25/2.40 % (16719)Termination phase: Saturation
% 8.25/2.40
% 8.25/2.40 % (16719)Memory used [KB]: 10106
% 8.25/2.40 % (16719)Time elapsed: 0.291 s
% 8.25/2.40 % (16719)Instructions burned: 1022 (million)
% 8.25/2.40 % (16719)------------------------------
% 8.25/2.40 % (16719)------------------------------
% 8.25/2.41 % (16732)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_16357 for (2989ds/31Mi)
% 8.25/2.42 % (16732)Instruction limit reached!
% 8.25/2.42 % (16732)------------------------------
% 8.25/2.42 % (16732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.25/2.42 % (16732)Termination reason: Unknown
% 8.25/2.42 % (16732)Termination phase: Saturation
% 8.25/2.42
% 8.25/2.42 % (16732)Memory used [KB]: 5628
% 8.25/2.42 % (16732)Time elapsed: 0.010 s
% 8.25/2.42 % (16732)Instructions burned: 34 (million)
% 8.25/2.42 % (16732)------------------------------
% 8.25/2.42 % (16732)------------------------------
% 8.25/2.43 % (16733)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_16357 for (2988ds/279Mi)
% 8.25/2.49 % (16731)Instruction limit reached!
% 8.25/2.49 % (16731)------------------------------
% 8.25/2.49 % (16731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.25/2.49 % (16731)Termination reason: Unknown
% 8.25/2.49 % (16731)Termination phase: Saturation
% 8.25/2.49
% 8.25/2.49 % (16731)Memory used [KB]: 6908
% 8.25/2.49 % (16731)Time elapsed: 0.103 s
% 8.25/2.49 % (16731)Instructions burned: 358 (million)
% 8.25/2.49 % (16731)------------------------------
% 8.25/2.49 % (16731)------------------------------
% 8.68/2.50 % (16734)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_16357 for (2988ds/258Mi)
% 8.68/2.52 % (16727)First to succeed.
% 8.68/2.52 % (16733)Instruction limit reached!
% 8.68/2.52 % (16733)------------------------------
% 8.68/2.52 % (16733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.52 % (16733)Termination reason: Unknown
% 8.68/2.52 % (16733)Termination phase: Saturation
% 8.68/2.52
% 8.68/2.52 % (16733)Memory used [KB]: 6012
% 8.68/2.52 % (16733)Time elapsed: 0.092 s
% 8.68/2.52 % (16733)Instructions burned: 279 (million)
% 8.68/2.52 % (16733)------------------------------
% 8.68/2.52 % (16733)------------------------------
% 8.68/2.53 % (16735)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_16357 for (2987ds/26Mi)
% 8.68/2.53 % (16727)Refutation found. Thanks to Tanya!
% 8.68/2.53 % SZS status Theorem for DTF2THF_16357
% 8.68/2.53 % SZS output start Proof for DTF2THF_16357
% 8.68/2.53 thf(type_def_5, type, a: $tType).
% 8.68/2.53 thf(func_def_0, type, a: $tType).
% 8.68/2.53 thf(func_def_22, type, ph1: !>[X0: $tType]:(X0)).
% 8.68/2.53 thf(func_def_23, type, sK2: a > a > $o).
% 8.68/2.53 thf(func_def_24, type, sK3: a > a > $o).
% 8.68/2.53 thf(func_def_25, type, sK4: a).
% 8.68/2.53 thf(func_def_26, type, sK5: a).
% 8.68/2.53 thf(func_def_27, type, sK6: a > $o).
% 8.68/2.53 thf(func_def_28, type, sK7: a).
% 8.68/2.53 thf(func_def_29, type, sK8: a).
% 8.68/2.53 thf(func_def_30, type, sK9: a).
% 8.68/2.53 thf(func_def_31, type, sK10: a > $o).
% 8.68/2.53 thf(func_def_32, type, sK11: a).
% 8.68/2.53 thf(func_def_33, type, sK12: a).
% 8.68/2.53 thf(func_def_34, type, sK13: a > $o).
% 8.68/2.53 thf(func_def_35, type, sK14: a > $o).
% 8.68/2.53 thf(func_def_36, type, sK15: a > $o).
% 8.68/2.53 thf(func_def_37, type, sK16: a > $o).
% 8.68/2.53 thf(func_def_38, type, sK17: a).
% 8.68/2.53 thf(func_def_39, type, sK18: a).
% 8.68/2.53 thf(func_def_40, type, sK19: a).
% 8.68/2.53 thf(func_def_41, type, sK20: a).
% 8.68/2.53 thf(func_def_42, type, sK21: a > $o).
% 8.68/2.53 thf(func_def_43, type, sK22: a > $o).
% 8.68/2.53 thf(func_def_44, type, sK23: a > $o).
% 8.68/2.53 thf(func_def_45, type, sK24: a > $o).
% 8.68/2.53 thf(func_def_46, type, sK25: a > $o).
% 8.68/2.53 thf(func_def_47, type, sK26: (a > $o) > a).
% 8.68/2.53 thf(func_def_48, type, sK27: a > $o).
% 8.68/2.53 thf(func_def_49, type, sK28: a).
% 8.68/2.53 thf(func_def_50, type, sK29: a).
% 8.68/2.53 thf(func_def_51, type, sK30: a).
% 8.68/2.53 thf(func_def_52, type, sK31: a).
% 8.68/2.53 thf(func_def_53, type, sK32: a).
% 8.68/2.53 thf(func_def_54, type, sK33: a > $o).
% 8.68/2.53 thf(func_def_55, type, sK34: a > $o).
% 8.68/2.53 thf(func_def_56, type, sK35: a).
% 8.68/2.53 thf(func_def_57, type, sK36: a).
% 8.68/2.53 thf(func_def_58, type, sK37: a).
% 8.68/2.53 thf(func_def_59, type, sK38: a).
% 8.68/2.53 thf(func_def_60, type, sK39: a).
% 8.68/2.53 thf(func_def_61, type, sK40: a).
% 8.68/2.53 thf(func_def_62, type, sK41: a).
% 8.68/2.53 thf(func_def_63, type, sK42: a).
% 8.68/2.53 thf(func_def_64, type, sK43: a).
% 8.68/2.53 thf(func_def_65, type, sK44: a).
% 8.68/2.53 thf(func_def_66, type, sK45: a).
% 8.68/2.53 thf(func_def_67, type, sK46: a).
% 8.68/2.53 thf(func_def_68, type, sK47: a).
% 8.68/2.53 thf(func_def_69, type, sK48: (a > $o) > a).
% 8.68/2.53 thf(func_def_70, type, sK49: a).
% 8.68/2.53 thf(func_def_71, type, sK50: a).
% 8.68/2.53 thf(func_def_72, type, sK51: a).
% 8.68/2.53 thf(func_def_73, type, sK52: a).
% 8.68/2.53 thf(func_def_74, type, sK53: a).
% 8.68/2.53 thf(func_def_75, type, sK54: a).
% 8.68/2.53 thf(func_def_76, type, sK55: a).
% 8.68/2.53 thf(func_def_77, type, sK56: a).
% 8.68/2.53 thf(func_def_78, type, sK57: a).
% 8.68/2.53 thf(func_def_79, type, sK58: a).
% 8.68/2.53 thf(f5379,plain,(
% 8.68/2.53 $false),
% 8.68/2.53 inference(avatar_sat_refutation,[status(thm)],[f27,f34,f128,f132,f205,f269,f285,f493,f521,f540,f710,f1097,f2679,f2685,f3476,f3627,f3694,f3736,f3893,f4110,f4457,f4728,f4863,f4924,f5018,f5378])).
% 8.68/2.53 thf(f5378,plain,(
% 8.68/2.53 ~spl0_3 | ~spl0_80),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f5377])).
% 8.68/2.53 thf(f5377,plain,(
% 8.68/2.53 $false | (~spl0_3 | ~spl0_80)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f5376])).
% 8.68/2.53 thf(f5376,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_3 | ~spl0_80)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f5375,f5299])).
% 8.68/2.53 thf(f5299,plain,(
% 8.68/2.53 ((sK6 @ sK58) = $false) | ~spl0_80),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f5285])).
% 8.68/2.53 thf(f5285,plain,(
% 8.68/2.53 ($false = (((sK6 @ sK57) & (sK3 @ sK57 @ sK58)) => (sK6 @ sK58))) | ~spl0_80),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f5284])).
% 8.68/2.53 thf(f5284,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (((sK6 @ sK57) & (sK3 @ sK57 @ Y0)) => (sK6 @ Y0))) @ sK58)) | ~spl0_80),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f5270])).
% 8.68/2.53 thf(f5270,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK57) & (sK3 @ sK57 @ Y0)) => (sK6 @ Y0))))) | ~spl0_80),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f5268])).
% 8.68/2.53 thf(f5268,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK6 @ Y1))))) @ sK57)) | ~spl0_80),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f4456])).
% 8.68/2.53 thf(f4456,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK6 @ Y1)))))) = $false) | ~spl0_80),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f4455])).
% 8.68/2.53 thf(f4455,definition,(
% 8.68/2.53 spl0_80 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK6 @ Y1)))))) = $false)),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_80])],[avatar_definition])).
% 8.68/2.53 thf(f5375,plain,(
% 8.68/2.53 ((sK6 @ sK58) = $true) | (~spl0_3 | ~spl0_80)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f5374])).
% 8.68/2.53 thf(f5374,plain,(
% 8.68/2.53 ($true = ($true => (sK6 @ sK58))) | (~spl0_3 | ~spl0_80)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f5373,f5341])).
% 8.68/2.53 thf(f5341,plain,(
% 8.68/2.53 ($true = (sK6 @ sK57)) | ~spl0_80),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f5300])).
% 8.68/2.53 thf(f5300,plain,(
% 8.68/2.53 ($true = ((sK6 @ sK57) & (sK3 @ sK57 @ sK58))) | ~spl0_80),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f5285])).
% 8.68/2.53 thf(f5373,plain,(
% 8.68/2.53 ($true = ((sK6 @ sK57) => (sK6 @ sK58))) | (~spl0_3 | ~spl0_80)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f5372])).
% 8.68/2.53 thf(f5372,plain,(
% 8.68/2.53 ($true = (($true & (sK6 @ sK57)) => (sK6 @ sK58))) | (~spl0_3 | ~spl0_80)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f5371])).
% 8.68/2.53 thf(f5371,plain,(
% 8.68/2.53 (((((sK2 @ sK57 @ sK58) | $true) & (sK6 @ sK57)) => (sK6 @ sK58)) = $true) | (~spl0_3 | ~spl0_80)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2721,f5343])).
% 8.68/2.53 thf(f5343,plain,(
% 8.68/2.53 ($true = (sK3 @ sK57 @ sK58)) | ~spl0_80),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f5342])).
% 8.68/2.53 thf(f5342,plain,(
% 8.68/2.53 (($true & (sK3 @ sK57 @ sK58)) = $true) | ~spl0_80),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f5300,f5341])).
% 8.68/2.53 thf(f2721,plain,(
% 8.68/2.53 ( ! [X2 : a,X1 : a] : (($true = ((((sK2 @ X1 @ X2) | (sK3 @ X1 @ X2)) & (sK6 @ X1)) => (sK6 @ X2)))) ) | ~spl0_3),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f2720])).
% 8.68/2.53 thf(f2720,plain,(
% 8.68/2.53 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((((sK2 @ X1 @ Y0) | (sK3 @ X1 @ Y0)) & (sK6 @ X1)) => (sK6 @ Y0))) @ X2))) ) | ~spl0_3),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f2719])).
% 8.68/2.53 thf(f2719,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((((sK2 @ X1 @ Y0) | (sK3 @ X1 @ Y0)) & (sK6 @ X1)) => (sK6 @ Y0)))))) ) | ~spl0_3),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f2718])).
% 8.68/2.53 thf(f2718,plain,(
% 8.68/2.53 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ X1) = $true)) ) | ~spl0_3),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f2707])).
% 8.68/2.53 thf(f2707,plain,(
% 8.68/2.53 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1))))))) | ~spl0_3),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f2706])).
% 8.68/2.53 thf(f2706,plain,(
% 8.68/2.53 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & $true) = $true) | ~spl0_3),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f2691,f2704])).
% 8.68/2.53 thf(f2704,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK6 @ Y0)))) = $true) | ~spl0_3),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f2691])).
% 8.68/2.53 thf(f2691,plain,(
% 8.68/2.53 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK6 @ Y0)))))) | ~spl0_3),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f2689])).
% 8.68/2.53 thf(f2689,plain,(
% 8.68/2.53 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK6 @ Y0))))) => (sK6 @ sK5))) | ~spl0_3),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f2688])).
% 8.68/2.53 thf(f2688,plain,(
% 8.68/2.53 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5))) @ sK6) = $false) | ~spl0_3),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f30])).
% 8.68/2.53 thf(f30,plain,(
% 8.68/2.53 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5))))) | ~spl0_3),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f29])).
% 8.68/2.53 thf(f29,definition,(
% 8.68/2.53 spl0_3 <=> ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 8.68/2.53 thf(f5018,plain,(
% 8.68/2.53 ~spl0_3 | ~spl0_85),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f5017])).
% 8.68/2.53 thf(f5017,plain,(
% 8.68/2.53 $false | (~spl0_3 | ~spl0_85)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f5016])).
% 8.68/2.53 thf(f5016,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_3 | ~spl0_85)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f5015,f4946])).
% 8.68/2.53 thf(f4946,plain,(
% 8.68/2.53 ((sK6 @ sK54) = $false) | ~spl0_85),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4937])).
% 8.68/2.53 thf(f4937,plain,(
% 8.68/2.53 ((((sK6 @ sK55) & (sK2 @ sK55 @ sK54)) => (sK6 @ sK54)) = $false) | ~spl0_85),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4936])).
% 8.68/2.53 thf(f4936,plain,(
% 8.68/2.53 (((^[Y0 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ sK54)) => (sK6 @ sK54))) @ sK55) = $false) | ~spl0_85),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f4931])).
% 8.68/2.53 thf(f4931,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ sK54)) => (sK6 @ sK54))))) | ~spl0_85),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4927])).
% 8.68/2.53 thf(f4927,plain,(
% 8.68/2.53 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))) @ sK54) = $false) | ~spl0_85),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f4862])).
% 8.68/2.53 thf(f4862,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))))) | ~spl0_85),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f4861])).
% 8.68/2.53 thf(f4861,definition,(
% 8.68/2.53 spl0_85 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_85])],[avatar_definition])).
% 8.68/2.53 thf(f5015,plain,(
% 8.68/2.53 ((sK6 @ sK54) = $true) | (~spl0_3 | ~spl0_85)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f5014])).
% 8.68/2.53 thf(f5014,plain,(
% 8.68/2.53 (($true => (sK6 @ sK54)) = $true) | (~spl0_3 | ~spl0_85)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f5013,f4994])).
% 8.68/2.53 thf(f4994,plain,(
% 8.68/2.53 ((sK6 @ sK56) = $true) | ~spl0_85),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4985])).
% 8.68/2.53 thf(f4985,plain,(
% 8.68/2.53 ($true = ((sK6 @ sK56) & (sK2 @ sK56 @ sK54))) | ~spl0_85),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f4970])).
% 8.68/2.53 thf(f4970,plain,(
% 8.68/2.53 ($false = (~ ((sK6 @ sK56) & (sK2 @ sK56 @ sK54)))) | ~spl0_85),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4969])).
% 8.68/2.53 thf(f4969,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (~ ((sK6 @ Y0) & (sK2 @ Y0 @ sK54)))) @ sK56)) | ~spl0_85),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f4951])).
% 8.68/2.53 thf(f4951,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK6 @ Y0) & (sK2 @ Y0 @ sK54)))))) | ~spl0_85),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4949])).
% 8.68/2.53 thf(f4949,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ sK54)) => $false)))) | ~spl0_85),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f4931,f4946])).
% 8.68/2.53 thf(f5013,plain,(
% 8.68/2.53 ($true = ((sK6 @ sK56) => (sK6 @ sK54))) | (~spl0_3 | ~spl0_85)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f5012])).
% 8.68/2.53 thf(f5012,plain,(
% 8.68/2.53 ((($true & (sK6 @ sK56)) => (sK6 @ sK54)) = $true) | (~spl0_3 | ~spl0_85)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f5011])).
% 8.68/2.53 thf(f5011,plain,(
% 8.68/2.53 (((($true | (sK3 @ sK56 @ sK54)) & (sK6 @ sK56)) => (sK6 @ sK54)) = $true) | (~spl0_3 | ~spl0_85)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2721,f4996])).
% 8.68/2.53 thf(f4996,plain,(
% 8.68/2.53 ($true = (sK2 @ sK56 @ sK54)) | ~spl0_85),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4995])).
% 8.68/2.53 thf(f4995,plain,(
% 8.68/2.53 (($true & (sK2 @ sK56 @ sK54)) = $true) | ~spl0_85),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f4985,f4994])).
% 8.68/2.53 thf(f4924,plain,(
% 8.68/2.53 ~spl0_3 | ~spl0_84),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f4923])).
% 8.68/2.53 thf(f4923,plain,(
% 8.68/2.53 $false | (~spl0_3 | ~spl0_84)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f4922])).
% 8.68/2.53 thf(f4922,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_3 | ~spl0_84)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4921])).
% 8.68/2.53 thf(f4921,plain,(
% 8.68/2.53 ($true = (~ $true)) | (~spl0_3 | ~spl0_84)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4920])).
% 8.68/2.53 thf(f4920,plain,(
% 8.68/2.53 ($true = (~ ($true | (sK3 @ sK4 @ sK53)))) | (~spl0_3 | ~spl0_84)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f4914,f4900])).
% 8.68/2.53 thf(f4900,plain,(
% 8.68/2.53 ((sK2 @ sK4 @ sK53) = $true) | ~spl0_84),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4882])).
% 8.68/2.53 thf(f4882,plain,(
% 8.68/2.53 ($false = ((sK2 @ sK4 @ sK53) => (sK6 @ sK53))) | ~spl0_84),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4880])).
% 8.68/2.53 thf(f4880,plain,(
% 8.68/2.53 (((^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0))) @ sK53) = $false) | ~spl0_84),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f4859])).
% 8.68/2.53 thf(f4859,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0))))) | ~spl0_84),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f4858])).
% 8.68/2.53 thf(f4858,definition,(
% 8.68/2.53 spl0_84 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_84])],[avatar_definition])).
% 8.68/2.53 thf(f4914,plain,(
% 8.68/2.53 ((~ ((sK2 @ sK4 @ sK53) | (sK3 @ sK4 @ sK53))) = $true) | (~spl0_3 | ~spl0_84)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4908])).
% 8.68/2.53 thf(f4908,plain,(
% 8.68/2.53 ((((sK2 @ sK4 @ sK53) | (sK3 @ sK4 @ sK53)) => $false) = $true) | (~spl0_3 | ~spl0_84)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2794,f4899])).
% 8.68/2.53 thf(f4899,plain,(
% 8.68/2.53 ((sK6 @ sK53) = $false) | ~spl0_84),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4882])).
% 8.68/2.53 thf(f2794,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = (((sK2 @ sK4 @ X1) | (sK3 @ sK4 @ X1)) => (sK6 @ X1)))) ) | ~spl0_3),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f2793])).
% 8.68/2.53 thf(f2793,plain,(
% 8.68/2.53 ( ! [X1 : a] : ((((^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK6 @ Y0))) @ X1) = $true)) ) | ~spl0_3),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f2704])).
% 8.68/2.53 thf(f4863,plain,(
% 8.68/2.53 spl0_84 | spl0_85 | ~spl0_6 | ~spl0_13),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f4854,f488,f126,f4861,f4858])).
% 8.68/2.53 thf(f126,definition,(
% 8.68/2.53 spl0_6 <=> ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 8.68/2.53 thf(f488,definition,(
% 8.68/2.53 spl0_13 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK9)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 8.68/2.53 thf(f4854,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))))) | (~spl0_6 | ~spl0_13)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4839])).
% 8.68/2.53 thf(f4839,plain,(
% 8.68/2.53 ($false = ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))))) | (~spl0_6 | ~spl0_13)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f4668])).
% 8.68/2.53 thf(f4668,plain,(
% 8.68/2.53 ($true = (~ ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))))))) | (~spl0_6 | ~spl0_13)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4666])).
% 8.68/2.53 thf(f4666,plain,(
% 8.68/2.53 ($true = (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))))) => $false)) | (~spl0_6 | ~spl0_13)),
% 8.68/2.53 inference(superposition,[status(thm)],[f4651,f4470])).
% 8.68/2.53 thf(f4470,plain,(
% 8.68/2.53 ($false = (sK6 @ sK9)) | (~spl0_6 | ~spl0_13)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4469])).
% 8.68/2.53 thf(f4469,plain,(
% 8.68/2.53 (($true => (sK6 @ sK9)) = $false) | (~spl0_6 | ~spl0_13)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4468])).
% 8.68/2.53 thf(f4468,plain,(
% 8.68/2.53 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) | $true) => (sK6 @ sK9))) | (~spl0_6 | ~spl0_13)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f4120,f489])).
% 8.68/2.53 thf(f489,plain,(
% 8.68/2.53 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK9))))) | ~spl0_13),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f488])).
% 8.68/2.53 thf(f4120,plain,(
% 8.68/2.53 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK9))))) => (sK6 @ sK9)) = $false) | ~spl0_6),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4114])).
% 8.68/2.53 thf(f4114,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))) @ sK9)) | ~spl0_6),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f127])).
% 8.68/2.53 thf(f127,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))))) | ~spl0_6),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f126])).
% 8.68/2.53 thf(f4651,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & (sK2 @ Y1 @ Y0)) => (X1 @ Y0))))))) => (X1 @ sK9)))) ) | ~spl0_13),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4650])).
% 8.68/2.53 thf(f4650,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK9))) @ X1))) ) | ~spl0_13),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f489])).
% 8.68/2.53 thf(f4728,plain,(
% 8.68/2.53 ~spl0_3 | ~spl0_79),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f4727])).
% 8.68/2.53 thf(f4727,plain,(
% 8.68/2.53 $false | (~spl0_3 | ~spl0_79)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f4726])).
% 8.68/2.53 thf(f4726,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_3 | ~spl0_79)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4725])).
% 8.68/2.53 thf(f4725,plain,(
% 8.68/2.53 ($true = (~ $true)) | (~spl0_3 | ~spl0_79)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4724])).
% 8.68/2.53 thf(f4724,plain,(
% 8.68/2.53 ((~ ((sK2 @ sK4 @ sK49) | $true)) = $true) | (~spl0_3 | ~spl0_79)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f4716,f4704])).
% 8.68/2.53 thf(f4704,plain,(
% 8.68/2.53 ((sK3 @ sK4 @ sK49) = $true) | ~spl0_79),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4687])).
% 8.68/2.53 thf(f4687,plain,(
% 8.68/2.53 (((sK3 @ sK4 @ sK49) => (sK6 @ sK49)) = $false) | ~spl0_79),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4686])).
% 8.68/2.53 thf(f4686,plain,(
% 8.68/2.53 (((^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK6 @ Y0))) @ sK49) = $false) | ~spl0_79),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f4453])).
% 8.68/2.53 thf(f4453,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK6 @ Y0)))) = $false) | ~spl0_79),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f4452])).
% 8.68/2.53 thf(f4452,definition,(
% 8.68/2.53 spl0_79 <=> ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK6 @ Y0)))) = $false)),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_79])],[avatar_definition])).
% 8.68/2.53 thf(f4716,plain,(
% 8.68/2.53 ((~ ((sK2 @ sK4 @ sK49) | (sK3 @ sK4 @ sK49))) = $true) | (~spl0_3 | ~spl0_79)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4712])).
% 8.68/2.53 thf(f4712,plain,(
% 8.68/2.53 ((((sK2 @ sK4 @ sK49) | (sK3 @ sK4 @ sK49)) => $false) = $true) | (~spl0_3 | ~spl0_79)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2794,f4703])).
% 8.68/2.53 thf(f4703,plain,(
% 8.68/2.53 ((sK6 @ sK49) = $false) | ~spl0_79),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4687])).
% 8.68/2.53 thf(f4457,plain,(
% 8.68/2.53 spl0_79 | spl0_80 | ~spl0_6 | ~spl0_14),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f4448,f491,f126,f4455,f4452])).
% 8.68/2.53 thf(f491,definition,(
% 8.68/2.53 spl0_14 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 8.68/2.53 thf(f4448,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK6 @ Y1)))))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK6 @ Y0)))) = $false) | (~spl0_6 | ~spl0_14)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4436])).
% 8.68/2.53 thf(f4436,plain,(
% 8.68/2.53 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK6 @ Y0))))) = $false) | (~spl0_6 | ~spl0_14)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f4294])).
% 8.68/2.53 thf(f4294,plain,(
% 8.68/2.53 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK6 @ Y0)))))) = $true) | (~spl0_6 | ~spl0_14)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4293])).
% 8.68/2.53 thf(f4293,plain,(
% 8.68/2.53 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK6 @ Y0))))) => $false)) | (~spl0_6 | ~spl0_14)),
% 8.68/2.53 inference(superposition,[status(thm)],[f4276,f4123])).
% 8.68/2.53 thf(f4123,plain,(
% 8.68/2.53 ($false = (sK6 @ sK9)) | (~spl0_6 | ~spl0_14)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4122])).
% 8.68/2.53 thf(f4122,plain,(
% 8.68/2.53 (($true => (sK6 @ sK9)) = $false) | (~spl0_6 | ~spl0_14)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4121])).
% 8.68/2.53 thf(f4121,plain,(
% 8.68/2.53 ($false = (($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK9))))) => (sK6 @ sK9))) | (~spl0_6 | ~spl0_14)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f4120,f492])).
% 8.68/2.53 thf(f492,plain,(
% 8.68/2.53 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))))) | ~spl0_14),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f491])).
% 8.68/2.53 thf(f4276,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & (sK3 @ Y0 @ Y1)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (X1 @ Y0))))) => (X1 @ sK9)))) ) | ~spl0_14),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4275])).
% 8.68/2.53 thf(f4275,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))) @ X1) = $true)) ) | ~spl0_14),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f492])).
% 8.68/2.53 thf(f4110,plain,(
% 8.68/2.53 ~spl0_3 | ~spl0_11),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f4109])).
% 8.68/2.53 thf(f4109,plain,(
% 8.68/2.53 $false | (~spl0_3 | ~spl0_11)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f4108])).
% 8.68/2.53 thf(f4108,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_3 | ~spl0_11)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f4107,f4040])).
% 8.68/2.53 thf(f4040,plain,(
% 8.68/2.53 ((sK6 @ sK42) = $false) | ~spl0_11),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4023])).
% 8.68/2.53 thf(f4023,plain,(
% 8.68/2.53 ((((sK3 @ sK41 @ sK42) & (sK6 @ sK41)) => (sK6 @ sK42)) = $false) | ~spl0_11),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4022])).
% 8.68/2.53 thf(f4022,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (((sK3 @ sK41 @ Y0) & (sK6 @ sK41)) => (sK6 @ Y0))) @ sK42)) | ~spl0_11),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f4013])).
% 8.68/2.53 thf(f4013,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((sK3 @ sK41 @ Y0) & (sK6 @ sK41)) => (sK6 @ Y0))))) | ~spl0_11),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f4011])).
% 8.68/2.53 thf(f4011,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ sK41)) | ~spl0_11),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f281])).
% 8.68/2.53 thf(f281,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) = $false) | ~spl0_11),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f280])).
% 8.68/2.53 thf(f280,definition,(
% 8.68/2.53 spl0_11 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) = $false)),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 8.68/2.53 thf(f4107,plain,(
% 8.68/2.53 ((sK6 @ sK42) = $true) | (~spl0_3 | ~spl0_11)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4106])).
% 8.68/2.53 thf(f4106,plain,(
% 8.68/2.53 (($true => (sK6 @ sK42)) = $true) | (~spl0_3 | ~spl0_11)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f4105,f4066])).
% 8.68/2.53 thf(f4066,plain,(
% 8.68/2.53 ($true = (sK6 @ sK41)) | ~spl0_11),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4041])).
% 8.68/2.53 thf(f4041,plain,(
% 8.68/2.53 ($true = ((sK3 @ sK41 @ sK42) & (sK6 @ sK41))) | ~spl0_11),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f4023])).
% 8.68/2.53 thf(f4105,plain,(
% 8.68/2.53 (((sK6 @ sK41) => (sK6 @ sK42)) = $true) | (~spl0_3 | ~spl0_11)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4104])).
% 8.68/2.53 thf(f4104,plain,(
% 8.68/2.53 ((($true & (sK6 @ sK41)) => (sK6 @ sK42)) = $true) | (~spl0_3 | ~spl0_11)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4103])).
% 8.68/2.53 thf(f4103,plain,(
% 8.68/2.53 (((((sK2 @ sK41 @ sK42) | $true) & (sK6 @ sK41)) => (sK6 @ sK42)) = $true) | (~spl0_3 | ~spl0_11)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2721,f4069])).
% 8.68/2.53 thf(f4069,plain,(
% 8.68/2.53 ($true = (sK3 @ sK41 @ sK42)) | ~spl0_11),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f4068])).
% 8.68/2.53 thf(f4068,plain,(
% 8.68/2.53 ($true = ((sK3 @ sK41 @ sK42) & $true)) | ~spl0_11),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f4041,f4066])).
% 8.68/2.53 thf(f3893,plain,(
% 8.68/2.53 ~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_12),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f3892])).
% 8.68/2.53 thf(f3892,plain,(
% 8.68/2.53 $false | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_12)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f3891])).
% 8.68/2.53 thf(f3891,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_12)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3890])).
% 8.68/2.53 thf(f3890,plain,(
% 8.68/2.53 ($true = (~ $true)) | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_12)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3889])).
% 8.68/2.53 thf(f3889,plain,(
% 8.68/2.53 ((~ ((sK2 @ sK7 @ sK40) | $true)) = $true) | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_12)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f3880,f3840])).
% 8.68/2.53 thf(f3840,plain,(
% 8.68/2.53 ($true = (sK3 @ sK7 @ sK40)) | ~spl0_12),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f3827])).
% 8.68/2.53 thf(f3827,plain,(
% 8.68/2.53 ($false = ((sK3 @ sK7 @ sK40) => (sK6 @ sK40))) | ~spl0_12),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f3823])).
% 8.68/2.53 thf(f3823,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: ((sK3 @ sK7 @ Y0) => (sK6 @ Y0))) @ sK40)) | ~spl0_12),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f284])).
% 8.68/2.53 thf(f284,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK7 @ Y0) => (sK6 @ Y0))))) | ~spl0_12),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f283])).
% 8.68/2.53 thf(f283,definition,(
% 8.68/2.53 spl0_12 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK7 @ Y0) => (sK6 @ Y0)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 8.68/2.53 thf(f3880,plain,(
% 8.68/2.53 ($true = (~ ((sK2 @ sK7 @ sK40) | (sK3 @ sK7 @ sK40)))) | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_12)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3867])).
% 8.68/2.53 thf(f3867,plain,(
% 8.68/2.53 ($true = (((sK2 @ sK7 @ sK40) | (sK3 @ sK7 @ sK40)) => $false)) | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_12)),
% 8.68/2.53 inference(superposition,[status(thm)],[f3724,f3842])).
% 8.68/2.53 thf(f3842,plain,(
% 8.68/2.53 ((sK6 @ sK40) = $false) | ~spl0_12),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3841])).
% 8.68/2.53 thf(f3841,plain,(
% 8.68/2.53 ($false = ($true => (sK6 @ sK40))) | ~spl0_12),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f3827,f3840])).
% 8.68/2.53 thf(f3724,plain,(
% 8.68/2.53 ( ! [X0 : a] : (($true = (((sK2 @ sK7 @ X0) | (sK3 @ sK7 @ X0)) => (sK6 @ X0)))) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3718])).
% 8.68/2.53 thf(f3718,plain,(
% 8.68/2.53 ( ! [X0 : a] : (($true = ((((sK2 @ sK7 @ X0) | (sK3 @ sK7 @ X0)) & $true) => (sK6 @ X0)))) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2721,f3699])).
% 8.68/2.53 thf(f3699,plain,(
% 8.68/2.53 ($true = (sK6 @ sK7)) | (~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f3697])).
% 8.68/2.53 thf(f3697,plain,(
% 8.68/2.53 ($false = ((sK6 @ sK7) => (sK6 @ sK8))) | (~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3696])).
% 8.68/2.53 thf(f3696,plain,(
% 8.68/2.53 ((((sK6 @ sK7) & $true) => (sK6 @ sK8)) = $false) | (~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3695])).
% 8.68/2.53 thf(f3695,plain,(
% 8.68/2.53 ($false = (((sK6 @ sK7) & ($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))))) => (sK6 @ sK8))) | (~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f2848,f201])).
% 8.68/2.53 thf(f201,plain,(
% 8.68/2.53 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8))))) | ~spl0_7),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f200])).
% 8.68/2.53 thf(f200,definition,(
% 8.68/2.53 spl0_7 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 8.68/2.53 thf(f2848,plain,(
% 8.68/2.53 ((((sK6 @ sK7) & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))))) => (sK6 @ sK8)) = $false) | ~spl0_5),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f2847])).
% 8.68/2.53 thf(f2847,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (((sK6 @ sK7) & ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK7 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) => (sK6 @ Y0))) @ sK8)) | ~spl0_5),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f2836])).
% 8.68/2.53 thf(f2836,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK7) & ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK7 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) => (sK6 @ Y0))))) | ~spl0_5),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f2834])).
% 8.68/2.53 thf(f2834,plain,(
% 8.68/2.53 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK6 @ Y1))))) @ sK7) = $false) | ~spl0_5),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f124])).
% 8.68/2.53 thf(f124,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK6 @ Y1)))))) = $false) | ~spl0_5),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f123])).
% 8.68/2.53 thf(f123,definition,(
% 8.68/2.53 spl0_5 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK6 @ Y1)))))) = $false)),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 8.68/2.53 thf(f3736,plain,(
% 8.68/2.53 ~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_68),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f3735])).
% 8.68/2.53 thf(f3735,plain,(
% 8.68/2.53 $false | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_68)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f3734])).
% 8.68/2.53 thf(f3734,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_68)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f3733,f3667])).
% 8.68/2.53 thf(f3667,plain,(
% 8.68/2.53 ($false = (sK6 @ sK39)) | ~spl0_68),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f3632])).
% 8.68/2.53 thf(f3632,plain,(
% 8.68/2.53 ($false = ((sK2 @ sK7 @ sK39) => (sK6 @ sK39))) | ~spl0_68),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f3630])).
% 8.68/2.53 thf(f3630,plain,(
% 8.68/2.53 (((^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))) @ sK39) = $false) | ~spl0_68),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f3475])).
% 8.68/2.53 thf(f3475,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))))) | ~spl0_68),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f3474])).
% 8.68/2.53 thf(f3474,definition,(
% 8.68/2.53 spl0_68 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_68])],[avatar_definition])).
% 8.68/2.53 thf(f3733,plain,(
% 8.68/2.53 ($true = (sK6 @ sK39)) | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_68)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3732])).
% 8.68/2.53 thf(f3732,plain,(
% 8.68/2.53 ($true = ($true => (sK6 @ sK39))) | (~spl0_3 | ~spl0_5 | ~spl0_7 | ~spl0_68)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f3731,f3699])).
% 8.68/2.53 thf(f3731,plain,(
% 8.68/2.53 (((sK6 @ sK7) => (sK6 @ sK39)) = $true) | (~spl0_3 | ~spl0_68)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3730])).
% 8.68/2.53 thf(f3730,plain,(
% 8.68/2.53 ((($true & (sK6 @ sK7)) => (sK6 @ sK39)) = $true) | (~spl0_3 | ~spl0_68)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3729])).
% 8.68/2.53 thf(f3729,plain,(
% 8.68/2.53 ($true = ((($true | (sK3 @ sK7 @ sK39)) & (sK6 @ sK7)) => (sK6 @ sK39))) | (~spl0_3 | ~spl0_68)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2721,f3668])).
% 8.68/2.53 thf(f3668,plain,(
% 8.68/2.53 ((sK2 @ sK7 @ sK39) = $true) | ~spl0_68),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f3632])).
% 8.68/2.53 thf(f3694,plain,(
% 8.68/2.53 ~spl0_3 | ~spl0_5 | ~spl0_8 | ~spl0_68),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f3693])).
% 8.68/2.53 thf(f3693,plain,(
% 8.68/2.53 $false | (~spl0_3 | ~spl0_5 | ~spl0_8 | ~spl0_68)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f3692])).
% 8.68/2.53 thf(f3692,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_3 | ~spl0_5 | ~spl0_8 | ~spl0_68)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3691])).
% 8.68/2.53 thf(f3691,plain,(
% 8.68/2.53 ($true = (~ $true)) | (~spl0_3 | ~spl0_5 | ~spl0_8 | ~spl0_68)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3690])).
% 8.68/2.53 thf(f3690,plain,(
% 8.68/2.53 ($true = (~ ($true | (sK3 @ sK7 @ sK39)))) | (~spl0_3 | ~spl0_5 | ~spl0_8 | ~spl0_68)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f3689,f3668])).
% 8.68/2.53 thf(f3689,plain,(
% 8.68/2.53 ((~ ((sK2 @ sK7 @ sK39) | (sK3 @ sK7 @ sK39))) = $true) | (~spl0_3 | ~spl0_5 | ~spl0_8 | ~spl0_68)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3678])).
% 8.68/2.53 thf(f3678,plain,(
% 8.68/2.53 ($true = (((sK2 @ sK7 @ sK39) | (sK3 @ sK7 @ sK39)) => $false)) | (~spl0_3 | ~spl0_5 | ~spl0_8 | ~spl0_68)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2880,f3667])).
% 8.68/2.53 thf(f2880,plain,(
% 8.68/2.53 ( ! [X0 : a] : (($true = (((sK2 @ sK7 @ X0) | (sK3 @ sK7 @ X0)) => (sK6 @ X0)))) ) | (~spl0_3 | ~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f2875])).
% 8.68/2.53 thf(f2875,plain,(
% 8.68/2.53 ( ! [X0 : a] : (($true = ((((sK2 @ sK7 @ X0) | (sK3 @ sK7 @ X0)) & $true) => (sK6 @ X0)))) ) | (~spl0_3 | ~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2721,f2861])).
% 8.68/2.53 thf(f2861,plain,(
% 8.68/2.53 ($true = (sK6 @ sK7)) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f2851])).
% 8.68/2.53 thf(f2851,plain,(
% 8.68/2.53 ($false = ((sK6 @ sK7) => (sK6 @ sK8))) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f2850])).
% 8.68/2.53 thf(f2850,plain,(
% 8.68/2.53 ((((sK6 @ sK7) & $true) => (sK6 @ sK8)) = $false) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f2849])).
% 8.68/2.53 thf(f2849,plain,(
% 8.68/2.53 ((((sK6 @ sK7) & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) | $true)) => (sK6 @ sK8)) = $false) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f2848,f204])).
% 8.68/2.53 thf(f204,plain,(
% 8.68/2.53 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true) | ~spl0_8),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f203])).
% 8.68/2.53 thf(f203,definition,(
% 8.68/2.53 spl0_8 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true)),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 8.68/2.53 thf(f3627,plain,(
% 8.68/2.53 ~spl0_3 | ~spl0_67),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f3626])).
% 8.68/2.53 thf(f3626,plain,(
% 8.68/2.53 $false | (~spl0_3 | ~spl0_67)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f3625])).
% 8.68/2.53 thf(f3625,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_3 | ~spl0_67)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f3624,f3523])).
% 8.68/2.53 thf(f3523,plain,(
% 8.68/2.53 ($false = (sK6 @ sK36)) | ~spl0_67),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f3511])).
% 8.68/2.53 thf(f3511,plain,(
% 8.68/2.53 ($false = (((sK2 @ sK35 @ sK36) & (sK6 @ sK35)) => (sK6 @ sK36))) | ~spl0_67),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f3510])).
% 8.68/2.53 thf(f3510,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (((sK2 @ sK35 @ Y0) & (sK6 @ sK35)) => (sK6 @ Y0))) @ sK36)) | ~spl0_67),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f3496])).
% 8.68/2.53 thf(f3496,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK35 @ Y0) & (sK6 @ sK35)) => (sK6 @ Y0)))) = $false) | ~spl0_67),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f3492])).
% 8.68/2.53 thf(f3492,plain,(
% 8.68/2.53 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ sK35) = $false) | ~spl0_67),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f3472])).
% 8.68/2.53 thf(f3472,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1))))))) | ~spl0_67),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f3471])).
% 8.68/2.53 thf(f3471,definition,(
% 8.68/2.53 spl0_67 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_67])],[avatar_definition])).
% 8.68/2.53 thf(f3624,plain,(
% 8.68/2.53 ($true = (sK6 @ sK36)) | (~spl0_3 | ~spl0_67)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3623])).
% 8.68/2.53 thf(f3623,plain,(
% 8.68/2.53 (($true => (sK6 @ sK36)) = $true) | (~spl0_3 | ~spl0_67)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f3622,f3592])).
% 8.68/2.53 thf(f3592,plain,(
% 8.68/2.53 ($true = (sK6 @ sK35)) | ~spl0_67),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f3524])).
% 8.68/2.53 thf(f3524,plain,(
% 8.68/2.53 ($true = ((sK2 @ sK35 @ sK36) & (sK6 @ sK35))) | ~spl0_67),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f3511])).
% 8.68/2.53 thf(f3622,plain,(
% 8.68/2.53 ($true = ((sK6 @ sK35) => (sK6 @ sK36))) | (~spl0_3 | ~spl0_67)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3621])).
% 8.68/2.53 thf(f3621,plain,(
% 8.68/2.53 ((($true & (sK6 @ sK35)) => (sK6 @ sK36)) = $true) | (~spl0_3 | ~spl0_67)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3620])).
% 8.68/2.53 thf(f3620,plain,(
% 8.68/2.53 (((($true | (sK3 @ sK35 @ sK36)) & (sK6 @ sK35)) => (sK6 @ sK36)) = $true) | (~spl0_3 | ~spl0_67)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2721,f3595])).
% 8.68/2.53 thf(f3595,plain,(
% 8.68/2.53 ($true = (sK2 @ sK35 @ sK36)) | ~spl0_67),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3594])).
% 8.68/2.53 thf(f3594,plain,(
% 8.68/2.53 ($true = ((sK2 @ sK35 @ sK36) & $true)) | ~spl0_67),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f3524,f3592])).
% 8.68/2.53 thf(f3476,plain,(
% 8.68/2.53 spl0_67 | spl0_68 | ~spl0_5 | ~spl0_8),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f3467,f203,f123,f3474,f3471])).
% 8.68/2.53 thf(f3467,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1))))))) | ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))))) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f3453])).
% 8.68/2.53 thf(f3453,plain,(
% 8.68/2.53 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))))) = $false) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f3074])).
% 8.68/2.53 thf(f3074,plain,(
% 8.68/2.53 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))))))) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f3071])).
% 8.68/2.53 thf(f3071,plain,(
% 8.68/2.53 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))))) => $false) = $true) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(superposition,[status(thm)],[f3058,f2863])).
% 8.68/2.53 thf(f2863,plain,(
% 8.68/2.53 ($false = (sK6 @ sK8)) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f2862])).
% 8.68/2.53 thf(f2862,plain,(
% 8.68/2.53 (($true => (sK6 @ sK8)) = $false) | (~spl0_5 | ~spl0_8)),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f2851,f2861])).
% 8.68/2.53 thf(f3058,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (X1 @ Y0)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (X1 @ Y0))))) => (X1 @ sK8)))) ) | ~spl0_8),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f3057])).
% 8.68/2.53 thf(f3057,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))) @ X1))) ) | ~spl0_8),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f204])).
% 8.68/2.53 thf(f2685,plain,(
% 8.68/2.53 spl0_28 | ~spl0_4 | ~spl0_16),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f2684,f519,f32,f1154])).
% 8.68/2.53 thf(f1154,definition,(
% 8.68/2.53 spl0_28 <=> ($true = (sK3 @ sK19 @ sK20))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition])).
% 8.68/2.53 thf(f32,definition,(
% 8.68/2.53 spl0_4 <=> ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))) => (Y0 @ Y2))))))) => (Y0 @ sK5)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 8.68/2.53 thf(f519,definition,(
% 8.68/2.53 spl0_16 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK10 @ Y0)) => (sK10 @ Y1)))))) = $false)),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 8.68/2.53 thf(f2684,plain,(
% 8.68/2.53 ($true = (sK3 @ sK19 @ sK20)) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f2683])).
% 8.68/2.53 thf(f2683,plain,(
% 8.68/2.53 (($false | (sK3 @ sK19 @ sK20)) = $true) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f1140,f1748])).
% 8.68/2.53 thf(f1748,plain,(
% 8.68/2.53 ($false = (sK2 @ sK19 @ sK20)) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f1723])).
% 8.68/2.53 thf(f1723,plain,(
% 8.68/2.53 ($true = (~ (sK2 @ sK19 @ sK20))) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f1722])).
% 8.68/2.53 thf(f1722,plain,(
% 8.68/2.53 ($true = ((sK2 @ sK19 @ sK20) => $false)) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(superposition,[status(thm)],[f1720,f1530])).
% 8.68/2.53 thf(f1530,plain,(
% 8.68/2.53 ((sK24 @ sK20) = $false) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f1511])).
% 8.68/2.53 thf(f1511,plain,(
% 8.68/2.53 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK24 @ Y0)) => (sK24 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK19 @ Y0) => (sK24 @ Y0))))) => (sK24 @ sK20)) = $false) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f1507])).
% 8.68/2.53 thf(f1507,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK19 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK20))) @ sK24)) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f1491])).
% 8.68/2.53 thf(f1491,plain,(
% 8.68/2.53 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK19 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK20)))) = $false) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f1490])).
% 8.68/2.53 thf(f1490,plain,(
% 8.68/2.53 (($false | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK19 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK20))))) = $false) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f1341,f1484])).
% 8.68/2.53 thf(f1484,plain,(
% 8.68/2.53 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK19 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK20)))) = $false) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f1341])).
% 8.68/2.53 thf(f1341,plain,(
% 8.68/2.53 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK19 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK20)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK19 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK20))))) = $false) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f1335])).
% 8.68/2.53 thf(f1335,plain,(
% 8.68/2.53 (($true & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK19 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK20)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK19 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK20)))))) = $false) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(superposition,[status(thm)],[f1315,f1137])).
% 8.68/2.53 thf(f1137,plain,(
% 8.68/2.53 ($true = (sK10 @ sK19)) | ~spl0_16),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f1125])).
% 8.68/2.53 thf(f1125,plain,(
% 8.68/2.53 ($true = (((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20)) & (sK10 @ sK19))) | ~spl0_16),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f1118])).
% 8.68/2.53 thf(f1118,plain,(
% 8.68/2.53 (((((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20)) & (sK10 @ sK19)) => (sK10 @ sK20)) = $false) | ~spl0_16),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f1117])).
% 8.68/2.53 thf(f1117,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: ((((sK2 @ sK19 @ Y0) | (sK3 @ sK19 @ Y0)) & (sK10 @ sK19)) => (sK10 @ Y0))) @ sK20)) | ~spl0_16),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f1112])).
% 8.68/2.53 thf(f1112,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: ((((sK2 @ sK19 @ Y0) | (sK3 @ sK19 @ Y0)) & (sK10 @ sK19)) => (sK10 @ Y0))))) | ~spl0_16),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f1107])).
% 8.68/2.53 thf(f1107,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK10 @ Y0)) => (sK10 @ Y1))))) @ sK19)) | ~spl0_16),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f520])).
% 8.68/2.53 thf(f520,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK10 @ Y0)) => (sK10 @ Y1)))))) = $false) | ~spl0_16),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f519])).
% 8.68/2.53 thf(f1315,plain,(
% 8.68/2.53 ( ! [X0 : a] : ((((sK10 @ X0) & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ X0 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK20)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ X0 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK20)))))) = $false)) ) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f1134])).
% 8.68/2.53 thf(f1134,plain,(
% 8.68/2.53 ( ! [X0 : a] : (($true = (~ ((sK10 @ X0) & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ X0 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK20)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ X0 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK20))))))))) ) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f1130])).
% 8.68/2.53 thf(f1130,plain,(
% 8.68/2.53 ( ! [X0 : a] : (($true = (((sK10 @ X0) & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ X0 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK20)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ X0 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK20)))))) => $false))) ) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(superposition,[status(thm)],[f610,f1127])).
% 8.68/2.53 thf(f1127,plain,(
% 8.68/2.53 ($false = (sK10 @ sK20)) | ~spl0_16),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f1126])).
% 8.68/2.53 thf(f1126,plain,(
% 8.68/2.53 (($true => (sK10 @ sK20)) = $false) | ~spl0_16),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f1118,f1125])).
% 8.68/2.53 thf(f610,plain,(
% 8.68/2.53 ( ! [X2 : a,X1 : a] : (($true = (((sK10 @ X1) & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ X1 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ X2)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ X1 @ Y1) => (Y0 @ Y1))))) => (Y0 @ X2)))))) => (sK10 @ X2)))) ) | ~spl0_4),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f609])).
% 8.68/2.53 thf(f609,plain,(
% 8.68/2.53 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK10 @ X1) & ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ X1 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ X1 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) => (sK10 @ Y0))) @ X2) = $true)) ) | ~spl0_4),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f605])).
% 8.68/2.53 thf(f605,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK10 @ X1) & ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ X1 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ X1 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) => (sK10 @ Y0)))))) ) | ~spl0_4),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f604])).
% 8.68/2.53 thf(f604,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK10 @ Y1))))) @ X1))) ) | ~spl0_4),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f543])).
% 8.68/2.53 thf(f543,plain,(
% 8.68/2.53 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK10 @ Y1))))))) | ~spl0_4),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f504])).
% 8.68/2.53 thf(f504,plain,(
% 8.68/2.53 (((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK10 @ Y1))))))) = $true) | ~spl0_4),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f500])).
% 8.68/2.53 thf(f500,plain,(
% 8.68/2.53 ($false = (((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK10 @ Y1))))))) => (sK10 @ sK5))) | ~spl0_4),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f499])).
% 8.68/2.53 thf(f499,plain,(
% 8.68/2.53 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))) => (Y0 @ Y2))))))) => (Y0 @ sK5))) @ sK10) = $false) | ~spl0_4),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f33])).
% 8.68/2.53 thf(f33,plain,(
% 8.68/2.53 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))) => (Y0 @ Y2))))))) => (Y0 @ sK5))))) | ~spl0_4),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f32])).
% 8.68/2.53 thf(f1720,plain,(
% 8.68/2.53 ( ! [X1 : a] : ((((sK2 @ sK19 @ X1) => (sK24 @ X1)) = $true)) ) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f1719])).
% 8.68/2.53 thf(f1719,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ sK19 @ Y0) => (sK24 @ Y0))) @ X1))) ) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f1714])).
% 8.68/2.53 thf(f1714,plain,(
% 8.68/2.53 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK19 @ Y0) => (sK24 @ Y0))))) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f1713])).
% 8.68/2.53 thf(f1713,plain,(
% 8.68/2.53 (($true & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK19 @ Y0) => (sK24 @ Y0))))) = $true) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f1531,f1712])).
% 8.68/2.53 thf(f1712,plain,(
% 8.68/2.53 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK24 @ Y0)) => (sK24 @ Y1))))))) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f1531])).
% 8.68/2.53 thf(f1531,plain,(
% 8.68/2.53 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK24 @ Y0)) => (sK24 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK19 @ Y0) => (sK24 @ Y0)))))) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f1511])).
% 8.68/2.53 thf(f1140,plain,(
% 8.68/2.53 ($true = ((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20))) | ~spl0_16),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f1139])).
% 8.68/2.53 thf(f1139,plain,(
% 8.68/2.53 ((((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20)) & $true) = $true) | ~spl0_16),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f1125,f1137])).
% 8.68/2.53 thf(f2679,plain,(
% 8.68/2.53 ~spl0_4 | ~spl0_16 | ~spl0_28),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f2678])).
% 8.68/2.53 thf(f2678,plain,(
% 8.68/2.53 $false | (~spl0_4 | ~spl0_16 | ~spl0_28)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f2677])).
% 8.68/2.53 thf(f2677,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_4 | ~spl0_16 | ~spl0_28)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f2669,f1781])).
% 8.68/2.53 thf(f1781,plain,(
% 8.68/2.53 ($false = (sK27 @ sK20)) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f1763])).
% 8.68/2.53 thf(f1763,plain,(
% 8.68/2.53 ($false = (((!! @ a @ (^[Y0 : a]: ((sK3 @ sK19 @ Y0) => (sK27 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK27 @ Y0)) => (sK27 @ Y1))))))) => (sK27 @ sK20))) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f1757])).
% 8.68/2.53 thf(f1757,plain,(
% 8.68/2.53 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK19 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK20))) @ sK27) = $false) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f1484])).
% 8.68/2.53 thf(f2669,plain,(
% 8.68/2.53 ($true = (sK27 @ sK20)) | (~spl0_4 | ~spl0_16 | ~spl0_28)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f2664])).
% 8.68/2.53 thf(f2664,plain,(
% 8.68/2.53 ($true = ($true => (sK27 @ sK20))) | (~spl0_4 | ~spl0_16 | ~spl0_28)),
% 8.68/2.53 inference(superposition,[status(thm)],[f2651,f1155])).
% 8.68/2.53 thf(f1155,plain,(
% 8.68/2.53 ($true = (sK3 @ sK19 @ sK20)) | ~spl0_28),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f1154])).
% 8.68/2.53 thf(f2651,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = ((sK3 @ sK19 @ X1) => (sK27 @ X1)))) ) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f2650])).
% 8.68/2.53 thf(f2650,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ sK19 @ Y0) => (sK27 @ Y0))) @ X1))) ) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f2633])).
% 8.68/2.53 thf(f2633,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK19 @ Y0) => (sK27 @ Y0)))) = $true) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f2632])).
% 8.68/2.53 thf(f2632,plain,(
% 8.68/2.53 ($true = ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK19 @ Y0) => (sK27 @ Y0)))) & $true)) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f1782,f2630])).
% 8.68/2.53 thf(f2630,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK27 @ Y0)) => (sK27 @ Y1)))))) = $true) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f1782])).
% 8.68/2.53 thf(f1782,plain,(
% 8.68/2.53 (((!! @ a @ (^[Y0 : a]: ((sK3 @ sK19 @ Y0) => (sK27 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK27 @ Y0)) => (sK27 @ Y1))))))) = $true) | (~spl0_4 | ~spl0_16)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f1763])).
% 8.68/2.53 thf(f1097,plain,(
% 8.68/2.53 ~spl0_4 | ~spl0_15 | ~spl0_17),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f1096])).
% 8.68/2.53 thf(f1096,plain,(
% 8.68/2.53 $false | (~spl0_4 | ~spl0_15 | ~spl0_17)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f1095])).
% 8.68/2.53 thf(f1095,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_4 | ~spl0_15 | ~spl0_17)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f1088,f720])).
% 8.68/2.53 thf(f720,plain,(
% 8.68/2.53 ($false = (sK16 @ sK12)) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f719])).
% 8.68/2.53 thf(f719,plain,(
% 8.68/2.53 (($true => (sK16 @ sK12)) = $false) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f694,f718])).
% 8.68/2.53 thf(f718,plain,(
% 8.68/2.53 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK16 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK16 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK16 @ Y0))))) = $true) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f694])).
% 8.68/2.53 thf(f694,plain,(
% 8.68/2.53 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK16 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK16 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK16 @ Y0))))) => (sK16 @ sK12))) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f691])).
% 8.68/2.53 thf(f691,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK12))) @ sK16)) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f581])).
% 8.68/2.53 thf(f581,plain,(
% 8.68/2.53 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK12)))) = $false) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f575])).
% 8.68/2.53 thf(f575,plain,(
% 8.68/2.53 ($false = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK12)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK12)))))) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f553])).
% 8.68/2.53 thf(f553,plain,(
% 8.68/2.53 ($true = (~ ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK12)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK12))))))) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f551])).
% 8.68/2.53 thf(f551,plain,(
% 8.68/2.53 ($true = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK12)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK12))))) => $false)) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(superposition,[status(thm)],[f548,f532])).
% 8.68/2.53 thf(f532,plain,(
% 8.68/2.53 ((sK10 @ sK12) = $false) | ~spl0_15),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f531])).
% 8.68/2.53 thf(f531,plain,(
% 8.68/2.53 (($true => (sK10 @ sK12)) = $false) | ~spl0_15),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f528,f530])).
% 8.68/2.53 thf(f530,plain,(
% 8.68/2.53 (((sK2 @ sK4 @ sK12) | (sK3 @ sK4 @ sK12)) = $true) | ~spl0_15),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f528])).
% 8.68/2.53 thf(f528,plain,(
% 8.68/2.53 ((((sK2 @ sK4 @ sK12) | (sK3 @ sK4 @ sK12)) => (sK10 @ sK12)) = $false) | ~spl0_15),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f524])).
% 8.68/2.53 thf(f524,plain,(
% 8.68/2.53 (((^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK10 @ Y0))) @ sK12) = $false) | ~spl0_15),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f517])).
% 8.68/2.53 thf(f517,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK10 @ Y0))))) | ~spl0_15),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f516])).
% 8.68/2.53 thf(f516,definition,(
% 8.68/2.53 spl0_15 <=> ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK10 @ Y0)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 8.68/2.53 thf(f548,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ X1)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ X1))))) => (sK10 @ X1)))) ) | ~spl0_4),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f547])).
% 8.68/2.53 thf(f547,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK10 @ Y0))) @ X1))) ) | ~spl0_4),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f546])).
% 8.68/2.53 thf(f546,plain,(
% 8.68/2.53 ($true = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK10 @ Y0))))) | ~spl0_4),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f545])).
% 8.68/2.53 thf(f545,plain,(
% 8.68/2.53 ($true = ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK10 @ Y0)))) & $true)) | ~spl0_4),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f504,f543])).
% 8.68/2.53 thf(f1088,plain,(
% 8.68/2.53 ($true = (sK16 @ sK12)) | (~spl0_4 | ~spl0_15 | ~spl0_17)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f1086])).
% 8.68/2.53 thf(f1086,plain,(
% 8.68/2.53 (($true => (sK16 @ sK12)) = $true) | (~spl0_4 | ~spl0_15 | ~spl0_17)),
% 8.68/2.53 inference(superposition,[status(thm)],[f1073,f536])).
% 8.68/2.53 thf(f536,plain,(
% 8.68/2.53 ((sK3 @ sK4 @ sK12) = $true) | ~spl0_17),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f535])).
% 8.68/2.53 thf(f535,definition,(
% 8.68/2.53 spl0_17 <=> ((sK3 @ sK4 @ sK12) = $true)),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 8.68/2.53 thf(f1073,plain,(
% 8.68/2.53 ( ! [X1 : a] : ((((sK3 @ sK4 @ X1) => (sK16 @ X1)) = $true)) ) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f1072])).
% 8.68/2.53 thf(f1072,plain,(
% 8.68/2.53 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK16 @ Y0))) @ X1) = $true)) ) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f874])).
% 8.68/2.53 thf(f874,plain,(
% 8.68/2.53 ($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK4 @ Y0) => (sK16 @ Y0))))) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f718])).
% 8.68/2.53 thf(f710,plain,(
% 8.68/2.53 ~spl0_4 | ~spl0_15 | ~spl0_18),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f709])).
% 8.68/2.53 thf(f709,plain,(
% 8.68/2.53 $false | (~spl0_4 | ~spl0_15 | ~spl0_18)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f708])).
% 8.68/2.53 thf(f708,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_4 | ~spl0_15 | ~spl0_18)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f701,f598])).
% 8.68/2.53 thf(f598,plain,(
% 8.68/2.53 ((sK14 @ sK12) = $false) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f592])).
% 8.68/2.53 thf(f592,plain,(
% 8.68/2.53 ((((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK14 @ Y0))))))) => (sK14 @ sK12)) = $false) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f590])).
% 8.68/2.53 thf(f590,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK12))) @ sK14)) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f585])).
% 8.68/2.53 thf(f585,plain,(
% 8.68/2.53 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK12)))) = $false) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f584])).
% 8.68/2.53 thf(f584,plain,(
% 8.68/2.53 (($false | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK12))))) = $false) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f575,f581])).
% 8.68/2.53 thf(f701,plain,(
% 8.68/2.53 ((sK14 @ sK12) = $true) | (~spl0_4 | ~spl0_15 | ~spl0_18)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f700])).
% 8.68/2.53 thf(f700,plain,(
% 8.68/2.53 (($true => (sK14 @ sK12)) = $true) | (~spl0_4 | ~spl0_15 | ~spl0_18)),
% 8.68/2.53 inference(superposition,[status(thm)],[f658,f539])).
% 8.68/2.53 thf(f539,plain,(
% 8.68/2.53 ((sK2 @ sK4 @ sK12) = $true) | ~spl0_18),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f538])).
% 8.68/2.53 thf(f538,definition,(
% 8.68/2.53 spl0_18 <=> ((sK2 @ sK4 @ sK12) = $true)),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 8.68/2.53 thf(f658,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = ((sK2 @ sK4 @ X1) => (sK14 @ X1)))) ) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f657])).
% 8.68/2.53 thf(f657,plain,(
% 8.68/2.53 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK14 @ Y0))) @ X1))) ) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f633])).
% 8.68/2.53 thf(f633,plain,(
% 8.68/2.53 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK14 @ Y0)))) = $true) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f599])).
% 8.68/2.53 thf(f599,plain,(
% 8.68/2.53 ($true = ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK14 @ Y0)))))))) | (~spl0_4 | ~spl0_15)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f592])).
% 8.68/2.53 thf(f540,plain,(
% 8.68/2.53 spl0_17 | spl0_18 | ~spl0_15),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f533,f516,f538,f535])).
% 8.68/2.53 thf(f533,plain,(
% 8.68/2.53 ((sK2 @ sK4 @ sK12) = $true) | ((sK3 @ sK4 @ sK12) = $true) | ~spl0_15),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f530])).
% 8.68/2.53 thf(f521,plain,(
% 8.68/2.53 spl0_15 | spl0_16 | ~spl0_1 | ~spl0_4),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f512,f32,f22,f519,f516])).
% 8.68/2.53 thf(f22,definition,(
% 8.68/2.53 spl0_1 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 8.68/2.53 thf(f512,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK10 @ Y0))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK10 @ Y0)) => (sK10 @ Y1)))))) = $false) | (~spl0_1 | ~spl0_4)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f509])).
% 8.68/2.53 thf(f509,plain,(
% 8.68/2.53 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK10 @ Y0)) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK10 @ Y0)))))) | (~spl0_1 | ~spl0_4)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f508])).
% 8.68/2.53 thf(f508,plain,(
% 8.68/2.53 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK10 @ Y0)) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK10 @ Y0))))))) | (~spl0_1 | ~spl0_4)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f507])).
% 8.68/2.53 thf(f507,plain,(
% 8.68/2.53 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK10 @ Y0)) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK10 @ Y0))))) => $false)) | (~spl0_1 | ~spl0_4)),
% 8.68/2.53 inference(superposition,[status(thm)],[f497,f506])).
% 8.68/2.53 thf(f506,plain,(
% 8.68/2.53 ($false = (sK10 @ sK5)) | ~spl0_4),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f505])).
% 8.68/2.53 thf(f505,plain,(
% 8.68/2.53 ($false = ($true => (sK10 @ sK5))) | ~spl0_4),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f500,f504])).
% 8.68/2.53 thf(f497,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (X1 @ Y0)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (X1 @ Y0))))) => (X1 @ sK5)) = $true)) ) | ~spl0_1),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f496])).
% 8.68/2.53 thf(f496,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5))) @ X1) = $true)) ) | ~spl0_1),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f23])).
% 8.68/2.53 thf(f23,plain,(
% 8.68/2.53 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5))))) | ~spl0_1),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f22])).
% 8.68/2.53 thf(f493,plain,(
% 8.68/2.53 spl0_13 | spl0_14 | ~spl0_6),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f486,f126,f491,f488])).
% 8.68/2.53 thf(f486,plain,(
% 8.68/2.53 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))))) | ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK9))))) | ~spl0_6),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f373])).
% 8.68/2.53 thf(f373,plain,(
% 8.68/2.53 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK9))))) = $true) | ~spl0_6),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f355])).
% 8.68/2.53 thf(f355,plain,(
% 8.68/2.53 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK9))))) => (sK6 @ sK9)) = $false) | ~spl0_6),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f351])).
% 8.68/2.53 thf(f351,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))) @ sK9)) | ~spl0_6),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f127])).
% 8.68/2.53 thf(f285,plain,(
% 8.68/2.53 spl0_11 | spl0_12 | ~spl0_5 | ~spl0_7),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f276,f200,f123,f283,f280])).
% 8.68/2.53 thf(f276,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK7 @ Y0) => (sK6 @ Y0))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) = $false) | (~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f271])).
% 8.68/2.53 thf(f271,plain,(
% 8.68/2.53 ($false = ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK7 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))))) | (~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f232])).
% 8.68/2.53 thf(f232,plain,(
% 8.68/2.53 ($true = (~ ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK7 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1))))))))) | (~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f229])).
% 8.68/2.53 thf(f229,plain,(
% 8.68/2.53 ($true = (((!! @ a @ (^[Y0 : a]: ((sK3 @ sK7 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1))))))) => $false)) | (~spl0_5 | ~spl0_7)),
% 8.68/2.53 inference(superposition,[status(thm)],[f218,f168])).
% 8.68/2.53 thf(f168,plain,(
% 8.68/2.53 ($false = (sK6 @ sK8)) | ~spl0_5),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f164])).
% 8.68/2.53 thf(f164,plain,(
% 8.68/2.53 ((((sK6 @ sK7) & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))))) => (sK6 @ sK8)) = $false) | ~spl0_5),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f163])).
% 8.68/2.53 thf(f163,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a]: (((sK6 @ sK7) & ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK7 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) => (sK6 @ Y0))) @ sK8)) | ~spl0_5),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f149])).
% 8.68/2.53 thf(f149,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK7) & ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK7 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) => (sK6 @ Y0))))) | ~spl0_5),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f148])).
% 8.68/2.53 thf(f148,plain,(
% 8.68/2.53 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK6 @ Y1))))) @ sK7) = $false) | ~spl0_5),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f124])).
% 8.68/2.53 thf(f218,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: ((sK3 @ sK7 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (X1 @ Y0)) => (X1 @ Y1))))))) => (X1 @ sK8)))) ) | ~spl0_7),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f217])).
% 8.68/2.53 thf(f217,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8))) @ X1))) ) | ~spl0_7),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f201])).
% 8.68/2.53 thf(f269,plain,(
% 8.68/2.53 ~spl0_2 | ~spl0_4),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f268])).
% 8.68/2.53 thf(f268,plain,(
% 8.68/2.53 $false | (~spl0_2 | ~spl0_4)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f267])).
% 8.68/2.53 thf(f267,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f26,f33])).
% 8.68/2.53 thf(f26,plain,(
% 8.68/2.53 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))) => (Y0 @ Y2))))))) => (Y0 @ sK5))))) | ~spl0_2),
% 8.68/2.53 inference(avatar_component_clause,[status(thm)],[f25])).
% 8.68/2.53 thf(f25,definition,(
% 8.68/2.53 spl0_2 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))) => (Y0 @ Y2))))))) => (Y0 @ sK5)))))),
% 8.68/2.53 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 8.68/2.53 thf(f205,plain,(
% 8.68/2.53 spl0_7 | spl0_8 | ~spl0_5),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f198,f123,f203,f200])).
% 8.68/2.53 thf(f198,plain,(
% 8.68/2.53 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8))))) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true) | ~spl0_5),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f189])).
% 8.68/2.53 thf(f189,plain,(
% 8.68/2.53 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))))) = $true) | ~spl0_5),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f188])).
% 8.68/2.53 thf(f188,plain,(
% 8.68/2.53 (($true & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))))) = $true) | ~spl0_5),
% 8.68/2.53 inference(backward_demodulation,[status(thm)],[f169,f187])).
% 8.68/2.53 thf(f187,plain,(
% 8.68/2.53 ($true = (sK6 @ sK7)) | ~spl0_5),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f169])).
% 8.68/2.53 thf(f169,plain,(
% 8.68/2.53 ($true = ((sK6 @ sK7) & ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK7 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))))))) | ~spl0_5),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f164])).
% 8.68/2.53 thf(f132,plain,(
% 8.68/2.53 ~spl0_1 | ~spl0_3),
% 8.68/2.53 inference(avatar_contradiction_clause,[status(thm)],[f131])).
% 8.68/2.53 thf(f131,plain,(
% 8.68/2.53 $false | (~spl0_1 | ~spl0_3)),
% 8.68/2.53 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 8.68/2.53 thf(f130,plain,(
% 8.68/2.53 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 8.68/2.53 inference(forward_demodulation,[status(thm)],[f23,f30])).
% 8.68/2.53 thf(f128,plain,(
% 8.68/2.53 spl0_5 | spl0_6 | ~spl0_2 | ~spl0_3),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f119,f29,f25,f126,f123])).
% 8.68/2.53 thf(f119,plain,(
% 8.68/2.53 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK6 @ Y1)))))) = $false) | (~spl0_2 | ~spl0_3)),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 8.68/2.53 thf(f100,plain,(
% 8.68/2.53 ($false = ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK6 @ Y1)))))))) | (~spl0_2 | ~spl0_3)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f53])).
% 8.68/2.53 thf(f53,plain,(
% 8.68/2.53 ((~ ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK6 @ Y1)))))))) = $true) | (~spl0_2 | ~spl0_3)),
% 8.68/2.53 inference(boolean_simplification,[status(thm)],[f52])).
% 8.68/2.53 thf(f52,plain,(
% 8.68/2.53 ((((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (sK6 @ Y1))))))) => $false) = $true) | (~spl0_2 | ~spl0_3)),
% 8.68/2.53 inference(superposition,[status(thm)],[f46,f39])).
% 8.68/2.53 thf(f39,plain,(
% 8.68/2.53 ((sK6 @ sK5) = $false) | ~spl0_3),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 8.68/2.53 thf(f38,plain,(
% 8.68/2.53 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK3 @ sK4 @ Y0)) => (sK6 @ Y0))))) => (sK6 @ sK5))) | ~spl0_3),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f37])).
% 8.68/2.53 thf(f37,plain,(
% 8.68/2.53 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5))) @ sK6) = $false) | ~spl0_3),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f30])).
% 8.68/2.53 thf(f46,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))) => (X1 @ Y1))))))) => (X1 @ sK5)))) ) | ~spl0_2),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f45])).
% 8.68/2.53 thf(f45,plain,(
% 8.68/2.53 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))) => (Y0 @ Y2))))))) => (Y0 @ sK5))) @ X1))) ) | ~spl0_2),
% 8.68/2.53 inference(pi_clausification,[status(thm)],[f26])).
% 8.68/2.53 thf(f34,plain,(
% 8.68/2.53 spl0_3 | spl0_4),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f20,f32,f29])).
% 8.68/2.53 thf(f20,plain,(
% 8.68/2.53 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))) => (Y0 @ Y2))))))) => (Y0 @ sK5))))) | ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5)))))),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 8.68/2.53 thf(f18,plain,(
% 8.68/2.53 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5)))) != (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))) => (Y0 @ Y2))))))) => (Y0 @ sK5)))))),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f17])).
% 8.68/2.53 thf(f17,plain,(
% 8.68/2.53 (((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK3 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK3 @ sK4 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ sK4 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK3 @ Y2 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6))))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))))) => (Y1 @ Y3))))))) => (Y1 @ Y0))))) @ sK5) != ((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK2 @ sK4 @ Y2) | (sK3 @ sK4 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0))))) @ sK5))),
% 8.68/2.53 inference(negative_extensionality,[status(thm)],[f16])).
% 8.68/2.53 thf(f16,plain,(
% 8.68/2.53 ((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK3 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK3 @ sK4 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ sK4 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK3 @ Y2 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6))))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))))) => (Y1 @ Y3))))))) => (Y1 @ Y0))))) != (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK2 @ sK4 @ Y2) | (sK3 @ sK4 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0))))))),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f15])).
% 8.68/2.53 thf(f15,plain,(
% 8.68/2.53 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK2 @ Y0 @ Y3) | (sK3 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1))))))) @ sK4) != ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (sK3 @ Y5 @ Y6)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((sK3 @ Y0 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK2 @ Y0 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (sK2 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((sK3 @ Y3 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y6 @ Y7) & (Y5 @ Y6)) => (Y5 @ Y7))))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y6 @ Y7) & (Y5 @ Y6)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))))) => (Y2 @ Y4))))))) => (Y2 @ Y1))))))) @ sK4))),
% 8.68/2.53 inference(negative_extensionality,[status(thm)],[f14])).
% 8.68/2.53 thf(f14,plain,(
% 8.68/2.53 ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK2 @ Y0 @ Y3) | (sK3 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (sK3 @ Y5 @ Y6)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((sK3 @ Y0 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK2 @ Y0 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (sK2 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((sK3 @ Y3 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y6 @ Y7) & (Y5 @ Y6)) => (Y5 @ Y7))))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y6 @ Y7) & (Y5 @ Y6)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))))) => (Y2 @ Y4))))))) => (Y2 @ Y1))))))))),
% 8.68/2.53 inference(equality_proxy_clausification,[status(thm)],[f13])).
% 8.68/2.53 thf(f13,plain,(
% 8.68/2.53 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK2 @ Y0 @ Y3) | (sK3 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1))))))) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (sK3 @ Y5 @ Y6)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((sK3 @ Y0 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK2 @ Y0 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (sK2 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((sK3 @ Y3 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y6 @ Y7) & (Y5 @ Y6)) => (Y5 @ Y7))))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y6 @ Y7) & (Y5 @ Y6)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))))) => (Y2 @ Y4))))))) => (Y2 @ Y1)))))))) = $false)),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f12])).
% 8.68/2.53 thf(f12,plain,(
% 8.68/2.53 (((^[Y0 : a > a > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y4 @ Y5) | (Y0 @ Y4 @ Y5)) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK2 @ Y1 @ Y4) | (Y0 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y0 @ Y6 @ Y7)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((Y0 @ Y1 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((sK2 @ Y1 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & (sK2 @ Y7 @ Y6)) => (Y5 @ Y6))))))) => (Y5 @ Y4))))) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y4 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y7 @ Y8) & (Y6 @ Y7)) => (Y6 @ Y8))))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y7 @ Y8) & (Y6 @ Y7)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((sK2 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))))))) @ sK3) = $false)),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f11])).
% 8.68/2.53 thf(f11,plain,(
% 8.68/2.53 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y4 @ Y5) | (Y0 @ Y4 @ Y5)) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK2 @ Y1 @ Y4) | (Y0 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y0 @ Y6 @ Y7)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((Y0 @ Y1 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((sK2 @ Y1 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & (sK2 @ Y7 @ Y6)) => (Y5 @ Y6))))))) => (Y5 @ Y4))))) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y4 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y7 @ Y8) & (Y6 @ Y7)) => (Y6 @ Y8))))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y7 @ Y8) & (Y6 @ Y7)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((sK2 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))))) => (Y3 @ Y5))))))) => (Y3 @ Y2)))))))))))),
% 8.68/2.53 inference(beta_eta_normalization,[status(thm)],[f10])).
% 8.68/2.53 thf(f10,plain,(
% 8.68/2.53 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y5 @ Y6) | (Y1 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (Y1 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y1 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y2 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y0 @ Y8 @ Y7)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: ((Y1 @ Y5 @ Y8) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y8 @ Y9) & (Y7 @ Y8)) => (Y7 @ Y9))))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) & (Y7 @ Y8)) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))))) => (Y4 @ Y6))))))) => (Y4 @ Y3))))))))))) @ sK2))),
% 8.68/2.53 inference(sigma_clausification,[status(thm)],[f7])).
% 8.68/2.53 thf(f7,plain,(
% 8.68/2.53 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y5 @ Y6) | (Y1 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (Y1 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y1 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y2 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y0 @ Y8 @ Y7)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: ((Y1 @ Y5 @ Y8) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y8 @ Y9) & (Y7 @ Y8)) => (Y7 @ Y9))))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) & (Y7 @ Y8)) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))))) => (Y4 @ Y6))))))) => (Y4 @ Y3)))))))))))) = $false)),
% 8.68/2.53 inference(not_proxy_clausification,[status(thm)],[f6])).
% 8.68/2.53 thf(f6,plain,(
% 8.68/2.53 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y5 @ Y6) | (Y1 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (Y1 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y1 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y2 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y0 @ Y8 @ Y7)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: ((Y1 @ Y5 @ Y8) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y8 @ Y9) & (Y7 @ Y8)) => (Y7 @ Y9))))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) & (Y7 @ Y8)) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))))) => (Y4 @ Y6))))))) => (Y4 @ Y3))))))))))))) = $true)),
% 8.68/2.53 inference(cnf_transformation,[status(thm)],[f5])).
% 8.68/2.53 thf(f5,plain,(
% 8.68/2.53 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y5 @ Y6) | (Y1 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (Y1 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y1 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y2 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y0 @ Y8 @ Y7)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: ((Y1 @ Y5 @ Y8) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y8 @ Y9) & (Y7 @ Y8)) => (Y7 @ Y9))))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) & (Y7 @ Y8)) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))))) => (Y4 @ Y6))))))) => (Y4 @ Y3))))))))))))) = $true)),
% 8.68/2.53 inference(fool_elimination,[status(thm)],[f4])).
% 8.68/2.53 thf(f4,plain,(
% 8.68/2.53 ~! [X0 : a > a > $o,X1 : a > a > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > $o] : ((! [X5 : a] : (((X0 @ X2 @ X5) | (X1 @ X2 @ X5)) => (X4 @ X5)) & ! [X6 : a,X7 : a] : (((X4 @ X7) & ((X0 @ X7 @ X6) | (X1 @ X7 @ X6))) => (X4 @ X6))) => (X4 @ X3)))) = (^[X8 : a, X9 : a] : (! [X10 : a > $o] : ((! [X11 : a,X12 : a] : (((! [X13 : a > $o] : ((! [X14 : a] : ((X1 @ X12 @ X14) => (X13 @ X14)) & ! [X15 : a,X16 : a] : (((X13 @ X16) & (X1 @ X16 @ X15)) => (X13 @ X15))) => (X13 @ X11)) | ! [X17 : a > $o] : ((! [X18 : a,X19 : a] : (((X17 @ X19) & (X0 @ X19 @ X18)) => (X17 @ X18)) & ! [X20 : a] : ((X0 @ X12 @ X20) => (X17 @ X20))) => (X17 @ X11))) & (X10 @ X12)) => (X10 @ X11)) & ! [X21 : a] : ((! [X22 : a > $o] : ((! [X23 : a,X24 : a] : (((X1 @ X23 @ X24) & (X22 @ X23)) => (X22 @ X24)) & ! [X25 : a] : ((X1 @ X8 @ X25) => (X22 @ X25))) => (X22 @ X21)) | ! [X26 : a > $o] : ((! [X27 : a] : ((X0 @ X8 @ X27) => (X26 @ X27)) & ! [X28 : a,X29 : a] : (((X0 @ X29 @ X28) & (X26 @ X29)) => (X26 @ X28))) => (X26 @ X21))) => (X10 @ X21))) => (X10 @ X9)))))),
% 8.68/2.53 inference(rectify,[status(thm)],[f2])).
% 8.68/2.53 thf(f2,negated_conjecture,(
% 8.68/2.53 ~! [X0 : a > a > $o,X1 : a > a > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > $o] : ((! [X5 : a] : (((X0 @ X2 @ X5) | (X1 @ X2 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : (((X4 @ X6) & ((X0 @ X6 @ X7) | (X1 @ X6 @ X7))) => (X4 @ X7))) => (X4 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > $o] : ((! [X7 : a,X6 : a] : (((! [X8 : a > $o] : ((! [X5 : a] : ((X1 @ X6 @ X5) => (X8 @ X5)) & ! [X11 : a,X10 : a] : (((X8 @ X10) & (X1 @ X10 @ X11)) => (X8 @ X11))) => (X8 @ X7)) | ! [X8 : a > $o] : ((! [X11 : a,X10 : a] : (((X8 @ X10) & (X0 @ X10 @ X11)) => (X8 @ X11)) & ! [X5 : a] : ((X0 @ X6 @ X5) => (X8 @ X5))) => (X8 @ X7))) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((! [X8 : a > $o] : ((! [X6 : a,X7 : a] : (((X1 @ X6 @ X7) & (X8 @ X6)) => (X8 @ X7)) & ! [X9 : a] : ((X1 @ X2 @ X9) => (X8 @ X9))) => (X8 @ X5)) | ! [X8 : a > $o] : ((! [X9 : a] : ((X0 @ X2 @ X9) => (X8 @ X9)) & ! [X7 : a,X6 : a] : (((X0 @ X6 @ X7) & (X8 @ X6)) => (X8 @ X7))) => (X8 @ X5))) => (X4 @ X5))) => (X4 @ X3)))))),
% 8.68/2.53 inference(negated_conjecture,[status(cth)],[f1])).
% 8.68/2.53 thf(f1,conjecture,(
% 8.68/2.53 ! [X0 : a > a > $o,X1 : a > a > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > $o] : ((! [X5 : a] : (((X0 @ X2 @ X5) | (X1 @ X2 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : (((X4 @ X6) & ((X0 @ X6 @ X7) | (X1 @ X6 @ X7))) => (X4 @ X7))) => (X4 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > $o] : ((! [X7 : a,X6 : a] : (((! [X8 : a > $o] : ((! [X5 : a] : ((X1 @ X6 @ X5) => (X8 @ X5)) & ! [X11 : a,X10 : a] : (((X8 @ X10) & (X1 @ X10 @ X11)) => (X8 @ X11))) => (X8 @ X7)) | ! [X8 : a > $o] : ((! [X11 : a,X10 : a] : (((X8 @ X10) & (X0 @ X10 @ X11)) => (X8 @ X11)) & ! [X5 : a] : ((X0 @ X6 @ X5) => (X8 @ X5))) => (X8 @ X7))) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((! [X8 : a > $o] : ((! [X6 : a,X7 : a] : (((X1 @ X6 @ X7) & (X8 @ X6)) => (X8 @ X7)) & ! [X9 : a] : ((X1 @ X2 @ X9) => (X8 @ X9))) => (X8 @ X5)) | ! [X8 : a > $o] : ((! [X9 : a] : ((X0 @ X2 @ X9) => (X8 @ X9)) & ! [X7 : a,X6 : a] : (((X0 @ X6 @ X7) & (X8 @ X6)) => (X8 @ X7))) => (X8 @ X5))) => (X4 @ X5))) => (X4 @ X3)))))),
% 8.68/2.53 file('/export/starexec/sandbox2/tmp/tmp.syb1jpMQsL/DTF2THF_16357.p',cTHM251A_pme)).
% 8.68/2.53 thf(f27,plain,(
% 8.68/2.53 spl0_1 | spl0_2),
% 8.68/2.53 inference(avatar_split_clause,[status(thm)],[f19,f25,f22])).
% 8.68/2.53 thf(f19,plain,(
% 8.68/2.53 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK3 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5))))) | ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))) => (Y0 @ Y2))))))) => (Y0 @ sK5)))))),
% 8.68/2.53 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 8.68/2.53 % SZS output end Proof for DTF2THF_16357
% 8.68/2.53 % (16727)------------------------------
% 8.68/2.53 % (16727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.53 % (16727)Termination reason: Refutation
% 8.68/2.53
% 8.68/2.53 % (16727)Memory used [KB]: 8315
% 8.68/2.53 % (16727)Time elapsed: 0.311 s
% 8.68/2.53 % (16727)Instructions burned: 932 (million)
% 8.68/2.53 % (16727)------------------------------
% 8.68/2.53 % (16727)------------------------------
% 8.68/2.53 % (16628)Success in time 1.224 s
%------------------------------------------------------------------------------